Gauge Field Theory

This paper develops the concept of autonegation as the destruction of supersymmetry within the framework of Meta-Monism ontology. Unlike Hegelian "negation of negation," autonegation is not a logical move, but a primordial ontological act in which chaos denies its own identity. Chaos is interpreted as absolute negativity: not a substance with attributes, but negativity itself, eternally negating itself. This act generates duality, relations, time, and dissipation. The argument unfolds in six steps: (1) chaos as supersymmetry (absolute selfidentity), (2) autonegation as its destruction, (3) duality (Being/Non-Being), (4) emergence of relations (AND/OR), (5) time as the scene of differentiation, and (6) dissipation as the tendency toward equilibrium. The paper situates this ontological model in dialogue with physics (symmetry breaking in supersymmetry, entropy, Seiberg-Witten theory), philosophy (Nagarjuna, Hegel, Schelling, Kant), and phenomenology of consciousness. Its unique contribution is the consistent assertion of negativity as the fundamental principle of reality. It offers not only an ontological explanation of the emergence of order from chaos, but also an ethical orientation: creativity as conscious selfnegation, the destruction of obsolete forms to allow the birth of new ones.

This paper proposes a first-principles explanation, within the framework of the Information-Causal Compression Field (ICCF) unified field theory, for why the Standard Model of particle physics adopts the specific gauge symmetry group SU(3)×SU(2)×U(1). Rather than treating this structure as an arbitrary postulate, we argue that it emerges as the universe’s unique and inevitable “Cosmic Resonance” mode, arising from the interplay of three fundamental principles: energy conservation, entropy increase, and the principle of least action. We identify SU(3), SU(2), and U(1) respectively with the three most basic resonance topologies in ICCF: causal saturation, causal reconstruction, and causal propagation. We further demonstrate that any deviation from this “triadic chord” of symmetries leads to instability, higher energy dissipation, and eventual elimination by the principle of least action. Thus, the Standard Model’s gauge structure is not an accident of nature, but the only stable resonance solution capable of sustaining a universe with stability (SU(3)), evolution (SU(2)), and communication (U(1)). Finally, the ICCF framework yields testable predictions, including harmonic mass spectra, coupling constant modulations, and observable “dissonances” in extreme cosmological events, positioning this theory as a physically grounded alternative to traditional symmetry-origin frameworks such as GUTs and string theory.

The fine structure constant α is one of the most precisely measured yet unexplained numbers in physics. In standard theory it is taken as a fundamental dimensionless input. Within the Chronoflux framework α is not arbitrary but emerges from the hydrodynamic properties of the fifth dimensional temporal fluid and the topological constraints of the compactified informational boundary. I show that α can be expressed as the ratio of two chronoflux determined quantities: the vacuum impedance Z 0 (H) and the topological flux quantum Φ 0 (H). The result is α(H) = πℏ Φ 2 0 (H) Z 0 (H) = Z 0 (H) 2R K (H) , where R K (H) = h/q 2 * (H) is the generalized von Klitzing constant and q * is the minimal Noether charge of the boundary U(1). This closes the map from the chronoflux Lagrangian to α with no free parameters once the background H A and compactification data are fixed.

The ghost sector of SU(3) gauge field theory is studied, and new BRST-invariant states are presented that do not have any analog in other SU(N) field theories. The new states come in either ghost doublets or triplets, and they appear exclusively in SU(3) due to the fact that the non-Abelian part of the BRST charge has 3 ghost operators, while SU(3) has 3 pairs of off-diagonal gauge constraints. The states have finite, positive norms even though the triplet states do not have well-defined ghost numbers. It is speculated that this special nature of the ghost sector of SU(3) could play some role in QCD confinement.

Nonlinear realizations of spacetime groups are presented as a versatile mathematical tool providing a common foundation for quite different formulations of gauge theories of gravity. We apply nonlinear realizations in particular to both the Poincaré and the affine group in order to develop Poincaré gauge theory (PGT) and metric-affine gravity (MAG) respectively. Regarding PGT, two alternative nonlinear treatments of the Poincaré group are developed, one of them being suitable to deal with the Lagrangian and the other one with the Hamiltonian version of the same gauge theory. We argue that our Hamiltonian approach to PGT is closely related to Ashtekar's approach to gravity. On the other hand, a brief survey on MAG clarifies the role played by the metric-affine metric tensor as a Goldsone field. All gravitational quantities in fact -the metric as much as the coframes and connections-are shown to acquire a simple gauge-theoretical interpretation in the nonlinear framework.

Sarfatti Star Fleet Academy UAP Physics Lecture Aug 17, 2025
In a previous Star Fleet Lecture we derived the following spin density tensor contribution to the symmetric part of the Einstein tensor G{u,v} (spin density) = k2^2Sab^c'Sc'^a^bguv since k2 has MKS dimensions Meter^2/Joule-sec and Sab^c' has dimensions Joule-sec/Meter^3 and G{uv} has dim Meter^-1. Note that {u,v} is the symmetrizer G{uv} = (1/2)[Guv + Guv]. Jack Sarfatti then added S-L Spin-Orbital Coupling to get G{u,v} = k1T{uv} + [ck1k2Mab^c'S^a^bc' + k2^2Sab^c'S^a^bc']guv where guv is the symmetric metric tensor of Einstein's 1915 GR. Therefore, Sarfatti pointed out that [ck1k2Mab^c'S^a^bc' + k2^2Sab^c'S^a^bc'] has same function as Einstein's cosmological constant. Comment on the meaning of this.

We revisit the instanton partition function for 5d N = 1 SO(N) gauge theories compactified on S 1 , computed from the topological vertex formalism with the O-vertex based on a 5-brane web diagram with an O5-plane. We introduce an identity that enables us to rewrite the unrefined partition function into a new expression in terms of the Nekrasov factors summed over Young diagrams, which can be interpreted as the freezing of an O7-plane. Based on this, we propose topological vertex formalism with an O7 +-plane.

In the holographic model of QCD, θ dependence sharply changes at the point of confinementdeconfinement phase transition. In large N QCD such a change in θ behavior can be related to the breakdown of the instanton expansion at some critical temperature Tc. Associating this temperature with confinement-deconfinement phase transition leads to the description of the latter in terms of dissociation of instantons into the fractionally charged instanton quarks. To elucidate this picture, we introduce the nonvanishing chiral condensate in the deconfining phase and assume a specific lagrangian for the η ′ field in the confining phase. In the resulting picture the high temperature phase of the theory consists of the dilute gas of instantons, while the low temperature phase is described in terms of freely moving fractional instanton quarks.

We suggest that the topological susceptibility in gluodynamics can be found in terms of the gluon condensate using renormalizability and heavy fermion representation of the anomaly. Analogous relations can also be obtained for other zero-momentum correlation functions involving the topological density operator. Using these relations, we find the θ dependence of the condensates , [Formula: see text] and of the partition function for small θ and an arbitrary number of colors.

This paper serves as a conceptual continuation of [20], wherein we proposed that spacetime curvature may be synthesized through electromagnetic (EM) fields. Herein, we refine this notion by positing that, for synthetic metrics to effectively function as inertial manipulation systems, the electromagnetic fields must be fully enclosed and isolated from the external environment. We suggest that the internal curvature is confined within the vehicle's structure and modulated via superconducting elements (e.g., Josephson junctions) coordinated by artificial intelligence systems. Although no gravitational curvature is directly transmitted outward, a residual Aharonov-Bohm-type effect may permeate the boundary, inducing topological phase shifts in the surrounding space. This "quasi-general relativity" coupling may constitute the sole external manifestation of the synthetic curvature, potentially explaining how such systems interact with spacetime without emitting classical radiation or exhaust. It is emphasized that the present work is philosophical and exploratory in nature, proposing a speculative framework for alternative propulsion paradigms. These ideas are partly inspired by credible military sightings-such as the 2004 USS Nimitz incident involving Commander David Fravor-that suggest inertial capabilities beyond conventional physics. We do not claim empirical proof, but argue that such phenomena motivate a reconsideration of propulsion mechanisms at the interface of field theory and spacetime geometry.

This paper introduces the CPT-Coherence (Mirror-Mind) Theory, a novel framework that unifies mass generation, gauge interactions, quantum collapse, gravity, and recursive identity through a hidden coherence dimension, τ. By modeling particles as recursive structures across τ, this theory explains the Standard Model mass spectrum as discrete recursion eigenstates, describes quantum measurement as τ-phase transitions (predicting subtle deviations from the Born rule), and derives gravity from τ-curvature. It further proposes a quantized ladder of sentience, integrating consciousness within a rigorous field framework. This approach bridges foundational gaps between quantum mechanics, general relativity, and the ontology of identity, offering a new pathway for experimental and philosophical exploration.

Both mesons and baryons are constructed from a set of three fundamental particles called aces. The aces break up into an isospin doublet and singlet. Each ace carries baryon number 1/3 and is fractionally charged. su 3 (but not the Eightfold Way) is adopted as a higher syrr..metry for the strong interactions. The breaking of this symmetry is assumed to be universal? being due to mass diffe:rences among the aces. Extensive space•-time and group theoretic structure is then predicted for both mesons and baryons, in agreement with existing experimental information. Quantitative speculations are presented concerning resonances that have not as yet been definitively classified into representations of su 3 • A weak interaction theory based on right and left handed aces is used to predict rates for ll~sl = 1 baryon leptonic decays. An experimental search for the aces is suggested. *) **) 8419/TH.412 Version I is CERN preprint 8182/TH.401, Jan. 17, 1964.

The following three geometrical structures on a manifold are studied in detail: Leibnizian: a nonvanishing one-form Ω plus a Riemannian metric 〈⋅,⋅〉 on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. Galilean: Leibnizian structure endowed with an affine connection ∇ (gauge field) which parallelizes Ω and 〈⋅,⋅〉. For any fixed vector field of observers Z(Ω(Z)≡1), an explicit Koszul-type formula which reconstructs bijectively all the possible ∇’s from the gravitational G≔∇ZZ and vorticity ω≔12 rot Z fields (plus eventually the torsion) is provided. Newtonian: Galilean structure with 〈⋅,⋅〉 flat and a field of observers Z which is inertial (its flow preserves the Leibnizian structure and ω≡0). Classical concepts in Newtonian theory are revisited and discussed.

H-type foliations (M, H, g H ) are studied in the framework of sub-Riemannian geometry with bracket generating distribution defined as the bundle transversal to the fibers. Equipping M with the Bott connection we consider the scalar horizontal curvature κ H as well as a new local invariant τ V induced from the vertical distribution. We extend recent results on the small-time asymptotics of the sub-Riemannanian heat kernel on quaternion-contact (qc-)manifolds due to A. Laaroussi and we express the second heat invariant in sub-Riemannian geometry as a linear combination of κ H and τ V . The use of an analog to normal coordinates in Riemannian geometry that are well-adapted to the geometric structure of H-type foliations allows us to consider the pull-back of Korányi balls to M. We explicitly obtain the first three terms in the asymptotic expansion of their Popp volume for small radii. Finally, we address the question of when M is locally isometric as a sub-Riemannian manifold to its H-type tangent group.

By showing that the radially reduced QCD of s-wave fermions outside the core of a GUT monopole can be treated in a way analogous to 't Hooft's QCD 2 in the large Nclimit, we are able to give a complete QFT treatment of all the relevant long-range gauge fields outside the monopole core. We prove that the original cluster argument for the existence of baryon number violating fermion "condensates" around the core, gives in fact, the correct result, despite the neglect of QCD strong interactions, which prevent the propagation of isolated quarks. We discuss briefly how a complete computational framework for a monopole induced hadron-lepton transition might be derived.

We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac-Moody Lie algebra e 9 . We investigate Kac-Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.

We propose a field-theoretic framework in which a vector field acts as a dynamical Lagrange multiplier to enforce spacetime translation symmetry. By coupling to the divergence of the energy-momentum tensor, the theory guarantees conservation of energy and momentum even in the presence of matter or background fields that would otherwise break translation symmetry. The field possesses its own dynamics and may be interpreted as the gauge field of local translations. We derive the field equations, analyze their implications, and discuss potential roles of in strong gravity contexts such as black holes and wormholes.

We propose a novel vector field that couples universally to the energy-momentum tensor of matter and acts to enforce spacetime translation symmetry dynamically. This field exists throughout spacetime in analogy with the Higgs field and interacts differently with various particle species. We show that the interaction enforces the conservation of energy-momentum even when the matter Lagrangian alone would violate translational invariance, thereby restoring symmetry through the dynamics of .

A construction of compact tachyon-free orientifolds of the nonsupersymmetric Type 0B string theory is presented. Moreover, we study effective non-supersymmetric gauge theories arising on self-dual D3-branes in Type 0B orbifolds and orientifolds.

One of the many remarkable features of MHV scattering amplitudes is their conjectured equality to lightlike polygon Wilson loops, which apparently holds at all orders in perturbation theory as well as non-perturbatively. This duality is usually expressed in terms of purely four-dimensional quantities obtained by appropriate subtraction of the IR and UV divergences from amplitudes and Wilson loops respectively. In this paper we demonstrate, by explicit calculation, the completely unanticipated fact that the equality continues to hold at two loops through O(ǫ) in dimensional regularization for both the four-particle amplitude and the (parity-even part of the) five-particle amplitude.

We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyper-planar and the entire moduli space stabilities may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a non-interacting basis at the zeros of the scalar curvature, where the scalar fields become un-correlated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilizations of gauge and string moduli.

The Hamilton-Jacobi method for constrained systems is discussed. The equations of motion for a free particle constrained to move on the surface of a torus are obtained without using any gauge-fixing conditions. The quantization of this model is also discussed.

Functional Geometry (FG): A Bottom-Up Alternative to Riemann–Cartan\\

1) Status Quo: “Top-Down” Geometry\\
  • In Riemannian approach you specify metric \(g_{ij}(x)\) up front\\
  • Then derive Christoffel symbols and curvature tensor\\

2) FG Paradigm Shift: “Bottom-Up”\\
  • Primary data: local frames \(X(t)\in GL(n)\) evolving in time\\
  • Integral synchronization 
   

\[
      F_i(u)=\int_{t_0}^u\|X_i(\tau)\|^2\,d\tau,\quad F_i(t)=y_i(t)
    \]

 
    ensures smooth, monotonic parametrization + noise averaging\\

3) From Frame to Geometry via Maurer–Cartan\\
  \(\omega = X^{-1}dX,\quad R = d\omega+\omega\wedge\omega,\quad g = X^T X\) 
  — no Christoffel symbols or extra covariant derivatives required\\

4) Automatic Torsion & Smooth SVD\\
  • If \(X\neq X^T\), a smooth SVD \(X=U\Sigma V^T\) yields orthonormal basis \(U\) and torsion terms\\
  • Spectral-gap control guarantees \(\mathcal C^k\) smoothness of \(U,V\)\\

5) Numerical Simplicity & Robustness\\
  • Integrate ODE for \(X(t)\), apply local SVD — no PDE solver needed\\
  • Built-in stability via integral synchronization “averages out” local noise\\

6) Equivalence & Global Consistency\\
  • We prove FG \(\Leftrightarrow\) classical Riemann–Cartan under standard topological hypotheses\\
  • Local charts glue by a smooth partition of unity into a global geometry\\

7) Key Advantages\\
  – No prior metric \(g_{ij}\) or orthonormal coframe needed\\
  – Natural handling of anisotropic, discrete, or fragmented data\\
  – Resistant to measurement noise and local fluctuations\\
  – Torsion arises automatically — no manual insertion\\

8) Real-World Applications\\
  • Seismic tomography \& gravimetry: recover spatial metrics from wavefront evolutions\\
  • Numerical relativity: evolve dynamic metrics (black hole, gravitational wave) via ODE+SVD\\
  • Interactive graphics & morphing: guarantee smooth, isometric deformations\\

9) Beyond the Real Case\\
  • Complex FG: holomorphic axes, Kähler forms, Calabi–Yau gluing on \(\mathbb{CP}^n\)\\
  • Non-commutative FG: spectral triple \(\,( \mathcal A,\mathcal H,D )\) for deformation quantization\\

10) Get Started Today\\
  • Read the preprint on Zenodo: DOI 10.5281/zenodo.15210673\\
  • Try code samples (Python/Matlab): ODE + SVD pipeline\\
  • Join our GitHub discussions & share your test results\\

The canonical quantization is performed at a light-front surface for the SU(N) Yang-Mills theory. The Weyl gauge is imposed as a gauge condition. The suitable parameterization is chosen for the transverse gauge field components in order to have Dirac brackets independent of interactions. The generating functional is defined for the perturbation theory and it is shown to coincide with its equal-time counterpart.

Abstract. This is a report based on a student research project con-ducted at San José State University in the Spring of 2009, which was a continuation of a similar project conducted in the Spring 2008. The goal of both projects was to investigate the possibility that the speed of a ...

Deformation theory requires solving Maurer-Cartan equation (MCE) associated to an DGLA (L-infinity algebra). The universal solution of [HS] is obtained iteratively, as a fixed point of a contraction, analogous to the Picard method. The role of the Kuranishi functor in this construction is emphasized. The parallel with Lie theory suggests that deformation theory is a higher “dimensional” version. The deformation determined by the solution of the Maurer-Cartan equation associated to a contraction, splits the epimorphism, leading to a “doubling and gluing” interpretation. The *-operator associated to a contraction is introduced, and the connection with Hodge structures and generalized complex structures ( dd∗ -lemma) is established. The relations with bialgebra deformation quantization on one hand and ConnesKreimer renormalization on the other, are suggested.

This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost quaternionic geometries. Exploiting some finite dimensional representation theory of simple Lie algebras, we give explicit formulae for distinguished invariant curved analogues of the standard operators in terms of the linear connections belonging to the structures in question, so in particular we prove their existence. Moreover, we prove that these formulae for kth order standard operators, k = 1, 2, . . . , are universal for all geometries in question. The Cartan connection and the invariant differential. So we suppose that a P -principal bundle G on M and the Cartan connection ω ∈ Ω 1 (G, g) is given on G (for the definition and properties of the Cartan connections, see [CSS1]).

We show how zero-modes and quasi-zero-modes of the Dirac operator in the adjoint representation can be used to construct an estimate of the action density distribution of a pure gauge field theory, which is less sensitive to the ultraviolet fluctuations of the field. This can be used to trace the topological structures present in the vacuum. The construction relies on the special properties satisfied by the supersymmetric zero-modes.

We show how zero-modes and quasi-zero-modes of the Dirac operator in the adjoint representation can be used to construct an estimate of the action density distribution of a pure gauge field theory, which is less sensitive to the ultraviolet fluctuations of the field. This can be used to trace the topological structures present in the vacuum. The construction relies on the special properties satisfied by the supersymmetric zero-modes.

Recently proposed Lagrangian for non-Abelian tensor gauge fields contains quadratic kinetic terms, as well as cubic and quartic terms describing non-linear interaction of tensor gauge fields with dimensionless coupling constant g. We analyze the free field equations for the lower rank non-Abelian tensor gauge fields. These equations are written in terms of the first order derivatives of extended field strength tensors, similarly to the electrodynamics and Yang-Mills theory. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. We present the free field equation for the general rank-(s + 1) tensor gauge field and its higher helicity solution.

Reparametrization invariant theories have a vanishing Hamiltonian and enforce their dynamics through constraints. We consider the model of N non-relativistic spinless particles coupled to an abelian Chern-Simons term, we make reparametrization of the time and using the Hamilton-Jacobi method to analyze the model. We obtain the canonical Hamiltonian and the canonical phase-space coordinates without using any gauge fixing conditions.

We extend a constrained version of Implicit Regularization (CIR) beyond one loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward-Slavnov-Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian Gauge Field Theories (scalar and spinorial QED) to two loop order and calculate the two-loop beta-function of the spinorial QED.

Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant, and we calculate the Feynman propagator using the extended phase space description. We show that the Feynman propagator's quantum phase is given by the boundary term of the canonical transformation of the extended phase space. We propose a new canonical transformation within the extended phase space that leads to a Lewis invariant generalization, and we sketch some possible applications.

Two particular types of consistent interactions of a single massless tensor field with the mixed symmetry corresponding to a two-column Young diagram (k, 1), dual to linearised gravity in D = k + 3, are considered: (a) self-interactions, and (b) crossinteractions with another dual formulation of linearised gravity in terms of a massless tensor field with the mixed symmetry of the linearised Riemann tensor. Under the standard hypotheses from gauge field theories, it is shown that: (1) there appear consistent self-interactions of a single massless tensor field with the mixed symmetry corresponding to a two-column Young diagram (k, 1) only if k is even, k = 2m and precisely in D = 4m spacetime dimensions; (2) there are allowed consistent cross-couplings to a single massless tensor field with the mixed symmetry of the linearised Riemann tensor, but only in D = k + 3. In both cases the coupled models exhibit deformed gauge transformations, but their algebra remains Abelian, like that of the free limit theories. In the latter case the first-order reducibility of the gauge transformations in the (k, 1) sector is also changed.

Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology of the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.

In this letter we make use of the Background Field Method (BFM) to compute the effective potential of an SU (2) gauge field theory, in the presence of chemical potential and temperature. The main idea is to consider the chemical potential as the background field. The gauge fixing condition required by the BFM turns out to be exactly the one we found in a previous article in a different context.

Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet de traiter des non linéarités très proches de la croissance critique. Les résultats obtenus nous ont motivé de travailler sur des équations polyharmoniques (-Δ)ku = f(x; u) avec notamment k = 2 et 3. Avec des hypothèses semblables à Yang [1998] sur f et des conditions au bord convenables, on obtient pour la première fois des estimations explicites de solution des équations polyha...

We investigate the following three consistency conditions for constructing string theories on orbifolds: i) the invariance of the energy-momentum tensors under twist operators, ii) the duality of amplitudes and iii) modular invariance of partition functions. It is shown that this investigation makes it possible to obtain the general class of consistent orbifold models, which includes a new class of orbifold models.

We investigate the following three consistency conditions for constructing string theories on orbifolds: i) the invariance of the energy-momentum tensors under twist operators, ii) the duality of amplitudes and iii) modular invariance of partition functions. It is shown that this investigation makes it possible to obtain the general class of consistent orbifold models, which includes a new class of orbifold models.

Next-to-leading order QCD fits are performed to F$ p , F£ n /F£ p , F% Fe and xF% Fe deep-inelastic scattering data using the F$ p data of either the EMC or BCDMS collaborations, appropriately renormalized for consistency with the reanalysed SLAC F% p data. The parton distributions from these fits are then used to predict next-toleading order prompt photon production cross-sections. The variation in the quality of the overall description of the deep-inelastic scattering and prompt photon production data simultaneously determines and the form of the gluon distribution of the proton. Next, cross-sections are predicted at next-to-leading order for the Drell-Yan process. Here, the quality of the overall description determines the antiquark content of the proton. Two sets of parton distributions are presented according to whether the EMC or BCDMS F£ p data were used in the analysis. Possible alternatives for the low-x behaviour of the gluon distributionoutside the range of the fitted data-are discussed and predictions are made for future experiments which have the potential to distinguish between these alternatives. I should like to express my thanks to Alan Martin, James Stirling, and Dick Roberts for their many helpful suggestions and their collaboration in three related publications, and also to Patrick Aurenche, Krzysztof Charchula, Jan Kwiecinski, Chris Maxwell, Mike Pennington, Mike Whalley and Marc Virchaux for miscellaneous help and encouragement. Thanks are also due to the fellow students and postdoctoral researchers without whom this thesis may well have been produced more quickly, but perhaps not as enjoyably: David Barclay,

A Clifford calculus on sections of a Clifford bundle associated with a (pseudo-) Riemannian metric is reviewed. Its use is illustrated by reference to the Einstein -Yang -Mills equations. The formalism highlights the difference between the Kahler and Dirac equations and their separability in a curved space-time is discussed. Some aspects of supersymmetric models are outlined.

Symmetries in modern physics are a fundamental theme under study that allows to appreciate the Particle Physics. In addition, gauge theories are tools that allow to do a description more complete. With this paper, we analyze a gauge symmetry that appears in complex holomorphic systems. A complex system can be reduced to different real systems, using different gauge conditions and several real systems are connected by gauge transformations in the complex space. We prove that the space of solutions of one system is related to another one using a gauge transformation. Gauge transformations are in some cases canonical transformations. However, in other cases are more general transformations that change the symplectic structure, but there is still a map between systems. We establish a construction extend of gauge transformations and show how to extend the analysis to the quantum case using path integrals by means of the Batalin-Fradkin-Vilkovisky theorem and with in the canonical formalism, where we show explicitly that solutions of the Schrödinger equation are gauge related.

Symmetries in modern physics are a fundamental theme under study that allows to appreciate the Particle Physics. In addition, gauge theories are tools that allow to do a description more complete. With this paper, we analyze a gauge symmetry that appears in complex holomorphic systems. A complex system can be reduced to different real systems, using different gauge conditions and several real systems are connected by gauge transformations in the complex space. We prove that the space of solutions of one system is related to another one using a gauge transformation. Gauge transformations are in some cases canonical transformations. However, in other cases are more general transformations that change the symplectic structure, but there is still a map between systems. We establish a construction extend of gauge transformations and show how to extend the analysis to the quantum case using path integrals by means of the Batalin-Fradkin-Vilkovisky theorem and with in the canonical formalism, where we show explicitly that solutions of the Schrödinger equation are gauge related.