We investigate two-parameter solutions of σ-models on two dimensional symmetric spaces contained ... more We investigate two-parameter solutions of σ-models on two dimensional symmetric spaces contained in E 11. Embedding such σ-model solutions in space-time gives solutions of M * and M-theory where the metric depends on general travelling wave functions, as opposed to harmonic functions typical in general relativity, supergravity and M-theory. Weyl reflection allows such solutions to be mapped to M-theory solutions where the wave functions depend explicitly on extra coordinates contained in the fundamental representation of E
Journal of Physics A: Mathematical and Theoretical, 2013
In an earlier paper it was argued that the conventional double-scaling limit of an O(N )-symmetri... more In an earlier paper it was argued that the conventional double-scaling limit of an O(N )-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative and thus the integral representing the partition function of the critical theory does not exist. In this earlier paper it was shown that for an O(N )-symmetric quantum field theory in zero-dimensional spacetime one can avoid this difficulty if one replaces the original quartic theory by its PT -symmetric analog. In the current paper an O(N )-symmetric quartic quantum field theory in onedimensional spacetime [that is, O(N )-symmetric quantum mechanics] is studied using the Schrödinger equation. It is shown that the global PT -symmetric formulation of this differential equation provides a consistent way to perform the double-scaling limit of the O(N )-symmetric anharmonic oscillator. The physical nature of the critical behavior is explained by studying the PT -symmetric quantum theory and the corresponding and equivalent Hermitian quantum theory.
The dynamics near a hyperbolic fixed point in phase space is modelled by an inverted harmonic osc... more The dynamics near a hyperbolic fixed point in phase space is modelled by an inverted harmonic oscillator. We investigate the effect of the classical instability on the open quantum dynamics of the oscillator, introduced through the interaction with a thermal bath, using both the survival probability function and the rate of von Neumann entropy increase, for large times. In this parameter range we prove, using influence functional techniques, that the survival probability function decreases exponentially at a rate, κ ′ , depending not only on the measure of instability in the model but also on the strength of interaction with the environment. We also show that κ ′ determines the rate of the von Neumann entropy increase and that this result is independent of the temperature of the environment. This generalises earlier results which are valid in the limit of vanishing dissipation. The validity of inferring similar rates of survival probability decrease and entropy increase for quantum chaotic systems is also discussed.
The long distance behavior of singlet current correlation functions of gauge theories on a lattic... more The long distance behavior of singlet current correlation functions of gauge theories on a lattice are found approximately using the renormalization group. For strong coupling the behavior is similar to that found in the lattice massive Schwinger model.
The response of a quantum field to classical chaos
J Phys a Math Gen, 1988
The quantum theory of a massless scalar field in a box with one chaotically moving wall is presen... more The quantum theory of a massless scalar field in a box with one chaotically moving wall is presented. The time dependence of normally ordered coherence functions is found to be chaotic, whereas the number of quanta present is insensitive to the details of the chaotic motion.
In the ftumtional approach to field theories (t) generating functionals are used. There are three... more In the ftumtional approach to field theories (t) generating functionals are used. There are three types in common use, which arc frequently denoted by Z[J], W[J] and F [J], where J is a c-number source. These arc functionals which generate connected as well as disconnected Grccn's functions, just c01meeted Green's functions and connected one-particle irreducible Green's functions, rcspcctively. Ward-Tak~hashi-Slavnov (WTS) identities (-") h:~ve until recently only been formulated for Z [J] and W[J]. WTS idcntities play a crucial role in the proof of renormalizability of massive gauge theories; herc massive theorics means theories that employ the Higgs-Kibblc mcchanism (3). In the renormaliz~tion programme it is one-particle irreducible vertices that we have to deal with and so it is desirable that WTS identities be expressed in terms of F[JJ. L~:F, (4) has formulated WTS identities recently in terms of F [J] for non-Abelian gauge theori~s. In this note we would lik~ to extend his results to the m()st g,u~cral gauge cortdition. Apart ft'om the d()siro,bility of compieteILess of the treatment of WTS identities the ease, when the gauge~ coi~diti~)n hivo~ves expressions quadratic in the fictds occurs often. Even in quantum electrodynamics the gauge in which A"A, is a constant has been used by DIRAC and ]!'Ir and fro]~, a more specific point of view these gaugcs may bc particularly useful (.5) in studying the effect of Fadd~ev-Popov (") ghosts in theories in which fliggs-Kibble scalpers at'e generated dynamically. We shall adopt a notat~ion very similar to that in (a). The method of quantization will be that of FADD~,eV and Poeov (s). W~ will denote the set of all fields in the theory (e. 9. g~uge fields as well as fermion and IIiggs-Kibble (a) scalar fields). W~ will trans-
A new theory of hydrodynamics of uniaxial nematic liquid crystal films in the presence of defects... more A new theory of hydrodynamics of uniaxial nematic liquid crystal films in the presence of defects is developed. A gauge field incorporating screening is introduced, resulting in the static elastic free energy having the form of a two-dimensional Abelian-Higgs model. Hydrodynamic equations are derived via the standard methods of de~Groot and Mazur. By working in the vicinity of the Bogomol'nyi equations consequences for defect centre motion are outlined.
The role of CPT invariance and consequences for bipartite entanglement of neutral (K) mesons are ... more The role of CPT invariance and consequences for bipartite entanglement of neutral (K) mesons are discussed. A relaxation of CPT leads to a modification of the entanglement which is known as the ω effect. The relaxation of assumptions required to prove the CPT theorem are examined within the context of models of space-time foam. It is shown that the evasion of the EPR type entanglement implied by CPT (which is connected with spin statistics) is rather elusive. Relaxation of locality (through non-commutative geometry) or the introduction of an environment do not by themselves lead to a destruction of the entanglement. One model of the environment, which is based on non-critical strings and D-particle capture and recoil, leads to a specific momentum dependent stochastic contribution to the space-time metric and consequent change in the neutral meson bipartite entanglement. Although the class of models producing the omega effect is non-empty, the lack of an omega effect is demonstrated for a wide class of models based on thermal like baths which are often considered as generic models appropriate for the study of space-time foam.
Light scattering spectrum of 4He for T>=Tlambda in three dimensions
Phys Rev B, 1981
The field-theoretic renormalization-group formalism is used to calculate the light scattering spe... more The field-theoretic renormalization-group formalism is used to calculate the light scattering spectrum of 4He for T>=Tλ self-consistently to second order in the loop expansion. It is shown that owing to the finite wave vector of the experiments the system never comes close to its fixed point (even for T=Tλ), and transients must be included consistently to explain the data. Previous explanations of the absence of temperature dependence of the linewidth, in terms of the effect of the weak-scaling fixed point, are shown to be incorrect.
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