Swap Operators and Electric Charges of Fermions

2010

2000

The quantum balance equations are derived for the number of particles, the momentum, the energy, and the magnetic moment density. These equations in the classical limit 0 → ! transform into the well-known balance equations. The equation for the magnetic moment is a generalization of the Bloch equation. It is also shown that the spin-spin interaction Hamiltonian, conventionally used in the quantum theory of a many-particle system, yields incorrect equations for the magnetic field in a medium and that this defect can be eliminated. An important role of the Bohm quantum potential is demonstrated for a system of identical bosons and fermions. Let us consider a system of N interacting fermions with identical masses, charges, and magnetic moments in an external electromagnetic field. A state of the system of N fermions is characterized by the wave function in the 3Ndimensional configurational space:

Physical Review D, 1972

We construct classes of Lagrangians which describe families of fermions containing an infinite number of particles. The Lagrangians depend on Rarita-Schwinger fields with k Lorentz indices, k =1, 2, ... , which have bilinear interactions among themselves. These Lagrangians are invariant under gauge transformations of the second kind. The physical states appear as the normal modes of these field theories, and by suitable choices of the masses of the underlying gauge fields, the physical fermions can be made to lie on linearly rising Regge trajectories. The currents have nontrivial diagonal matrix elements, and also have matrix elements between states of different spin. By considering time-ordered products of currents between single-particle states, we are able to construct onand off-mass-shell N-point functions in the narrow-resonance approximation.

2013

Four-fermion operators have been utilized in the past to link the quarkexchange processes in the interaction of hadrons with the effective mesonexchange amplitudes. In this paper, we apply the similar idea of Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of nucleon and electron. We explain the motivation of using four-fermion operators and discuss the advantage of this method in computing electromagnetic processes.

We present the bundle (Aff(3)⊗C⊗ )(R 3 ), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (C ⊗ )(R 3 ) describes an electroweak doublet. The Dirac equation has a doublerfree staggered spatial discretization on the lattice space (Aff(3) ⊗ C)(Z 3 ). This space allows a simple physical interpretation as a phase space of a lattice of cells.

J. Phys. A: Math. Gen. 32 1197

We show that the quantum field theoretical formulation of the tau-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that (i) the partial charge transformations preserving the neutral sector are Laplace transformations, (ii) the basic vertex operators are Lévy and adjoint Lévy transformations and (iii) the diagonal soliton vertex operators generate fundamental transformations. We also show that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinear identity for the multidimensional quadrilateral lattice equations.

Communications in Mathematical Physics, 1967

The representation of the canonical commutation relations involved in the construction of boson operators from fermion operators according to the recipe of the neutrino theory of light is studied. Starting from a cyclic Fockrepresentation for the massless fermions the boson operators are reduced by the spectral projectors of two charge-operators and form an infinite direct sum of cyclic Fock-representations. Kronig's identity expressing the fermion kinetic energy in terms of the boson kinetic energy and the squares of the charge operators is verified as an identity for strictly self adjoint operators. It provides the key to the solubility of LTJTTINGER'S model. A simple sufficient condition is given for the unitary equivalence of the representations linked by the canonical transformation which diagonalizes the total Hamiltonian.

2014

We establish equations for scalar and fermion fields using results obtained from a study on a phase space representation of quantum theory that we have performed in a previous work. Our approaches are similar to the historical ones to obtain Klein-Gordon and Dirac equations but the main difference is that ours are based on the use of properties of operators called dispersion-codispersion operators. We begin with a brief recall about the dispersion-codispersion operators. Then, introducing a mass operator with its canonical conjugate coordinate and applying rules of quantization, based on the use of dispersion - codispersion operators, we deduce a second order differential operator relation from the relativistic expression relying energy, momentum and mass. Using Dirac matrices, we derive from this second order differential operator relation a first order one. The application of the second order differential operator relation on a scalar function gives the equation for the scalar field and the use of the first order differential operator relation leads to the equation for fermion field.

EPJ Quantum Technology, 2014

The key dynamic properties of fermionic systems, like controllability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. It just requires knowing drift and control Hamiltonians of an experimental setup. Then one can easily determine all the states that can be reached from any given initial state. Likewise all the quantum operations that can be simulated with a given setup can be identified. Observing the parity superselection rule, we treat the fully controllable and quasifree cases of fermions, as well as various translation-invariant and particle-number conserving cases. We determine the respective dynamic system Lie algebras to express reachable sets of pure (and mixed) states by explicit orbit manifolds.