Consistent gauge interaction involving dynamical coupling and anomalous current

We show a possible way to construct a consistent formalism where the effective electric charge can change with space and time without destroying the gauge invariance. In the previous work[Formula: see text] we took the gauge coupling to be of the form [Formula: see text] where [Formula: see text] is an auxiliary field, [Formula: see text] is a scalar field and the current [Formula: see text] is the Dirac current. This term produces a constraint [Formula: see text] which can be related to MIT bag model by boundary condition. In this paper, we show that when we use the term [Formula: see text], instead of the auxiliary field [Formula: see text], there is a possibility to produce a theory with dynamical coupling constant, which does not produce any constraint or confinement. The coupling [Formula: see text] where [Formula: see text] is an anomalous current is also discussed.

Confining boundary conditions from dynamical coupling constants for Abelian and non-Abelian symmetries

The present work represents among other things a generalization to the non-Abelian case of our previous result where the Abelian case was studied. In the U(1) case the coupling to the gauge field contains a term of the form g(ϕ)jμ(Aμ +∂μB), where B is an auxiliary field and jμ is the Dirac current. The scalar field ϕ determines the local value of the coupling of the gauge field to the Dirac particle. The consistency of the equations determines the condition ∂μϕjμ = 0 which implies that the Dirac current cannot have a component in the direction of the gradient of the scalar field. As a consequence, if ϕ has a soliton behavior, we obtain that jμ cannot have a flux through the wall of the bubble, defining a confinement mechanism where the fermions are kept inside those bags. In this paper, we present more models in Abelian case which produce constraint on the Dirac or scalar current and also spin. Furthermore a model that gives the MIT confinement condition for gauge fields is obtained. We generalize this procedure for the non-Abelian case and we find a constraint that can be used to build a bag model. In the non-Abelian case, the confining boundary conditions hold at a specific surface of a domain wall.

Computational Determination of the Dirac-Theory Adjunctator

A number of particle properties stem from the use ofγ0as adjunctator (Bargmann-Pauli) in the Dirac theory (spin alignment, Dirac current, etc.). The early motivations for acceptingγ0as adjunctator were representation-dependent, mildly bearing relation to the actual conditions forcingγ0as adjunctator. Representation-independent approaches to the physical predictions of the Dirac equation are somewhat new, here presented as being the reasons forγ0as adjunctator of the Dirac theory, together with the essential role of the latter in the physical aspects of the theory.

Nonlinear electron solutions and their characteristics at infinity

The Maxwell-Dirac equations model an electron in an electromagnetic field. The two equations are coupled via the Dirac current which acts as a source in the Maxwell equation, resulting in a nonlinear system of partial differential equations (PDE's). Well-behaved solutions, within reasonable Sobolev spaces, have been shown to exist globally as recently as 1997 [12]. Exact solutions have not been found—except in some simple cases.We have shown analytically in [6, 18] that any spherical solution surrounds a Coulomb field and any cylindrical solution surrounds a central charged wire; and in [3] and [19] that in any stationary case, the surrounding electron field must be equal and opposite to the central (external) field. Here we extend the numerical solutions in [6] to a family of orbits all of which are well-behaved numerical solutions satisfying the analytic results in [6] and [11]. These solutions die off exponentially with increasing distance from the central axis of symmetry. The results in [18] can be extended in the same way. A third case is included, with dependence on z only yielding a related fourth-order ordinary differential equation (ODE) [3].

PARTICLE PRODUCTION IN DE SITTER SPACE–TIME

The definition of vacuum in curved space–time is a delicate object. With Minkowski-like vacuum definition, the current has a characteristic behavior in Robertson–Walker space–time. In this work we study the behavior of Dirac current in a de Sitter space–time. The rapid oscillations of current is observed with respect to time and indicate vigorous instability in initial vacuum and is interpreted as vigorous particle production.

GORDON DECOMPOSITION OF DIRAC SPINORS IN GRAVITATIONAL BACKGROUND

The scheme outlined earlier is continued here to investigate the structure of Dirac spinors in the background of a gravitational field within the context of cosmological Robertson-Walker metric where the treatment is based on general considerations of spatially curved (non-flat) hypersurfaces embracing open as well as closed versions of the Universe. A Gordon decomposition of the generalized Dirac current is then carried out in terms of the polarization and the magnetization densities. We also take a look at the Klein-Gordon equation in the curved space formalism.