4,166 research outputs found

### Electromagnetism and multiple-valued loop-dependent wave functionals

We quantize the Maxwell theory in the presence of a electric charge in a
"dual" Loop Representation, i.e. a geometric representation of magnetic
Faraday's lines. It is found that the theory can be seen as a theory without
sources, except by the fact that the wave functional becomes multivalued. This
can be seen as the dual counterpart of what occurs in Maxwell theory with a
magnetic pole, when it is quantized in the ordinary Loop Representation. The
multivaluedness can be seen as a result of the multiply-connectedness of the
configuration space of the quantum theory.Comment: 5 page

### Dirac equation for membranes

Dirac's idea of taking the square root of constraints is applied to the case
of extended objects concentrating on membranes in D=4 space-time dimensions.
The resulting equation is Lorentz invariant and predicts an infinite hierarchy
of positive and negative masses (tension). There are no tachyonic solutions.Comment: 5 pages, 1 figure, v2: improved version, accepted for publication as
a Brief Report in Physical Review

### The 'Square Root' of the Interacting Dirac Equation

The 'square root' of the interacting Dirac equation is constructed. The
obtained equations lead to the Yang-Mills superfield with the appropriate
equations of motion for the component fields.Comment: 6 page

### Properties of noncommutative axionic electrodynamics

Using the gauge-invariant but path-dependent variables formalism, we compute
the static quantum potential for noncommutative axionic electrodynamics, and
find a radically different result than the corresponding commutative case. We
explicitly show that the static potential profile is analogous to that
encountered in both non-Abelian axionic electrodynamics and in Yang-Mills
theory with spontaneous symmetry breaking of scale symmetry.Comment: 4 pages. To appear in PR

### The dynamical equation of the spinning electron

We obtain by invariance arguments the relativistic and non-relativistic
invariant dynamical equations of a classical model of a spinning electron. We
apply the formalism to a particular classical model which satisfies Dirac's
equation when quantised. It is shown that the dynamics can be described in
terms of the evolution of the point charge which satisfies a fourth order
differential equation or, alternatively, as a system of second order
differential equations by describing the evolution of both the center of mass
and center of charge of the particle. As an application of the found dynamical
equations, the Coulomb interaction between two spinning electrons is
considered. We find from the classical viewpoint that these spinning electrons
can form bound states under suitable initial conditions. Since the classical
Coulomb interaction of two spinless point electrons does not allow for the
existence of bound states, it is the spin structure that gives rise to new
physical phenomena not described in the spinless case. Perhaps the paper may be
interesting from the mathematical point of view but not from the point of view
of physics.Comment: Latex2e, 14 pages, 5 figure

### Nonlinear QED and Physical Lorentz Invariance

The spontaneous breakdown of 4-dimensional Lorentz invariance in the
framework of QED with the nonlinear vector potential constraint
A_{\mu}^{2}=M^{2}(where M is a proposed scale of the Lorentz violation) is
shown to manifest itself only as some noncovariant gauge choice in the
otherwise gauge invariant (and Lorentz invariant) electromagnetic theory. All
the contributions to the photon-photon, photon-fermion and fermion-fermion
interactions violating the physical Lorentz invariance happen to be exactly
cancelled with each other in the manner observed by Nambu a long ago for the
simplest tree-order diagrams - the fact which we extend now to the one-loop
approximation and for both the time-like (M^{2}>0) and space-like (M^{2}<0)
Lorentz violation. The way how to reach the physical breaking of the Lorentz
invariance in the pure QED case taken in the flat Minkowskian space-time is
also discussed in some detail.Comment: 16 pages, 2 Postscript figures to be published in Phys. Rev.

### Interacting dark energy in $f(R)$ gravity

The field equations in $f(R)$ gravity derived from the Palatini variational
principle and formulated in the Einstein conformal frame yield a cosmological
term which varies with time. Moreover, they break the conservation of the
energy--momentum tensor for matter, generating the interaction between matter
and dark energy. Unlike phenomenological models of interacting dark energy,
$f(R)$ gravity derives such an interaction from a covariant Lagrangian which is
a function of a relativistically invariant quantity (the curvature scalar $R$).
We derive the expressions for the quantities describing this interaction in
terms of an arbitrary function $f(R)$, and examine how the simplest
phenomenological models of a variable cosmological constant are related to
$f(R)$ gravity. Particularly, we show that $\Lambda c^2=H^2(1-2q)$ for a flat,
homogeneous and isotropic, pressureless universe. For the Lagrangian of form
$R-1/R$, which is the simplest way of introducing current cosmic acceleration
in $f(R)$ gravity, the predicted matter--dark energy interaction rate changes
significantly in time, and its current value is relatively weak (on the order
of 1% of $H_0$), in agreement with astronomical observations.Comment: 8 pages; published versio

### P.A.M. Dirac and the Discovery of Quantum Mechanics

Dirac's contributions to the discovery of non-relativistic quantum mechanics
and quantum electrodynamics, prior to his discovery of the relativistic wave
equation, are described

### Lagrangian and Hamiltonian formulations of higher order Chern-Simons theories

We consider models involving the higher (third) derivative extension of the
abelian Chern-Simons (CS) topological term in D=2+1 dimensions. The
polarisation vectors in these models reveal an identical structure with the
corresponding expressions for usual models which contain, at most, quadratic
structures. We also investigate the Hamiltonian structure of these models and
show how Wigner's little group acts as gauge generator.Comment: 13 pages, Late

### On the transformations of hamiltonian gauge algebra under rotations of constraints

By explicit calculation of the effect of a ghost-dependent canonical
transformation of BRST-charge, we derive the corresponding transformation law
for structure coefficients of hamiltonian gauge algebra under rotation of
constraints.We show the transformation law to deviate from the behaviour
(expected naively) characteristic to a genuine connection.Comment: 11 pages, some misprints remove

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