3,182 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
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
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
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
On the Implementation of Constraints through Projection Operators
Quantum constraints of the type Q \psi = 0 can be straightforwardly
implemented in cases where Q is a self-adjoint operator for which zero is an
eigenvalue. In that case, the physical Hilbert space is obtained by projecting
onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however,
nontrivial to identify and project onto H_phys when zero is not in the point
spectrum but instead is in the continuous spectrum of Q, because in this case
the kernel of Q is empty.
Here, we observe that the topology of the underlying Hilbert space can be
harmlessly modified in the direction perpendicular to the constraint surface in
such a way that Q becomes non-self-adjoint. This procedure then allows us to
conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on
which one can project as usual. In the simplest case, the necessary change of
topology amounts to passing from an L^2 Hilbert space to a Sobolev space.Comment: 22 pages, LaTe
On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions
It is shown that the well-known triviality of the Einstein field equations in
two dimensions is not a sufficient condition for the Einstein-Hilbert action to
be a total divergence, if the general covariance is to be preserved, that is, a
coordinate system is not fixed. Consequently, a Hamiltonian formulation is
possible without any modification of the two dimensional Einstein-Hilbert
action. We find the resulting constraints and the corresponding gauge
transfromations of the metric tensor.Comment: 9 page
Non-quantized Dirac monopoles and strings in the Berry phase of anisotropic spin systems
The Berry phase of an anisotropic spin system that is adiabatically rotated
along a closed circuit C is investigated. It is shown that the Berry phase
consists of two contributions: (i) a geometric contribution which can be
interpreted as the flux through C of a non-quantized Dirac monopole, and (ii) a
topological contribution which can be interpreted as the flux through C of a
Dirac string carrying a non-quantized flux, i.e., a spin analogue of the
Aharonov-Bohm effect. Various experimental consequences of this novel effect
are discussed.Comment: 4 pages, 3 figures (RevTeX + eps); v2 (revised paper): 4 pages, 4
figure
- …