376 research outputs found
Quantization of (2+1)-spinning particles and bifermionic constraint problem
This work is a natural continuation of our recent study in quantizing
relativistic particles. There it was demonstrated that, by applying a
consistent quantization scheme to a classical model of a spinless relativistic
particle as well as to the Berezin-Marinov model of 3+1 Dirac particle, it is
possible to obtain a consistent relativistic quantum mechanics of such
particles. In the present article we apply a similar approach to the problem of
quantizing the massive 2+1 Dirac particle. However, we stress that such a
problem differs in a nontrivial way from the one in 3+1 dimensions. The point
is that in 2+1 dimensions each spin polarization describes different fermion
species. Technically this fact manifests itself through the presence of a
bifermionic constant and of a bifermionic first-class constraint. In
particular, this constraint does not admit a conjugate gauge condition at the
classical level. The quantization problem in 2+1 dimensions is also interesting
from the physical viewpoint (e.g. anyons). In order to quantize the model, we
first derive a classical formulation in an effective phase space, restricted by
constraints and gauges. Then the condition of preservation of the classical
symmetries allows us to realize the operator algebra in an unambiguous way and
construct an appropriate Hilbert space. The physical sector of the constructed
quantum mechanics contains spin-1/2 particles and antiparticles without an
infinite number of negative-energy levels, and exactly reproduces the
one-particle sector of the 2+1 quantum theory of a spinor field.Comment: LaTex, 24 pages, no figure
Canonical form of Euler-Lagrange equations and gauge symmetries
The structure of the Euler-Lagrange equations for a general Lagrangian theory
is studied. For these equations we present a reduction procedure to the
so-called canonical form. In the canonical form the equations are solved with
respect to highest-order derivatives of nongauge coordinates, whereas gauge
coordinates and their derivatives enter in the right hand sides of the
equations as arbitrary functions of time. The reduction procedure reveals
constraints in the Lagrangian formulation of singular systems and, in that
respect, is similar to the Dirac procedure in the Hamiltonian formulation.
Moreover, the reduction procedure allows one to reveal the gauge identities
between the Euler-Lagrange equations. Thus, a constructive way of finding all
the gauge generators within the Lagrangian formulation is presented. At the
same time, it is proven that for local theories all the gauge generators are
local in time operators.Comment: 27 pages, LaTex fil
Two-dimensional metric and tetrad gravities as constrained second order systems
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method
for analyzing singular systems, we consider the Hamiltonian formulation of
metric and tetrad gravities in two-dimensional Riemannian spacetime treating
them as constrained higher-derivative theories. The algebraic structure of the
Poisson brackets of the constraints and the corresponding gauge transformations
are investigated in both cases.Comment: replaced with revised version published in
Mod.Phys.Lett.A22:17-28,200
Photon propagation in noncommutative QED with constant external field
We find dispersion laws for the photon propagating in the presence of
mutually orthogonal constant external electric and magnetic fields in the
context of the -expanded noncommutative QED. We show that there is no
birefringence to the first order in the noncommutativity parameter
By analyzing the group velocities of the photon eigenmodes we show that there
occurs superluminal propagation for any direction. This phenomenon depends on
the mutual orientation of the external electromagnetic fields and the
noncommutativity vector. We argue that the propagation of signals with
superluminal group velocity violates causality in spite of the fact that the
noncommutative theory is not Lorentz-invariant and speculate about possible
workarounds
Comments on ``A note on first-order formalism and odd-derivative actions'' by S. Deser
We argue that the obstacles to having a first-order formalism for
odd-derivative actions presented in a pedagogical note by Deser are based on
examples which are not first-order forms of the original actions. The general
derivation of an equivalent first-order form of the original second-order
action is illustrated using the example of topologically massive
electrodynamics (TME). The correct first-order formulations of the TME model
keep intact the gauge invariance presented in its second-order form
demonstrating that the gauge invariance is not lost in the Ostrogradsky
process.Comment: 6 pages, references are adde
Nilpotent noncommutativity and renormalization
We analyze renormalizability properties of noncommutative (NC) theories with
a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model
which is renormalizable at all orders of the loop expansion. We show that this
model has an infrared stable fixed point (at the one-loop level). We check that
the NC QED (which is one-loop renormalizable with usual NC parameter) remains
renormalizable when the NC parameter is bifermionic, at least to the extent of
one-loop diagrams with external photon legs. Our general conclusion is that
bifermionic noncommutativity improves renormalizablility properties of NC
theories.Comment: 5 figures, a reference adde
Entanglement of two-qubit photon beam by magnetic field
We have studied the possibility of affecting the entanglement measure of
2-qubit system consisting of two photons with different fixed frequencies but
with two arbitrary linear polarizations, moving in the same direction, by the
help of an applied external magnetic field. The interaction between the
magnetic field and the photons in our model is achieved through intermediate
electrons that interact with both the photons and the magnetic field. The
possibility of exact theoretical analysis of this scheme is based on known
exact solutions that describe the interaction of an electron subjected to an
external magnetic field (or a medium of electrons not interacting with each
other) with a quantized field of two photons. We adapt these exact solutions to
the case under consideration. Using explicit wave functions for the resulting
electromagnetic field, we calculate the entanglement measure of the photon beam
as a function of the applied magnetic field and parameters of the electron
medium
On Quantization of Time-Dependent Systems with Constraints
The Dirac method of canonical quantization of theories with second class
constraints has to be modified if the constraints depend on time explicitly. A
solution of the problem was given by Gitman and Tyutin. In the present work we
propose an independent way to derive the rules of quantization for these
systems, starting from physical equivalent theory with trivial
non-stationarity.Comment: 4 page
Pseudoclassical description of the massive Dirac particles in odd dimensions
A pseudoclassical model is proposed to describe massive Dirac (spin one-half)
particles in arbitrary odd dimensions. The quantization of the model reproduces
the minimal quantum theory of spinning particles in such dimensions. A
dimensional duality between the model proposed and the pseudoclassical
description of Weyl particles in even dimensions is discussed.Comment: 12 pages, LaTeX (RevTeX
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