851 research outputs found
Functional integral over velocities for a spinning particle with and without anomalous magnetic moment in a constant electromagnetic field
The technique of functional integration over velocities is applied to the
calculation of the propagator of a spinning particle with and without anomalous
magnetic moment. A representation for the spin factor is obtained in this
context for the particle in a constant electromagnetic field. As a by-product,
we also obtain a Schwinger representation for the first case.Comment: latex, 19 page
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 quantization of the relativistic particle in static spacetimes
We perform the canonical quantization of a relativistic spinless particle
moving in a curved and static spacetime. We show that the classical theory
already describes at the same time both particle and antiparticle. The analyses
involves time-depending constraints and we are able to construct the
two-particle Hilbert space. The requirement of a static spacetime is necessary
in order to have a well defined Schr\"odinger equation and to avoid problems
with vacuum instabilities. The severe ordering ambiguities we found are in
essence the same ones of the well known non-relativistic case.Comment: Revtex, 9 page
Covariant quantizations in plane and curved spaces
We present covariant quantization rules for nonsingular finite dimensional
classical theories with flat and curved configuration spaces. In the beginning,
we construct a family of covariant quantizations in flat spaces and Cartesian
coordinates. This family is parametrized by a function ,
, which describes an ambiguity of the quantization.
We generalize this construction presenting covariant quantizations of theories
with flat configuration spaces but already with arbitrary curvilinear
coordinates. Then we construct a so-called minimal family of covariant
quantizations for theories with curved configuration spaces. This family of
quantizations is parametrized by the same function . Finally, we describe a more wide family of covariant quantizations in
curved spaces. This family is already parametrized by two functions, the
previous one and by an additional function . The above mentioned minimal family is a part at of
the wide family of quantizations. We study constructed quantizations in detail,
proving their consistency and covariance. As a physical application, we
consider a quantization of a non-relativistic particle moving in a curved
space, discussing the problem of a quantum potential. Applying the covariant
quantizations in flat spaces to an old problem of constructing quantum
Hamiltonian in Polar coordinates, we directly obtain a correct result.Comment: 38 pages, 2 figures, version published in The European Physical
Journal
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
Canonical and D-transformations in Theories with Constraints
A class class of transformations in a super phase space (we call them
D-transformations) is described, which play in theories with second-class
constraints the role of ordinary canonical transformations in theories without
constraints.Comment: 16 pages, LaTe
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
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
Path integral and pseudoclassical action for spinning particle in external electromagnetic and torsion fields
Starting from the Dirac equation in external electromagnetic and torsion
fields we derive a path integral representation for the corresponding
propagator. An effective action, which appears in the representation, is
interpreted as a pseudoclassical action for a spinning particle. It is just a
generalization of Berezin-Marinov action to the background under consideration.
Pseudoclassical equations of motion in the nonrelativistic limit reproduce
exactly the classical limit of the Pauli quantum mechanics in the same case.
Quantization of the action appears to be nontrivial due to an ordering problem,
which needs to be solved to construct operators of first-class constraints, and
to select the physical sector. Finally the quantization reproduces the Dirac
equation in the given background and, thus, justifies the interpretation of the
action.Comment: 18 pages, LaTeX. Small modifications, some references added. To be
published in International Journal of Modern Physics
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