Comments on spin operators and spin-polarization states of 2+1 fermions

In this brief article we discuss spin polarization operators and spin polarization states of 2+1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2+1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2+1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.Comment: 6 page

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

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

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

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

The mean value of the one-loop energy-momentum tensor in thermal QED with electric-like background that creates particles from vacuum is calculated. The problem differes essentially from calculations of effective actions (similar to that of Heisenberg--Euler) in backgrounds that do not violate the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and its duration under which one can neglect the back-reaction of created particles are established.Comment: 7 pages, Talk presented at Workshop "Quantum Field Theory under the Influence of External Conditions", Leipzig, September 17-21, 2007; introduction extended, version accepted for publication in J.Phys.

Anomaly and Condensate in the Light-Cone Schwinger Model

The axial anomaly and fermion condensate in the light cone Schwinger model are studied following path integral methods. This formalism allows for a simple and direct calculation for these and other vacuum dependent phenomena.Comment: 10pp, Revte

Pseudoclassical theories of Majorana, Weyl and Majorana--Weyl particles

A pseudoclassical theories of Majorana, Weyl and Majorana--Weyl particles in the space--time dimensions $D=2n$ are constructed. The canonical quantization of these theories is carried out and as a result we obtain the quantum mechanical description of neutral particle in $D=2n$ , Weyl particle in $D=2n$ and neutral Weyl particle in $D=4n+2$. In $D=2,4({\rm mod}8)$ dimensional space--time the description of the neutral particle coincides with the field theoretical description of the Majorana particle in the Foldy--Wouthuysen representation. In $D=8k+2$ dimensions the neutral Weyl particle coincides with the Majorana--Weyl particle in the Foldy--Wouthuysen representation.Comment: LATEX, 17 pages, no figure