Dmitri M. Gitman

Causality of massive spin-2 field in external gravity

Abstract We investigate the structure of equations of motion and lagrangian constraints in a general theory of massive spin-2 field interacting with external gravity. We demonstrate how consistency with the flat limit can be achieved in a number of specific spacetimes. One such example is an arbitrary static spacetime though equations of motion in this case may lack causal properties. Another example is provided by external gravity fulfilling vacuum Einstein equations with arbitrary cosmological constant. In the latter case there exists one-parameter family of theories describing causal propagation of the correct number of degrees of freedom for the massive spin-2 field in arbitrary dimension. For a specific value of the parameter a gauge invariance with a vector parameter appears, this value is interpreted as massless limit of the theory. Another specific value of the parameter produces gauge invariance with a scalar parameter and this cannot be interpreted as a consistent massive or massless theory.

Finite field-energy of a point charge in QED

We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, to show that it possesses a regularizing ability sufficient to make the field energy of a point charge finite. The model is exactly solved in the class of static central-symmetric electric fields. Collation with quantum electrodynamics (QED) results in the total field energy of a point elementary charge about twice the electron mass. The proof of the finiteness of the field energy is extended to include any polynomial selfinteraction, thereby the one that stems from the truncated expansion of the Euler–Heisenberg local Lagrangian in QED in powers of the field strength.

Spin factor in the path integral representation for the Dirac propagator in external fields

We study the problem of the spin factor both in 3+1 and 2+1 dimensions, two cases which are essentially different in this respect. Doing all Grassmann integrations in the corresponding path integral representations for the Dirac propagator we get representations with a spin factor in an arbitrary external field. Thus, the propagator appears to be presented by means of a bosonic path integral only. Then we use the representations with a spin factor for calculations of the propagator in some configurations of external fields: namely, in a constant uniform electromagnetic field and in its combination with a plane wave field. {copyright} {ital 1997} {ital The American Physical Society}

Path integrals and pseudoclassical description for spinning particles in arbitrary dimensions

Abstract The propagator of a spinning particle in an external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has distinct solutions in even and odd dimensions. In even dimensions the representation is just a generalization of the one in four dimensions (which is already known). In this case the gauge invariant part of the effective action in the path integral has the form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the solution is presented for the first time and, in particular, it turns out that the gauge invariant part of the effective action differs from the standard one. We propose this new action as a candidate to describe spinning particles in odd dimensions. Studying the Hamiltonization of the pseudoclassical theory with the new action we show that the operator quantization leads to an adequate minimal quantum theory of spinning particles in odd dimensions. Finally the consideration is generalized for the case of a particle with an anomalous magnetic moment.

Classical description of spinning degrees of freedom of relativistic particles by means of commuting spinors

We consider a possibility of describing spin one-half and higher spins of massive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables xμ, ξα, χα, where ξ, χ are commuting Majorana spinors. In the course of quantization both models reproduce Dirac equation. We analyze the possibility of introducing an interaction with an external electromagnetic background into the models and generalizing them to higher spin description. The first model admits a minimal interaction with the external electromagnetic field, but leads to reducible representations of the Poincare group being generalized for higher spins. The second model turns out to be appropriate for description of the massive higher spins. However, it seems to be difficult to introduce a minimal interaction with an external electromagnetic field into this model. We compare our approach with one, which uses Grassmann variables, and establish a relation between them.

Poincaré group and relativistic wave equations in dimensions

Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2 + 1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2 + 1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed.

Spinor and isospinor structure of relativistic particle propagators

Abstract Representations by means of path integrals are used to find spinor and isospinor structure of relativistic particle propagators in external fields. For Dirac propagator in an external electromagnetic field all grassmannian integrations are performed and a general result is presented via a bosonic path integral. The spinor structure of the integrand is given explicitly by its decomposition in the independent γ-matrix structures. Similar technique is used to get the isospinor structure of the scalar particle propagator in an external non-Abelian field.

PSEUDOCLASSICAL MODEL OF SPINNING PARTICLE WITH ANOMALOUS MAGNETIC MOMENTUM

A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic momentum is given. The action is written in reparametrization and supergauge invariant form. The Dirac quantization, based on the Hamiltonian analyzes of the model, leads to the Dirac-Pauli equation for a particle with an anomalous magnetic momentum in an external electromagnetic field. Due to the structure of first class constraints in that case, the Dirac quantization demands for consistency to take into account an operator’s ordering problem.

Interaction of orientable object fields with gauge fields

We consider a scalar field f(g) on the Poincare group M(3, 1). This scalar field describes objects that are characterized by a position x and an orientation z, g=(x,z). The field f(x, z) admits two kinds of transformations, corresponding to a change of the space-fixed reference frame, as well as to a change of the body-fixed reference frame, which form the group M(3, 1)ext×M(3, 1)int, and also phase transformations U(1)ch of orientational variables z. Elementary particles considered as elementary orientable objects are described by the scalar functions transforming according to irreps of the group M(3, 1)ext×M(3, 1)int×U(1)ch. Correspondingly, their continuous symmetries can be divided into external, which form the Poincare group M(3, 1)ext, and internal M(3, 1)int×U(1)ch. The assumption that the internal symmetries in the theory of orientable objects are gauge ones allows one to obtain important features of the known fundamental interactions—the electroweak and the gravitational. Localization of the group of the right translations T(4)int leads to the teleparallel theory of gravity, which is equivalent to general relativity. Localization of the compact subgroup SU(2)int×U(1)ch leads to the theory of electroweak interactions. Thus, the suggested approach can be considered as a possible way to gravitational–electroweak unification.

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 the classical model of a spinless relativistic particle as well as to the Berezin–Marinov model of a 3 + 1 Dirac particle, it is possible to obtain a consistent relativistic quantum mechanics of such particles. In the present paper, 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.