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.

ON THE INDEPENDENT-PARTICLE APPROXIMATION OF GAUGE-THEORIES - A SIMPLE EXAMPLE

In this work the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1 + 1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed.

HELICITY WAVE-FUNCTIONS FOR MASSLESS AND MASSIVE SPIN-2 PARTICLES

Starting from general properties of a spin-2 field, we construct helicity wave functions in the framework of the Weyl-van der Waerden spinor formalism. We discuss here the cases of massless and massive spin-2 particles.

CAUSAL APPROACH TO (2+1)-DIMENSIONAL QED

It is shown that the causal approach to (2 + 1)-dimensional quantum electrodynamics yields a well-defined perturbative theory. In particular, and in contrast to renormalized perturbative quantum field theory, it is free of any ambiguities and ascribes a nonzero value to the dynamically generated, nonperturbative photon mass. (C) 1994 Academic Press, Inc.

Helicity amplitudes for matter-coupled gravity

The great simplicity attained by the Weyl-van der Waerden spinor technique in the evaluation of helicity invariant amplitudes is shown to apply in the cumbersome calculations within the framework of linearized gravitation. Once the graviton couplings to spin-0, 1/2, 1, and 3/2 particles are given, we exhibit the reach of this method by evaluating, as an example, the helicity amplitudes for the process electron + positron → photon + graviton in a very straightforward way. © 1994 Plenum Publishing Corporation.

Fermion helicity flip in higher-derivative electromagnetism

It is shown that massive fermions have their helicity flipped on account of their interaction with an electromagnetic field described by Podolsky's generalized electrodynamics. Massless fermions, in turn, seem to be unaffected by the electromagnetic field as far as their helicity is concerned. © Springer-Verlag 1997.

Extra dimensions in superstring theory

It was earlier shown that an SO(9,1) θα spinor variable can be constructed from RNS matter and ghost fields. θα has a bosonic world-sheet super-partner λα which plays the role of a twistor variable, satisfying λΓμ λ = ∂xμ + iθΓμ ∂θ. For Type IIA superstrings, the left-moving [θL α, λL α] and right-moving [θRα, λRα] can be combined into 32-component SO(10,1) spinors [θA, λA]. This suggests that λAΓAB 11 λB = 2λL αλRα can be interpreted as momentum in the eleventh direction. Evidence for this interpretation comes from the zero-momentum vertex operators of the Type IIA superstring and from consideration of DD-branes. As in the work of Bars, one finds an SO(10,2) structure for the Type IIA superstring and an SO(9, 1) × SO(2, 1) structure for the Type IIB superstring. © 1997 Elsevier Science B.V.

Chiral asymmetry and gravitation theory

In this letter we apply an alternative approach, recently developed, to the description of massless particles of arbitrary spin to the case of spin-two particles. This provides a non-geometrical approach to the theory of linearized gravitation. Within this method the chiral components of a spinor field are treated as independent field variables. The free field Lagrangian is built up from the requirement of chiral invariance. This formulation is parallel to the neutrino theory and leads to a formulation that generalizes, to particles of spin-two, the two-component neutrino theory. At the free field level the analog of curvature tensor, spin connection tensor, and metric tensor are independent quantities. By introducing left-right asymmetric linear interactions of these chiral components we get the linearized gravitation theory.

The action for the (propagating) torsion and the limits on the torsion parameters from present experimental data

Starting from the well established form of the Dirac action coupled to the electromagnetic and torsion field we find that there is some additional softly broken local symmetry associated with torsion. This symmetry fixes the form of divergences of the effective action after the spinor fields are integrated out. Then the requirement of renormalizability fixes the torsion field to be equivalent to some massive pseudovector and its action is fixed with accuracy to the values of coupling constant of torsion-spinor interaction, mass of the torsion and higher derivative terms. Implementing this action into the abelian sector of the Standard Model we establish the upper bounds on the torsion mass and coupling. In our study we used results of present experimental limits on four-fermion contact interaction (LEP, HERA, SLAC, SLD, CCFR) and TEVATRON limits on the cross section of new gauge boson, which could be produced as a resonance at high energy pp̄ collisions. © 1998 Elsevier Science B.V. All rights reserved.

Axial anomaly through analytic regularization

In this work we consider the two-point Green's functions in (1 + 1)-dimensional quantum electrodynamics and show that the correct implementation of analytic regularization gives a gauge invariant result for the vacuum polarization amplitude and the correct coefficient for the axial anomaly.

Torsion action and its possible observables

The methods of effective field theory are used to explore the theoretical and phenomenological aspects of the torsion field. The spinor action coupled to the electromagnetic field and torsion possesses an additional softly broken gauge symmetry. This symmetry enables one to derive the unique form of the torsion action compatible with unitarity and renormalizability. It turns out that the antisymmetric torsion field is equivalent to a massive axial vector field. The introduction of scalars leads to serious problems which are revealed after the calculation of the leading two-loop divergences. Thus the phenomenological aspects of torsion may be studied only for the fermion-torsion systems. In this part of the paper we obtain upper bounds for the torsion parameters using present experimental data on forward-backward Z-pole asymmetries, data on the experimental limits on four-fermion contact interaction (LEP, HERA, SLAC, SLD, CCFR) and also TEVATRON limits on the cross section of a new gauge boson, which could be produced as a resonance at high energy pp collisions. The present experimental data enable one to put limits on the torsion parameters for the various ranges of the torsion mass. We emphasize that for a torsion mass of the order of the Planck mass no independent theory for torsion is possible, and one must directly use string theory. © 1999 Elsevier Science B.V.

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories. © 2000 Elsevier Science B.V. All rights reserved.

Constraints on space-time manifold in Euclidean supergravity in terms of Dirac eigenvalues

We generalize a previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the space-time manifold, under which space-time admits Dirac eigenvalues as observables, are derived.

Quadratic effective action for QED in D=2,3 dimensions

We calculate the effective action for quantum electrodynamics (QED) in D=2,3 dimensions at the quadratic approximation in the gauge fields. We analyze the analytic structure of the corresponding nonlocal boson propagators nonperturbatively in k/m. In two dimensions for any nonzero fermion mass, we end up with one massless pole for the gauge boson. We also calculate in D=2 the effective potential between two static charges separated by a distance L and find it to be a linearly increasing function of L in agreement with the bosonized theory (massive sine-Gordon model). In three dimensions we find nonperturbatively in k/m one massive pole in the effective bosonic action leading to screening. Fitting the numerical results we derive a simple expression for the functional dependence of the boson mass upon the dimensionless parameter e2/m. ©2000 The American Physical Society.

Gravitomagnetic moments of the fundamental fields

The quadratic form of the Dirac equation in a Riemann space-time yields a gravitational gyromagnetic ratio κ(S) = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio κ(S) = 1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square-root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account.