Path Integral Framework Research Articles

Adler-Bardeen theorem in path integral formulation

The higher order contributions to Jacobian in Fujikawa’s path integral framework is considered and the form of anomaly equation in higher orders is established. An argument for the Adler-Bardeen theorem in this formulation is given.

A non-Abelian Aharonov-Bohm effect in the framework of Feynman pseudo-classical path integrals

The authors analyse the non-Abelian Aharonov-Bohm effect in the Feynman path integral framework generalised to pseudo-classical mechanics.

On the compactification of the bosonic string at higher loops

We analyze the procedure of string compactification on a lattice Λ in the framework of Polyakov's path integral for arbitrary genus of the string world sheet. It is demonstrated how compactification, factorizability into left and right movers and modular invariance are related. The constraints on Λ of being an even, self-dual lattice, as well as the relation among the radius of compactification and the string tension, known from the heterotic string occur naturally. We present the “correction factor” R for arbitrary genus of the string world sheet.

Functional treatment of the meson exchange currents

Two alternative formulations of the meson exchange currents (MEC) and of the associated response to an electromagnetic field are derived in the path integral framework for a system of nucleons and pion with either a pseudoscalar or a pseudovector interaction. In the first approach, by integrating out the pionic and the electromagnetic fields configurations, we deduce a fermionic effective action S eff F leading, in conventional perturbation theory, to the standard expression for the MEC. In the second one, instead, by integrating out the fermions and electromagnetic fields configuration, we obtain a bosonic effective action S eff B . We evaluate the functional generator Z C associated to the latter in the stationary phase approximation (mean field) plus leading order quantum fluctuations. The corresponding response, most suited to deal with the physics at high energies and densities, includes RPA dressed pion propagators, the exchange interaction between the particle and the hole, the full variety of the two particles-two holes diagrams as well as the so-called bubbles into bubble (to leading order) and the nucleon self-energy (to infinite order). Thus the functional expansion, closely related to the loop expansion of the field theory, yields an unambiguous prescription for the diagrams to be kept in order to achieve a consistent many-body description of the response of a system of pions and nucleons to an electromagnetic field.

Path-integral bosonization for the Abelian Avan-de Vega two-dimensional model.

We study the bosonization of the Abelian version of the Avan-de Vega two-dimensional fermion model in the framework of path integrals.

Path integrals on half-line

In the framework of path integrals we present a solution to the Schrodinger equation for a free particle confined to the half-linex > 0. A solution in question corresponds to the boundary condition (∂ψ/∂x) (0,t)=α ψ(0,t) whereα is a real constant.

Current-algebra results in the path-integral framework.

Current-algebra results in the path-integral framework.

Path-integral bosonization for massive fermion models in two dimensions.

We study the bosonization of the massive Thirring model in the framework of path integrals.

Abelian and non-Abelian bosonization in the path-integral framework.

Abelian and non-Abelian bosonization of two-dimensional models is discussed within the path-integral framework. Concerning the Abelian case, the equivalence between the massive Thirring and the sine-Gordon models is rederived in a very simple way by making a chiral change in the fermionic path-integral variables. The massive Schwinger model is also studied using the same technique. The extension of this bosonization approach to the solution of non-Abelian models is performed in a very natural way, showing the appearance of the Wess-Zumino functional through the Jacobian associated with the non-Abelian chiral change of variables. Relevant features of massless two-dimensional QCD are discussed in this context.

Bosonization of fermion currents in two-dimensional quantum chromodynamics

Bosonization rules for fermion currents in QCD 2 are constructed using a very simple approach within the path-integral framework, based on the existence of a gauge condition in which fermions can be decoupled.

Chiral anomaly and the Wess-Zumino condition.

The connection between the Wess-Zumino condition and the chiral anomaly is discussed in the path-integral framework. When the non-Abelian anomaly exists, the Dirac operator detDLSL can be specified in various ways. The different specifications of detDLSL in the path integral lead to different forms of Ward-Takahashi identities and to different definitions of composite current operators involved. The Wess-Zumino condition imposes the generalized Bose symmetry among the gauge vertices, and thus it introduces a particular definition of current operators. For example, the axial-vector hypercharge current of an SU(3) theory, which is constructed to be consistent with the Wess-Zumino condition and global chiral symmetry, may be reduced to a U(1) current of the SU(2) subtheory; this particular construction of the U(1) current, however, does not satisfy the Atiyah-Singer index theorem expected for the SU(2) theory. We also discuss a semiperturbative regularization which automatically gives the non-Abelian anomaly for chiral fermions in the presence of electroweak fields.

Perturbation expansions for the transport quantities of dilute polymer solutions

The dynamics of a single polymer chain in solution is formulated in the framework of path integrals. The method enables one to obtain the perturbation expansions of the transport quantities in power of the excluded volume and the hydrodynamic interactions. The inelastic scattering function and the diffusion coefficient are considered in the first-order perturbation theory.

Path-integral derivation of the chiral anomalies of Dirac fermions coupled to gauge and gravitational fields in even space-time dimensions

The anomalies associated with chiral rotations of Dirac fermions coupled to vector gauge fields in a curved space of arbitrary even dimension are derived within the path-integral framework. Special cases of the general formula agree with all results previously obtained.

The formulation of spontaneous breakdown in the path-integral method

We examine the problem of formulating spontaneous breakdown of symmetries in the path-integral framework; since different solutions of the field equations correspond to different boundary conditions, the possibility of different boundary conditions must be incorporated in the generating functional itself. We propose a modification of the generating functional that provides the required flexibility that can lead to different solutions. We apply our formalism to a model of scalar complex fields with invariance under phase transformations of the first kind and derive Ward-Takahashi identities and the Goldstone theorem.