Hamiltonian Approach to Lagrangian Gauge Symmetries

We reconsider the problem of finding all local symmetries of a Lagrangian. Our approach is completely Hamiltonian without any reference to the associated action. We present a simple algorithm for obtaining the restrictions on the gauge parameters entering in the definition of the generator of gauge transformations.Comment: LaTex, 8 pages, Latex error correcte

Master Equation for Lagrangian Gauge Symmetries

Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily reproduced from this equation. We also discuss the connection with the purely Lagrangian approach. The general considerations are applied to the Yang-Mills theory.Comment: 14 pages, Late

Two-Dimensional Thermofield Bosonization

The main objective of this paper is to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real time formalism of Thermofield Dynamics. Formally the results parallel those of the T = 0 case. The well known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. In order to emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized.Comment: 30 pages, no figure. Submitted to Annals of Physic

Decoupled path integral formulation of chiral QCD2_2 with aJR=2a_{JR}=2

We analyse the BRST constraints and corresponding Hilbert-space structure of chiral QCD$_2$ in the decoupled formulation for the case of the Jackiw-Rajaraman parameter $a=2$. We show that despite formal similarities this theory is not equivalent to QCD$_2$, and that its extension to U(N) does not lead to an infinite vacuum degeneracy.Comment: LaTeX, 22 page

BRST Cohomology and Hilbert Spaces of Non-Abelian Models in the Decoupled Path Integral Formulation

The existence of several nilpotent Noether charges in the decoupled formulation of two-dimensional gauge theories does not imply that all of these are required to annihilate the physical states. We elucidate this matter in the context of simple quantum mechanical and field theoretical models, where the structure of the Hilbert space is known. We provide a systematic procedure for deciding which of the BRST conditions is to be imposed on the physical states in order to ensure the equivalence of the decoupled formulation to the original, coupled one.Comment: 31 pages,Late

Two-Dimensional Thermofield Bosonization II: Massive Fermions

We consider the perturbative computation of the N-point function of chiral densities of massive free fermions at finite temperature within the thermofield dynamics approach. The infinite series in the mass parameter for the N-point functions are computed in the fermionic formulation and compared with the corresponding perturbative series in the interaction parameter in the bosonized thermofield formulation. Thereby we establish in thermofield dynamics the formal equivalence of the massive free fermion theory with the sine-Gordon thermofield model for a particular value of the sine-Gordon parameter. We extend the thermofield bosonization to include the massive Thirring model.Comment: 21 pages, to be published in Annals of Physic

BFT Hamiltonian Embedding of Non-Abelian Self-Dual Model

Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin, we embed the second-class non-abelian self-dual model of P. K. Townsend et al into a gauge theory. The strongly involutive Hamiltonian and constraints are obtained as an infinite power series in the auxiliary fields. By formally summing the series we obtain a simple interpretation for the first-class Hamiltonian, constraints and observables.Comment: LaTeX, 12 Page

Gauge Invariant Variational Approach with Fermions: the Schwinger Model

We extend the gauge invariant variational approach of Phys. Rev. D52 (1995) 3719, hep-th/9408081, to theories with fermions. As the simplest example we consider the massless Schwinger model in 1+1 dimensions. We show that in this solvable model the simple variational calculation gives exact results.Comment: 14 pages, 1 figur

Metafluid dynamics and Hamilton-Jacobi formalism

Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach.Comment: 7 page

Induced Parity-Breaking Term at Finite Chemical Potential and Temparature

We exactly calculated the parity-odd term of the effective action induced by the fermions in 2+1 dimensions at finite chemical potential and finite temperature. It shows that gauge invariance is still respected. A more gerneral class of background configurations is considered. The knowledge of the reduced 1+1 determinant is required in order to draw exact conclusions about the gauge invariance of the parity-odd term in this latter case.Comment: 8 pages, LATEX, no figure