Narrow Results

The analysis of the equivalence between the Hamiltonian and Lagrangian formalisms, for a sp(2) BRST theory, is achieved. The proof of this equivalence, apart from its intrinsic importance, allows the explanation of some results which seem artificially implanted in the theory: the structure of the extended spaces, and the form of the master equation. As a new image on the BRST operator, this paper suggests that its action can be split into a canonical part and a noncanonical part.

The Euclidean space, obtained by the analytical continuation of time, to an imaginary time, is used to model thermal systems. In this work, it is taken a step further to systems with spatial thermal variation, by developing an equivalence between the spatial variation of temperature in a thermal bath and the curvature of the Euclidean space. The variation in temperature is recast as a variation in the metric, leading to a curved Euclidean space. The equivalence is substantiated by analyzing the Polyakov loop, the partition function and the periodicity of the correlation function. The bulk thermodynamic properties like the energy, entropy and the Helmholtz free energy are calculated from the partition function, for small metric perturbations, for a neutral scalar field. The Dirac equation for an external Dirac spinor, traversing a thermal bath with spatial thermal gradients, is solved in the curved Euclidean space. The fundamental behavior exhibited by the Dirac spinor eigenstate, may provide a possible mechanism to validate the theory, at a more basal level, than examining only bulk thermodynamic properties. Furthermore, in order to verify the equivalence at the level of classical mechanics, the geodesic equation is analyzed in a classical backdrop. The mathematical apparatus is borrowed from the physics of quantum theory in a gravity-induced space–time curvature. As spatial thermal variations are obtainable at quantum chromodynamic or quantum electrodynamic energies, it may be feasible for the proposed formulation to be validated experimentally.