Orthogonal functions applied to data representation in binary-alloy thermodynamics

Detailed examples are used to consider the advantages of orthogonal Legendre polynomials in describing the concentration dependence for thermodynamic functions, particularly enthalpies of mixing in two-component systems. The study relates to processing and storing information in thermodynamic data banks.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 2, pp. 198–203, March–April, 1987.     

General solution to the quantum master equation in the finite-dimensional case

The general solution to the quantum master equation (and its Sp(2) symmetric counterpart) is explicity constructed in the case of a finite number of variables. It is shown that the finite-dimensional solution is physically trivial and, therefore, cannot be directly extended to a local field theory. Thus, the locality condition is important in obtaining nontrivial physical results when quantizing gauge field theories in the field-antifield formalism. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 114. No. 2, pp. 250–270, February 1998.     

Invariant realization of functional integration over a local gauge group

An invariant functional formulation of the nonlinear chiral theories as well as of their generalizations is developed. To guarantee the manifest invariance of the generating functional under different choices of the local coordinates in the inner space (parametrization) new variables are utilized which are the left side of the classical equations of motions (with or without the source). In terms of the new variables an invariant regularization is introduced and an invariant perturbation theory is developed.     

Multiplicative Renormalizability of Yang-Mills Theory with the Background Field Method in the BV Formalism

Theoretical and Mathematical Physics - Studying the gauge-invariant renormalizability of four-dimensional Yang-Mills theory using the background field method and the BV formalism, we derive a...     

Superfield generating equation of field–antifield formalism as a hyper-gauge theory

Within a superfield approach, we formulate a simple quantum generating equation of the field–antifield formalism. Then we derive the Schroedinger equation with the Hamiltonian whose \(\Delta \)-exact part serves as a generator to the quantum master transformations. We show that these generators do satisfy a nice composition law in terms of the quantum antibrackets. We also present an Sp(2) symmetric extension to the main construction, with specific features caused by the principal fact that all basic equations become Sp(2) vector-valued ones.     

Reducible gauge algebra of BRST-invariant constraints

We show that it is possible to formulate the most general first-class gauge algebra of the operator formalism by only using BRST-invariant constraints. In particular, we extend a previous construction for irreducible gauge algebras to the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd, mutually anti-commuting BRST operators that bear structural similarities with BRST/anti-BRST theories but with shifted ghost number assignments. In both cases we show how the extended BRST algebra can be encoded into an operator master equation. A unitarizing Hamiltonian that respects the two BRST symmetries is constructed with the help of a gauge-fixing boson. Abelian reducible theories are shown explicitly in full detail, while non-Abelian theories are worked out for the lowest reducibility stages and ghost momentum ranks.