Abstract
We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.
Highlights
Solving the different problems in classical and quantum descriptions of the gauge systems
In this paper we will use the anticanonical transformations to find out the general solution to classical master equation that allows the construction of an arbitrary gauge-invariant deformation of a given gauge theory
We briefly describe the basic notions of the BV-formalism which will be essentially used in the paper to describe a general gauge-invariant deformation of the classical gauge theory
Summary
We briefly describe the basic notions of the BV-formalism which will be essentially used in the paper to describe a general gauge-invariant deformation of the classical gauge theory. Taking into account the gauge invariance of the initial action (2.1) and the boundary condition (2.7), one can write the action S = S[φ, φ∗] up to the terms linear in antifields in the form. It leads to the statement that any of the two solutions of classical master equation (2.6), satisfying the same boundary condition (2.7), are related one to another by some anticanonical transformation [1, 2].4. Taking some solution of the classical master equation satisfying the given boundary condition and using an arbitrary anticanonical transformation in this solution, we will get again a solution of the classical master equation This fact will be used to construct a gauge-invariant deformation of the gauge theories. We suppose that for the problem under consideration, the description of anticanonical transformations with the help of generating functional seems to be more preferable
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