$A_{\infty }$ perspective to Sen's formalism

Abstract

Sen's formalism is a mechanism for eliminating constraints on the dynamical fields that are imposed independently from equations of motion by employing spurious free fields. In this note a cyclic homotopy associative algebra underlying Sen's formalism is developed. The novelty lies in the construction of a symplectic form and cyclic $A_{\infty }$ maps on an extended algebra that combines the dynamical and spurious fields. This algebraic presentation makes the gauge invariance of theories using Sen's formulation manifest.

15 pages; v2: journal version

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