$A_\infty$ perspective to Sen's formalism

TL;DR

This paper develops an $A_ abla$-algebraic framework for Sen's formalism, revealing its underlying cyclic homotopy associative algebra structure, which clarifies gauge invariance and extends the algebraic understanding of the formalism.

Contribution

It introduces a cyclic $A_ abla$-algebra structure on an extended algebra combining dynamical and spurious fields, providing a new algebraic perspective on Sen's formalism.

Findings

Constructed a symplectic form on the extended algebra.

Defined cyclic $A_ abla$-maps that encode gauge invariance.

Made the gauge invariance of Sen's formalism manifest through algebraic structure.

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.