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

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 $A_{\mathrm{\infty }}$ 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.