**Title:** Variational calculus in the Batalin-Vilkovisky formalism and general covariance

**Speaker:** Ezra Getzler

**Speaker Info:** Northwestern

**Brief Description:** Pre-talk at 1pm in Lunt 107

**Special Note**:

**Abstract:**

Motivated by supersymmetry, Batalin and Vilkovisky reformulated the equations governing Lagrangian mechanics in the variational calculus as a Maurer-Cartan equation (vanishing of curvature). This allowed them to arrive at a new understanding of symmetries off-shell (i.e. where the Euler-Lagrange equation does not hold).In this talk, I will show how a modification of their Maurer-Cartan equation can handle the action of the diffeomorphism group on the world-sheet (i.e. general covariance of the theory). Our approach involves the introduction of a curvature to Maurer-Cartan equation. This curvature is central (a scalar multiple of the identity matrix): this is analogous to the Berry phase in the Hamiltonian approach to quantum theory (though this is really nothing more than a formal analogy).

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