Olaf Holm: Quantum mechanics via cohomology and factorization algebras

Abstract

I introduce a reformulation of the quantum mechanics of the harmonic oscillator and the spin-1/2 system in terms of the cohomology of Batalin-Vilkovisky (BV) algebras and factorization algebras, following a program by Costello and Gwilliam. This formulation is `off-shell’ in that it is based on classical off-shell configurations and thus similar to the path integral. There is a quasi-isomorphism to the canonical formulation of quantum mechanics, viewed as a factorization algebra.