Abstract: Classical BV formalism can be viewed as a theory about higher (derived, stacky) geometry. However, this point of view has not been much explored in understanding field theories in Lorentzian space-time. In this talk we shall start by describing a general structure of classical and (re-)quantum BV formalism in the perturbative sense that has been tailored to incorporate the power of infinite dimensional analysis, and then use this framework to understand the Yang-Mills-Higgs sector of electroweak theory in standard model physics. One of the interesting phenomena is that the unshifted Poisson structure (Peierls structure) on the classical moduli is related to the shifted Poisson structure on the derived moduli using homological arguments over complete bornological vector spaces. Due to the hyperbolic nature of the system, the gauge-fixing needs also to be reformulated. This finally enables us to describe the Higgs mechanism. The talk is based on joint work with James Wallbridge.
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