Smooth sets as a convenient setting for Lagrangian field theory

Abstract: In this talk, I will indicate how the sheaf topos of smooth sets serves as a sufficiently powerful and convenient context to host classical (bosonic) Lagrangian field theory. As motivation, I will recall the textbook description of variational Lagrangian field theory, and list desiderata for an ambient category in which this can rigorously be phrased. I will then explain how sheaves over Cartesian spaces naturally satisfy all the desiderata, and furthermore allow to rigorously formalize several more field theoretic concepts. Time permitting, I will indicate how the setting naturally generalizes to include the description of (perturbative) infinitesimal structure, fermionic fields, and (gauge) fields with internal symmetries. This is based on joint work with Hisham Sati.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

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Topology and Geometry Seminar (Texas, Kansas)