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Speaker:
Stephan Stolz
Affiliation:
University of Notre Dame
Date:
Thu, 23/05/2024 - 12:00 - 13:30
Location:
MPIM Lecture Hall
Parent event:
Physical Math Seminar Costello and Gwilliam developed a systematic approach to perturbative quantization of field theories that describes classical and quantum observables as factorization algebras on the space-time manifold. In the simple case of the linear sigma model whose fields are smooth maps from the real line to an inner product space (aka the free boson), the algebra of quantum observables is the Weyl algebra of differential operators on . For the free fermion, where is replaced by its odd analog, the algebra of quantum observables is the Clifford algebra generated by .
In this talk, based on joint work with Bill Dwyer, I will discuss how to enhance the free fermion by suitable boundary conditions to obtain a factorization algebra of “bulk-boundary quantum observables”, which can be evaluated on open intervals as well as half-open intervals. The challenge is that there is a space of boundary conditions, each of which yields a bulk-boundary factorization algebra, but unlike for the free boson (where there are Dirichlet and Neumann boundary conditions), there is no distinguished boundary condition. Our main result is that a spin structure on yields a distinguished bulk-boundary factorization algebra of quantum observables.
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