Reflection Structures and Spin Statistics in Low Dimensions

Abstract: In physics the spin of a particle determines its statistics.

Furthermore, physical systems (in Euclidean signature) usually have a reflection structure, i.e. an identification of orientation reversal with complex conjugation. Neither of these two structures is part of Atiyah's original definition of topological quantum field theories.

They can be formulated in the setting of functorial field theories as equivariant symmetric monoidal functors from a bordism category to an appropriate target. Based on the cobordism hypothesis I will present a complete classification of such functors in dimension one and two. The answers can be formulated in terms of algebraic objects associated to an internal fermionic symmetry (2-)group. The talk is based on joint work in progress with Luuk Stehouwer.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home