Glasnik Matematicki, Vol. 55, No. 1 (2020), 67-83.

ON THE FAITHFULNESS OF 1-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES

Sonja Telebaković Onić

Faculty of Mathematics, Studentski trg 16, 11 000 Belgrade, Serbia
e-mail: sonjat@matf.bg.ac.rs

Abstract.   This paper explores 1-dimensional topological quantum field theories. We separately deal with strict and strong 1-dimensional topological quantum field theories. The strict one is regarded as a symmetric monoidal functor between the category of 1-cobordisms and the category of matrices, and the strong one is a symmetric monoidal functor between the category of 1-cobordisms and the category of finite dimensional vector spaces. It has been proved that both strict and strong 1-dimensional topological quantum field theories are faithful.

2010 Mathematics Subject Classification.   15A69, 15B34, 18M05, 57R56

Key words and phrases.   Symmetric monoidal category, oriented manifold, cobordism, topological quantum field theory, Brauerian representation, Kronecker product, commutation matrix

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https://doi.org/10.3336/gm.55.1.06

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