Construction of Some Topological Quantum Field Theories

一些拓樸場論之構造

李育浚(Yu-Jun Li)

指導教授 ： 鄭志豪

國立清華大學/理學院/數學系/碩士(2012年)

摘要

Topological Quantum Field Theory(TQFT) is an axiomatic theory of quantum field theory.
In this thesis, we start from studying the classical cobordism theory of manifolds, which serves
as the basic model for defining general TQFT, and then construct Euler TQFT and finite total
homotopy TQFT. Furthermore, we show that there is an one-to-one correspondence between
2D-TQFT and Frobenius algebras.

關鍵字

拓樸量子場論 ； 拓樸場論

並列摘要

Topological Quantum Field Theory(TQFT) is an axiomatic theory of quantum field theory.
In this thesis, we start from studying the classical cobordism theory of manifolds, which serves
as the basic model for defining general TQFT, and then construct Euler TQFT and finite total
homotopy TQFT. Furthermore, we show that there is an one-to-one correspondence between
2D-TQFT and Frobenius algebras.

並列關鍵字

Topological Quantum Field Theory

參考文獻

[1] Lowell Abrams, Two-Dimensional Topological Quantum Field Theories and Frobenius

[2] M.F. Atiyah, Topological quantum eld theories, Publ. Math. de l'IHES, 68 (1989), p.175-186.

[3] S. Axler, F.W. Gehring and K.A. Ribet, Algebraic Topology from a Homotopical Viewpoint,

Universitext, Springer-Verlag, 2002.

[4] John C. Baez and James Dolan, Higher-Dimensional Algebra and Topological Quantum Field