 Topological quantum field theory

A quantum field theory assigning vector spaces to closed spatial manifolds and linear maps to interpolating spacetime cobordisms, compatibly with composition and disjoint union. Its TQFT partition function on $\Sigma \times S^1$ is the trace of the identity of the state space on $\Sigma$, hence its dimension.

Topological Quantum Field Theory (TQFT) is a branch of theoretical physics and mathematics that explores the relationships between quantum field theory and topology, a branch of mathematics that studies properties of space that are preserved under continuous transformations. ### Key Concepts of TQFT: 1. **Quantum Field Theory (QFT)**: - QFT is a framework for constructing quantum mechanical models of subatomic particles in particle physics. It combines classical field theory, special relativity, and quantum mechanics.