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 is the trace of the identity of the state space on , hence its dimension.
The scalar assigned to a closed spacetime manifold by a topological quantum field theory. Gluing the two ends of a cylinder over a spatial manifold gives . This is the ground-state degeneracy when the state space describes the topological ground sector of a gapped system.
A topological quantum field theory TQFT partition function for a closed oriented three-manifold presented by Dehn surgery on a framed link. With normalized Kirby color on each surgery component and the convention , it is times the colored link evaluation. Here is the signature of the linking matrix and is the chiral central charge.
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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.