Spin Foam State Sums and Chern-Simons Theory
Aleksandar Mikovic, Joao Faria Martins
TL;DR
This paper reviews spin foam state-sum invariants of 3-manifolds, their connection to Chern-Simons theory, and explains the Chain-Mail formalism as a quantum-group regularization of BF theory path integrals.
Contribution
It elucidates the relationship between spin foam invariants, Chern-Simons theory, and the Chain-Mail formalism, providing a unified perspective on these quantum topology tools.
Findings
Clarifies the connection between spin foam invariants and Chern-Simons theory
Explains the Chain-Mail formalism as a quantum-group regularization
Links known spin network invariants to manifold invariants
Abstract
We review the spin foam state-sum invariants of 3-manifolds, and explain their relationship to manifold invariants coming from the Chern-Simons theory. We also explain the relationship between the known invariants of spin networks by using the Chain-Mail formalism of J. Roberts. This formalism can be understood as a quantum-group regularization of the BF theory path integrals.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Topological and Geometric Data Analysis