# CLASSICAL CHERN-SIMONS THEORY, PART 2

@inproceedings{Freed1992CLASSICALCT, title={CLASSICAL CHERN-SIMONS THEORY, PART 2}, author={Daniel S. Freed}, year={1992} }

There is a large mathematical literature on classical mechanics and field theory, especially on the relationship to symplectic geometry. One might think that the classical Chern-Simons theory, which is topological and so has vanishing hamiltonian, is completely trivial. However, this theory exhibits interesting geometry that is usually absent from ordinary field theories. (The same is true on the quantum level; topological quantum field theories exhibit geometric properties not usually seen in…

## 92 Citations

Classical Chern-simons Theory, Part 2

- Mathematics
- 1993

Connections in fiber bundles, particularly in principal bundles, appear in many parts of differential geometry. For example, the basic invariant of a Riemannian metric—the Riemann curvature tensor—is…

Topological Quantum Field Theories from Compact Lie Groups

- Mathematics
- 2009

It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in…

Lectures on Topological Quantum Field Theory

- Physics
- 1993

What follows are lecture notes about Topological Quantum Field Theory. While the lectures were aimed at physicists, the content is highly mathematical in its style and motivation. The subject of…

A Higher Stacky Perspective on Chern–Simons Theory

- Physics
- 2015

The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern–Simons-type gauge field theories. We explain in some detail how…

Classical Chern-Simons on manifolds with spin structure

- Mathematics
- 2005

We construct a 2+1 dimensional classical gauge theory on manifolds with spin structure whose action is a refinement of the Atiyah-Patodi- Singer eta-invariant for twisted Dirac operators. We…

Twisted Equivariant Matter

- Mathematics, Physics
- 2012

We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical threefold way of real/complex/…

v 2 8 J un 1 99 3 REVISED VERSION Higher Algebraic Structures and Quantization

- Mathematics
- 1993

Very Abstract. We derive (quasi-)quantum groups in 2+1 dimensional topological field theory directly from the classical action and the path integral. Detailed computations are carried out for the…

A higher Chern-Weil derivation of AKSZ sigma-models

- Mathematics
- 2013

Chern–Weil theory provides for each invariant polynomial on a Lie algebra 𝔤 a map from 𝔤-connections to differential cocycles whose volume holonomy is the corresponding Chern–Simons theory action…

A Chern-Simons action for noncommutative spaces in general with the example SU_q(2)

- Mathematics
- 2012

Witten constructed a topological quantum field theory with the Chern-Simons action as Lagrangian. We define a Chern-Simons action for 3-dimensional spectral triples. We prove gauge invariance of the…

Dirac Charge Quantization and Generalized Differential Cohomology

- Mathematics
- 2000

The main new result here is the cancellation of global anomalies in the Type I superstring, with and without D-branes. Our argument here depends on a precise interpretation of the 2-form abelian…

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