Search

Summary

The topological charge of smooth Yang–Mills gauge fields is discussed, describing in particular the SU(2) instanton. This leads to the Adler–Bell–Jackiw anomaly and to θ-vacuum states, which are similar to energy bands in a crystal. We finally discuss the Atiyah–Singer index theorem in the continuum and more explicitly on the lattice.

Summary

This chapter presents Feynman’s formulation of quantum mechanics, based on a path integral representation of the evolution operator. The chapter presents detailed examples which make it possible to understand clearly Feynman’s “sum over paths,” and it contains a complete discussion of how to calculate Gaussian path integrals. It also discusses the Euclidean version of the path integral, as well as Wick’s theorem and Feynman diagrams. Finally, it discusses instantons in quantum mechanics.

A spectral sequence is established whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $E_{2}$ page is a characteristic-2 version of $F_{5}$ homology in Khovanov's classification.

Search Results

Refine search

Refine search

Actions for selected content:

3 results

19 - Topology of Gauge Fields

Summary

4 - The Path Integral Formulation of Quantum Mechanics

Summary

Instantons and Bar-Natan homology

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

3 results

19 - Topology of Gauge Fields

Summary

4 - The Path Integral Formulation of Quantum Mechanics

Summary

Instantons and Bar-Natan homology