Examples of physical interpretations of pieces of mathematics.
the orbit method – the representation theory of compact Lie groups is equivalently the quantum mechanics of certain topological particles (1d Wilson line TQFT).
Morse theory is naturally interpreted as the study of the supersymmetric vacua in supersymmetric quantum mechanics (which in turn exists on more general abstract grounds). the Morse function is interpreted as a “superpotential” for a bispinorial quantum particle propagating on the given manifold.
Equivariant elliptic cohomology in QFT, nLab
Functoriality as global equivariance, comment
Witten (pdf):
Quantum field theory and String Theory contain many mathematical secrets. I believe that they will play an important role in mathematics for a long time. For various technical reasons, these subjects are difficult to grapple with mathematically. Until the mathematical world is able to overcome some of these technical difficulties and to grapple with quantum fields and strings per se, and not only with their implications for better-established areas of mathematics, physicists working in these areas will continue to be able to surprise the mathematical world with interesting and surprising insights.
Last revised on October 29, 2016 at 11:54:45. See the history of this page for a list of all contributions to it.