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For questions about mathematical problems arising from quantum field theory, the branch of physics which describes subatomic particles and their interactions in terms of perturbations of the corresponding scalar, vector or tensor fields.

59 votes
Accepted

How do we give mathematical meaning to 'physical dimensions'?

Mathematically, the concept of a physical dimension is expressed using one-dimensional vector spaces and their tensor products. For example, consider mass. You can add masses together and you know how …
Dmitri Pavlov's user avatar
9 votes
Accepted

Practical consequences of the geometric cobordism hypothesis

My question is: does this lead to a more-or-less explicit construction of any non-trivial quantum field theories? If so, this would be extremely interesting since only a handful of interacting quantu …
Dmitri Pavlov's user avatar
2 votes
Accepted

Path integral derivation of extended TQFT

The physics motivation for extended QFTs (and not just TQFTs) comes from the locality principle (no spooky action at a distance). The mathematical expression of locality is the descent property for ex …
Dmitri Pavlov's user avatar