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Results tagged with mp.mathematical-physics
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user 402
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
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 …
- 37.8k
10
votes
Accepted
Supermanifolds — elementary introduction?
There is a short elementary survey by Hohnhold, Stolz, and Teichner:
Super manifolds: an incomplete survey.
- 37.8k
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 …
- 37.8k
6
votes
Translation of an article
Download the PDF file of the original article here: http://www.mathnet.ru/php/getFT.phtml?jrnid=im&paperid=3076&volume=29&year=1965&issue=4&fpage=835&what=fullt&option_lang=eng
and apply Google Transl …
- 37.8k
6
votes
Group cohomology version of Deligne-Beilinson cohomology
The nth Deligne cohomology is defined as cohomology with coefficients
in a truncated chain complex of sheaves of U(1)-valued differential forms:
U(1)→Ω^1→Ω^2→⋯→Ω^n for some n≥0.
Thus starting with an …
- 37.8k
5
votes
1d TQFT minus connection =?
Going into more detail (and consequently making more and more mistakes), a vector bundle with connection allows to assign to a point the fibre over that point, and to a path the monodromy (or holon …
- 37.8k
4
votes
Categorifying the definition of a principal $G$ bundle
A modern presentation that fully covers the indicated cases can be found in the work of Nikolaus–Schreiber–Stevenson:
Principal ∞-bundles – General theory.
Principal ∞-bundles – Presentations.
In …
- 37.8k
3
votes
Accepted
Connection on a Hilbert bundle
This is an answer to the refined question formulated in the comments:
the base space is the unitary dual of a Lie group $G$.
The definition can be carried out in the setting of stacks in groupoids (or …
- 37.8k
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 …
- 37.8k