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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.
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
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
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
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
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
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
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
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