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Results tagged with mp.mathematical-physics
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user 10475
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
111
votes
Accepted
Does Physics need non-analytic smooth functions?
As a physicist "in nature" perhaps I can give a few examples that illustrate how non-analytic functions
can appear in physics and counter the idea that physicists do not worry about the justification
…
- 5,546
41
votes
Examples of non-rigorous but efficient mathematical methods in physics
Perhaps it would not be out of place to quote Miles Reid's Bourbaki seminar on the
McKay correspondence here:
"The physicists want to do path integrals, that is, they want to integrate
some "Action M …
40
votes
Mathematician trying to learn string theory
Many string theorists would like to know more algebraic geometry. There are a few of us who know algebraic geometry at a pretty high level (not me) but many more who would like to learn more and feel …
20
votes
What makes four dimensions special?
$4=11-7$ and $11$ is the maximal dimension for supersymmetry with spins $\le 2$ while $7$
is the first dimension in which there exist compact manifolds of exceptional holonomy.
19
votes
What is the motivation for a vertex algebra?
The answers here have focused on the mathematical aspects of VOAs and the motivation coming from QFT, the specialization to Conformal Field Theory, and then the further specialization to two-dimension …
- 5,546
14
votes
String theory "computation" for math undergrad audience
I agree that computing partition functions has many pretty applications.
My favorite is the use of Jacobi's abstruse identity between theta functions,
$\theta_3^4-\theta_4^4=\theta_2^4$, to show the …
- 5,546
10
votes
Accepted
The use of Hall algebras in physics
In supersymmetric field theories and string theories there are special states called BPS
states which are annihilated by some of the supercharges and whose mass is determined
in terms of their charges …
- 5,546
9
votes
Accepted
Dimensional regularization in odd dimensions
There a number of papers by Alain Connes on Dimensional Regularization (Dim Reg) in the context of noncommutative field theory. Some of his papers cite
P. Breitenlohner and D. Maison, "Dimensional re …
- 5,546
9
votes
What do correlation functions compute in CFT?
I'm not sure exactly what kind of information you want, and CFT is an enormous subject, but here is some information
on the physical interpretation of the complex coordinates and correlation functions …
- 5,546
8
votes
mirror symmetry with algebraic geometry?
Part of the physics motivation for mirror symmetry involves properties of the chiral ring
of N=2 superconformal field theories. Some of these have a description in terms of the polynomials appearing i …
- 5,546
8
votes
Is there a relation between 4-dimensional general relativity and exotic smooth structures on...
Regarding the first part of this question, in four spacetime dimensions there are no known generic violations of the cosmic censorship hypothesis while above four dimensions there is good evidence tha …
- 5,546
8
votes
Number theory and physics
The rational numbers $\mathbb{Q}$ are central to number theory, so I think it would be reasonable to claim a connection between number theory and ``real” physics if there were a physical system with p …
- 5,546
7
votes
The proof that a vertex algebra can lead to a Wightman QFT
You might find "An Introduction to Conformal Field Theory" by M. Gaberdiel (arXiv:hep-th/9910156v2) useful. He has a brief discussion of how in some cases chiral algebras can be assembled into Conform …
- 5,546
7
votes
Accepted
Relation between TQFT and Wilson lines, boundary conditions, surface defects etc
Greg Moore recently gave the Felix Klein lectures and a draft of notes for his lectures is available at
http://www.physics.rutgers.edu/~gmoore/FelixKleinLectureNotes.pdf
You will find in the first …
- 5,546
6
votes
Higgs mechanism from a deformation quantization point of view
The Higgs mechanism in the Standard Model doesn't have much to do with deformation quantization as other people have explained. However there is a version of the Higgs mechanism in string theory which …
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