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Results tagged with mp.mathematical-physics
Search options questions only
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user 27004
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
15
votes
1
answer
1k
views
Borel-Écalle re-summation and resurgence: criteria and results
This is about the theory of Borel-Écalle re-summation and resurgence, see Refs below.
This states that the perturbative series (say of the vacuum expectation value of an operator $\mathcal{O}$ in quan …
CommunityBot
- 1
21
votes
2
answers
912
views
Define the 3d Chern-Simons TQFT on a discrete simplicial complex
Question: What is the challenge and the current status to define the 3d Chern-Simons(-Witten) (CSW) theory on a simplicial complex or on a discrete lattice? (Or is there a no-go or an obstruction behi …
- 5,984
11
votes
3
answers
1k
views
Navier-Stokes fluid dynamics, Einstein gravity and holography
There was some activity a while ago, like 10 years ago, string theoreists try to relate
the fluid dynamics, for example, governed by Navier-Stokes equation,
to
the Einstein gravity, and its re …
- 1
6
votes
0
answers
501
views
Yang–Mills existence and mass gap official statement on Euclidean $\mathbb{R}^4$, why not Mi...
Yang–Mills existence and mass gap problem is officially stated by Clay Mathematics Institute:
Yang–Mills Existence and Mass Gap.'' Prove that for any compact simple gauge group G, a non-trivial quant …
CommunityBot
- 1
12
votes
1
answer
1k
views
Coleman–Mandula theorem and a mathematical proof
Coleman–Mandula theorem (by Sidney Coleman and Jeffrey Mandula) [1] is a no-go theorem in theoretical physics. It states that "space-time and internal symmetries cannot be combined in any but a trivia …
- 2,821
14
votes
0
answers
974
views
Witten zeta function v.s. Riemann zeta function
From a talk, we learned that
The symplectic volume of the space $M$ of gauge equivalence classes of flat G connections is given by the “Witten zeta function”:
where we sum over irreducible repres …
- 223
10
votes
3
answers
611
views
Group cohomology version of Deligne-Beilinson cohomology
I appreciate Deligne-Beilinson cohomology as a topological cohomology generalization of de Rham cohomology, which concerns the topological structure of manifolds.
On the other hand, we know that ther …
- 4,519
2
votes
0
answers
293
views
Maxwell $U(1)$ gauge theory's electric and magnetic sources turned on simultaneously in the ...
Question:
How do we couple $U(1)$ electric (E) and magnetic (M) sources simultaneously in the classical differential geometry language, in a $U(1)$ gauge theory based on $U(1)$ gauge bundle and its $U …
- 10.5k
6
votes
1
answer
465
views
$T\bar{T}$ deformation: Stress-energy momentum tensor deformed in CFT and in QFT for various...
The $T\bar{T}$ deformation is based on the original work of Zamolochikov [1] explored deformations of two-dimensional conformal field
theories (CFT) by an operator that is quadratic in the stress-ener …
- 11
3
votes
0
answers
144
views
$e^{2\pi ic_{-}/8}$ and $e^{2\pi ic_{-}/24}$ in unitary modular category (UMC)
Background
Unitary modular categories (UMC) do not capture the central charge $c_{-}$ of the topological quantum field theory (TQFT). However, there is a relation that fixes,
$c_{-}\bmod
8$:
\begin{e …
- 10.5k
11
votes
1
answer
2k
views
Vafa-Witten invariants for mathematicians
As Richard Thomas has written (we paraphrase just slightly), mathematical physicists Vafa and Witten introduced new "invariants" of four-dimensional spaces in a paper:
A Strong Coupling Test of S-Du …
CommunityBot
- 1
3
votes
1
answer
249
views
Supersymmetry charge $Q$ as anti-linear and anti-unitary operator
We know the supersymmetry (SUSY) charge $Q$ satisfies the following relation respect to fermion parity operator $(-1)^F$:
$$
(-1)^F Q + Q (-1)^F :=\{Q, (-1)^F \} =0
$$
which defines the anti-commutat …
- 63.9k
17
votes
2
answers
2k
views
Mathematical/Physical uses of $SO(8)$ and Spin(8) triality
Triality is a relationship among three vector spaces. It describes those special features of the Dynkin diagram D4 and the associated Lie group Spin(8), the double cover of 8-dimensional rotation grou …
CommunityBot
- 1
18
votes
0
answers
1k
views
Number Theory and Gravity
Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by Robert Langlands at IAS (1967, 1970), it seeks to relate Galois …
CommunityBot
- 1
5
votes
0
answers
394
views
Yang-Mills theory v.s. Kaluza–Klein theory: Classical actions
In general Yang-Mills theory [1] seems to be different from the dimensional reduced Kaluza–Klein theory.
However, the historical account was that people tried to trace back the origin of non-Abelian …
- 10.5k