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Results tagged with mp.mathematical-physics
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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.
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 …
- 10.5k
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
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
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 …
- 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 …
- 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 …
- 10.5k
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 …
- 10.5k
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
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 …
- 10.5k
8
votes
3
answers
603
views
Physical Applications of Locally Symmetric Spaces
Locally Symmetric Spaces are the basis of the Langlands program—a set of ambitious and interconnected conjectures connecting representation theory to number theory, firstly proposed in 1967 by Robert …
- 10.5k
11
votes
0
answers
1k
views
Yang-Mills theory with non-compact gauge groups G
Physicists are familiar working with Yang-Mills theory with compact and semi-simple gauge groups $G$ (Lie groups).
However, it is not entirely clear the formulation of Yang-Mills theory with non-comp …
- 10.5k
5
votes
0
answers
122
views
GSO projection and $H^d(M, \mathbb{Z}_2)$
This follows up the comment which suggests that asking the later 2nd part of subquestion in "GSO (Gliozzi-Scherk-Olive) projection and its Mathematics" as a new different question
GSO (Gliozzi-Scherk- …
- 10.5k
7
votes
0
answers
238
views
GSO (Gliozzi-Scherk-Olive) projection and its Mathematics?
GSO (Gliozzi-Scherk-Olive) projection is an ingredient used in constructing a consistent model in superstring theory. The projection is a selection of a subset of possible vertex operators in the worl …
- 10.5k
3
votes
0
answers
167
views
Holomorphic map, Instantons of Complex Projective Space and Loop Group
It seems that holomorphic (or rational) maps play a crucial role to relate the following data:
Instanton in 1-dimensional complex Projective Space $$\mathbb{P}^1$$
in a 2 dimensional (2d) spacetime. …
- 10.5k
5
votes
0
answers
448
views
Chern-Simons theory with non-compact gauge groups G
This is related to a previous question, where a nonlinear σ model (NLSM) describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. There we ask the general …
- 10.5k