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6h
comment References for Yang-Mills Theory
Are you referring to the classical Yang-Mills theory or to the quantum Yang-Mills theory (or both)?
Apr
24
asked Symplectic invariance of Hodge numbers?
Apr
17
awarded  Necromancer
Apr
17
awarded  Self-Learner
Apr
17
answered In Gromov-Witten theory, why is the string coupling constant weighted by $2g-2$?
Apr
17
awarded  Revival
Apr
17
answered Why is the CM closure of $\mathbb{Q}$ the “ultimate” coefficient field for motives?
Apr
9
awarded  Enthusiast
Mar
27
revised Semisimplicity of Frobenius operation on etale cohomology?
added 7 characters in body
Mar
26
asked Smoothness of the “Archimedean special fiber” in Arakelov geometry
Mar
9
reviewed Approve Counting lattice points inside a three-dimensional ellipsoid
Jan
23
awarded  Custodian
Jan
23
comment Why $M \times S^1 $ becomes a manifold with G_2 structure, when $M$ is CY?
As suggested by Igor Belegradek, this is essentially obvious if one uses the correct definition of $G_2$. To give a useful answer one should know which definition of $G_2$ you are starting with.
Dec
30
comment Why should affine lie algebras and quantum groups have equivalent representation theories?
Related: mathoverflow.net/questions/178113/… The "natural" relation indeed involves $k$ positive integer and integrable representations but the proof uses the theorem of Kazhdan-Lusztig via a relation between level $k-h$ and $-k-h$ due to Finkelberg (-k<0 so one can applies Kazhdan-Lusztig).
Dec
28
comment Number theory and physics
From a mathematical point of view this story is related to the non-commutative tori and so to the various ways to "go at infinity" in the moduli space of elliptic curves.
Dec
28
comment Number theory and physics
from a circle of ideas which are only partly mathematically well founded, which have been developed by physicists and which have evolved continuously from a "real" physics problem along an often complicated history.
Dec
28
comment Number theory and physics
This question seems to partly relies on the difference between "real" and "unreal" physics. I don't think that a mathematician should care about what is "real" in physics. When someone says "the motivation comes from physics", he probably means theoretical physics and it is maybe what "unrealistic physics" is. But the fact that the part of theoretical physics in question is "real" or not, which probably means "directly related to the experience", is irrelevant from the mathematician point of view. In general, "come from physics" does not mean "come from a precise experimental fact" but come...
Dec
17
answered Derived categories of arithmetic schemes?
Dec
11
comment Does quantum mechanics ever really quantize classical mechanics?
... the space of classical states (which is not a vector space)
Dec
11
comment Does quantum mechanics ever really quantize classical mechanics?
It seems to me that there is a confusion between states and observables in this question. The analogue of the classical $\frac{d}{dt}\rho = \{H,\rho\}$, where $\rho$ is a function on the phase space, so a classical observable, is $\frac{d}{dt}A=[H,A]$ where $A$ is an operator acting on the space of states, i.e. a quantum observable. The algebra of quantum observables is indeed a deformation of the algebra of classical observables but I don't know what "relevant representations" means. The algebra of quantum algebra acts on the space of quantum states but the classical algebra does not act on..