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References for YangMills Theory
Are you referring to the classical YangMills theory or to the quantum YangMills theory (or both)? 
Apr
24 
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Apr
17 
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Apr
17 
answered  In GromovWitten theory, why is the string coupling constant weighted by $2g2$? 
Apr
17 
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Apr
17 
answered  Why is the CM closure of $\mathbb{Q}$ the “ultimate” coefficient field for motives? 
Apr
9 
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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 
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Jan
23 
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Jan
23 
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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 
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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 KazhdanLusztig via a relation between level $kh$ and $kh$ due to Finkelberg (k<0 so one can applies KazhdanLusztig). 
Dec
28 
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Number theory and physics
From a mathematical point of view this story is related to the noncommutative tori and so to the various ways to "go at infinity" in the moduli space of elliptic curves. 
Dec
28 
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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 
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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 
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Does quantum mechanics ever really quantize classical mechanics?
... the space of classical states (which is not a vector space) 
Dec
11 
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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.. 