# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

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### Confusion with Virtual Displacement

I have just been introduced to the notion of virtual displacement and I am quite confused. My professor simply defined a virtual displacement as an infinitesimal displacement that occurs ...
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### How to do the classification of Yangian invariant?

From Nima's paper:Scattering Amplitudes and the Positive Grassmannian arxiv:1212.5605 page91, we can see that there is a complete classification for $k=2$ Yangian inariants. But I have two questions ...
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### Commutator of rotation matrices

How do you compute the commutator of rotation matrices in two different directions by different angles? Let $R_{x}(\alpha)$ be the rotation matrix about the $x$-axis and $R_{z}(\beta)$ be the ...
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### Dervie a lagrangian formulation from an eulerian One

in the solidification of a binary alloy : X18%Y . where the nominal concentration of Y in the alloy phase is 18% , the goal is to determine the variation of < C> ;the average concentration over ...
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### Why isn't the Segal-Bargmann space used more often in Quantum Mechanics?

The Stone-von Neumann Theorem states that a Hilbert space on which is defined an irreducible set of operators which satisfy the exponentiated canonical commutation relations is unitarily equivalent to ...
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### Why do we need conformal compactification to define the global conformal group?

First I have the definition of a conformal map. Let $(M,g)$ and $(M',g')$ be two pseudo-Riemannian manifolds of same dimension. Let $U\subset M$ and $V\subset M'$, we say that a smooth map of maximal ...
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### Solution for inverse square potential in $d=3$ spatial dimensions in quantum mechanics [duplicate]

Can a particle in an inverse square potential $$V(r)=-1/r^{2}$$ in $d=3$ spatial dimensions be solved exactly? Also please explain me the physical significance of this potential in comparison with ...
### The mathematical structure of $\widehat{su(2)}_k$
Some of my colleagues work on CFT's and quantum groups and I hear them talk a lot about $\widehat{su(2)}_k$ algebras. According to them (and the general physics literature) these are what ...