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Results tagged with mp.mathematical-physics
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user 13917
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
3
votes
Calogero-Moser system: relationship between dual variables and the KKS construction
I) Let us introduce a collective notation $z_i$, $i\in I$, for OP's $x_i$'s and $y_i$'s (which by the way do not have to be equal in numbers). Here $I$ is a finite index set. We assume that the map $z …
- 390
4
votes
Matrix integral identity
Let us first slightly generalize OP's first integral to
$$\tag{1} I(x,y,A,B)
~:=~ \int_{{\rm Mat}_{n\times n}(\mathbb{C})} \! dZ~dZ^{\dagger}
\frac{e^{-{\rm tr}(ZZ^{\dagger})}\left(xe^{{\rm tr}(ZA)}- …
- 390
15
votes
Can the equation of motion with friction be written as Euler-Lagrange equation, and does it ...
Well, there is always the trivially enforced solution
$$\tag{1} S[x,\lambda]~=~\int\! dt \sum_{i=1}^3\lambda_i(t) \left(\ddot{x}^i(t)+\alpha \dot{x}^i(t) \right),$$
where $\lambda_i(t)$ are three La …
- 390
2
votes
graded generalization of the Moyal–Weyl product
Graded generalizations of the Moyal–Weyl product must undoubtedly have been known already early-on to F.A. Berezin and his students, see e.g. Refs. 1-2.
Graded versions (where both Grassmann-even and …
- 390