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Results tagged with mp.mathematical-physics
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user 2149
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
3
votes
Deriving symmetries of a Gauge theory
Unless for some reason you absolutely must work within the Hamiltonian approach, you can just directly look for the complete set of (infinitesimal Lie point) symmetries of the Euler--Lagrange equation …
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8
votes
What kind of Lagrangians can we have?
Let me comment on your second question:
When we don't know what the Lagrangian is, do we have to just guess and hope it is compatible with the dynamical equations we had already?
If you want the …
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1
vote
Examples of Poisson schemes
There is also another Kaledin's paper that you may wish to look at, Normalization of a Poisson algebra is Poisson.
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2
votes
Good references for Rigged Hilbert spaces?
The Springer online Encyclopedia of Mathematics' entry on RHS looks more rigorous albeit also more succinct than Wikipedia; for another online intro see the nlab entry. In addition to the references l …
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12
votes
Accepted
Connection between bi-Hamiltonian systems and complete integrability
Your understanding is essentially correct. There are three basic (and closely related) approaches to
constructing the integrals of motion required for complete integrability: through separation of var …
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1
vote
Homogeneous linear differential equation system with simple periodical coefficient matrix
Another thing to consider: introduce new independent variable $\tau=(1/\alpha)sin(\alpha z+\Phi_a)$. Also note that we have
$$cos(\alpha z+\Phi_b)=cos(x+\delta)$$
and
$$
cos(x+\delta)=cos(x)cos(\delta …
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3
votes
Two questions on Zuber's "KdV and W-flows"
As for $I_4$ and $I_j$ for all $j\geqslant 4$ up to overall sign factors, see e.g. equation (1.9) of these lecture notes with $u=-r$. Also you may wish to look at this link.
Regarding the bracket at …
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9
votes
Theoretical physics: Why not just $\mathbb{R}^4$?
I am not an expert but I guess there is a number of "historical" reasons explaining the lack of exploration of physical consequences of exotic differential structures:
many physicists are inclined to …
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16
votes
Accepted
What was Casimir's precise role in describing the center of the universal enveloping algebra...
At the first glance it appears that he more or less just gave the first nontrivial example(s) of what was later called the Casimir operators.
His obituary says:
On 1 May 1931 he wrote a letter from …
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4
votes
A reading list for topological quantum field theory?
A recent addition is provided by the recent text Topological Field Theory, Higher Categories, and Their Applications of Anton Kapustin
0
votes
fundamental solution of radial wave equation
If you need something more mathematical, try looking into Section 5.2 of the paper
Related Partial Differential Equations and Their Applications by L. R. Bragg and J. W. Dettman in SIAM Journal on App …
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2
votes
What is an "integrable hierarchy"? (to a mathematician)
In brief, an integrable hierarchy is an infinite (usually countable) set of integrable partial differential systems such that any two systems in this set are compatible. Such hierarchies are usually g …
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4
votes
1
answer
808
views
A name for PDE systems which are neither under- nor overdetermined?
The concepts of overdetermined and underdetermined PDE systems are well known. However, all sources I have so far looked into appear to avoid giving any name to PDE systems which are neither overdeter …
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21
votes
What is an integrable system?
The above answers deal mostly with finite-dimensional systems. As for the (systems of) PDEs, you typically need the Lax pair or a zero curvature representation (see e.g. the Takhtajan--Faddeev book me …
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