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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

21 votes
2 answers
2k views

Uncertainty principle and Cramer-Rao bound - is there relation?

Just out of curiosity. The two things sounds a little bit similar - 1) Uncertainty principle 2) Cramer-Rao bound. Saying that we cannot measure something with certain accuracy. However looking closer …
51 votes
9 answers
9k views

The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?

Starting from 80-ies the ideas either coming from physics, or by physicists themselves (e.g. Witten) are shaping many directions in mathematics. It is tempting to paraphrase E. Wigner, saying about " …
36 votes
9 answers
18k views

Why does bosonic string theory require 26 spacetime dimensions?

I do not think it is possible really believe or experimentally check (now), but all modern physical doctrines suggest that out world is NOT 4-dimensional, but higher. The least sophisticated candidat …
12 votes
2 answers
930 views

Is the quantum algebra unique (up to isomorphism) in deformation quantization ?

Consider a Poisson algebra A (i.e. commutative algebra with Poisson bracket). Let $\hat A$ be a deformation quantization of the algebra A. We know that construction of deformation quantization and mo …
14 votes
1 answer
1k views

Coherent states vs quantization of Lagrangian submanifold

Coherent states http://en.wikipedia.org/wiki/Coherent_states are vectors in the Hilbert space which in certain sense are strongly localized and "corresponds" to points in classical phase space (see be …