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Questions tagged [mp.mathematical-physics]

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

2124 questions
82
votes
8 answers

What is the motivation for a vertex algebra?

The mathematical definition of a vertex algebra can be found here: http://en.wikipedia.org/wiki/Vertex_operator_algebra Historically, this object arose as an axiomatization of "vertex operators" in "conformal field theory" from physics; I don't know…
user332
  • 3,878
40
votes
10 answers

Examples of non-rigorous but efficient mathematical methods in physics

There are situations of applications of mathematics in physics which seem to work well enough for physicists (for example they agree with the experimental data) but are considered unacceptable or at least non-rigorous to mathematicians Please help…
Cristi Stoica
  • 4,304
29
votes
8 answers

In what ways is physical intuition about mathematical objects non-rigorous?

I'm asking this question as a mathematician who is very far removed from the Physics world, and has little to no knowledge of what math goes into it, and what math comes out of it. What I do hear is that people have "physical intuition" about…
James D. Taylor
  • 6,178
26
votes
3 answers

The specificity of dimension $1+3$ for the real world

I have been asked sometimes, and I ask myself, to what extent the dimension $1+3$ is important for our real world, say compared to an hypothetical $(1+d)$-dimensional world. I have two answers in mind. The Huygens principle. If you switch off a…
Denis Serre
  • 51,599
24
votes
1 answer

Statement of Millenium Problem: Yang-Mills Theory and Mass Gap

I'm wondering what the statement is that one has to prove for the Millenium Problem "Quantum Yang-Mills Theory". According to the official article, it is required to show that for every simple Lie group G there exists a YM quantum field theory for G…
Florian
  • 2,210
15
votes
2 answers

Geometric Quantization

I'm curious about geometric quantization. Of course, I know the procedure: Start with a classical phase space $T^{*}X$, $X$ is the configuration space, then do prequantization by creating a prequantum (complex) line bundle (of course, the symplectic…
user62675
14
votes
2 answers

Questions from Chern-Simons theory

I am currently reading an article about TFTs (DW - Group Cohomology and TFTs), and I have a few questions: (1) Let $M$ be a 3-man., then we know there exists some 4-man. $B$ such that $\partial B = M$. Now, let $E$ be a $G$-bundle over $M$, when…
Kevin Wray
  • 1,689
12
votes
7 answers

A good primer for geometric quantization.

Hello everyone: I'm searching for a good primer on geometric quantization. I found the following: Mathematical foundations of geometric quantization (A. Echeverria-Enriquez, et al.) Symplectic geometry and geometric quantization (M. Blau) Geometric…
Sadiq Ahmed
  • 121
11
votes
2 answers

Review of Tim Maudlin's New Foundations for Physical Geometry

Tim Maudlin, a philosopher of science at NYU, has a book out called: New Foundations for Physical Geometry: The Theory of Linear Structures. The section on about the book says the following: Topology is the mathematical study of the most basic…
user53046
  • 119
10
votes
4 answers

Witten's QFT and Jones Poly paper

Data: $M$ is an oriented 3-dim manifold, $E$ is a $G$-bundle over $M$, with $G$ compact simple Lie group. Question: How does $\pi_3(G)\cong \mathbb{Z}$ imply that there exists non-trivial gauge transformations (i.e., continuous maps $M\rightarrow…
Kevin Wray
  • 1,689
10
votes
1 answer

Is there a proof of the Hawking bound for the efficiency of a black holes merger?

Consider two black holes with masses $m_1,m_2$ and zero angular momenta merging to form a single one with the mass $m$ and the rotation parameter $a=J/m$. Hawking, in "Black Holes in General Relativity" Commun. math. Phys. 25 (1972), 152—166…
Alex Gavrilov
  • 6,851
9
votes
3 answers

Existence of connections on principal bundles

Is it always true that a principal $G$-bundle $E$ admits a connection (on the total space, not a local connection on the base manifold $M$)? I know that it must be true, since almost every construction starts off with ...fix a connection on $E$...,…
Kevin Wray
  • 1,689
9
votes
1 answer

Rigorous scaling limit for Navier-Stokes and Boltzmann equation

In the now 35 years old survey paper ''Kinetic equations from Hamiltonian dynamics'', Herbert Spohn mentions two important unsolved problems in mathematical physics: On p.571 the hydrodynamic limit, and on p.603 the derivation of the nonlinear…
Arnold Neumaier
  • 3,771
9
votes
4 answers

Anderson localization - an embarassment of riches

I am looking for a good, not too technical discussion of Anderson Localization, and some explanation of why it exists. Googling "Anderson Localization" produces an infinite number of possibilities, so perhaps someone knowledgeable can recommend…
Igor Rivin
  • 95,560
7
votes
4 answers

Applications of classical field theory

What are the applications (physical and mathematical) of classical field theory beyond electrodynamics and gravity? By such applications, I mean that either the field theory viewpoint adds some genuinely new insight into the underlying physics or…
Michal Kotowski
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