Physics Stack Exchange
Physics Stack Exchange

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.

Mathematical physics is the application of mathematics to problems in physics and mathematical methods suitable for such applications, e.g., partial differential equations (PDEs), functional analysis, variational calculus, and potential theory. It also includes the study of problems inspired by physics within a mathematically rigorous framework, such as rigorous derivation of an atomic energy spectrum, rigorous construction of a quantum field theoretic model, and rigorous description of a phase transition.

Do not use just because your question involves math!

See also Wikipedia's article on mathematical physics.

2455 questions
134
votes
1 answer

Linear sigma models and integrable systems

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I faced difficulties in penetrating the literature... I'd highly appreciate any help with the following question: My aim is to relate…
user5831
  • 1,331
127
votes
4 answers

The Role of Rigor

The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into five specific questions. Update February, 12,…
Gil Kalai
  • 2,113
123
votes
15 answers

Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?

In the time-dependent Schrodinger equation, $ H\Psi = i\hbar\frac{\partial}{\partial t}\Psi,$ the Hamiltonian operator is given by $$\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V.$$ Why can't we consider $\displaystyle…
Revo
  • 17,504
123
votes
6 answers

Trace of a commutator is zero - but what about the commutator of $x$ and $p$?

Operators can be cyclically interchanged inside a trace: $${\rm Tr} (AB)~=~{\rm Tr} (BA).$$ This means the trace of a commutator of any two operators is zero: $${\rm Tr} ([A,B])~=~0.$$ But what about the commutator of the position and momentum…
Joe
  • 3,554
120
votes
6 answers

What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?

This question was listed as one of the questions in the proposal (see here), and I didn't know the answer. I don't know the ethics on blatantly stealing such a question, so if it should be deleted or be changed to CW then I'll let the mods change…
Logan M
  • 4,614
118
votes
4 answers

Intuitively, why are bundles so important in Physics?

I've seem the notion of bundles, fiber bundles, connections on bundles and so on being used in many different places on Physics. Now, in mathematics a bundle is introduced to generalize the topological product: describe spaces that globally are not…
Gold
  • 38,087
  • 19
  • 112
  • 289
116
votes
11 answers

Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any similar statement for discrete symmetries?
Tobias Kienzler
  • 6,950
104
votes
13 answers

Best books for mathematical background?

What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory? Some subjects off the top of my head that probably need covering: Differential geometry, Manifolds, etc. Lie groups, Lie…
ahh
  • 141
92
votes
11 answers

Quantum Field Theory from a mathematical point of view

I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view. Are there any good books or other reference material which can help in learning about quantum field…
user774025
  • 1,431
78
votes
5 answers

Is the converse of Noether's first theorem true: Every conservation law has a symmetry?

Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is the converse true: Any conservation law of a physical system has a differentiable symmetry of its action?
Larry Harson
  • 5,456
77
votes
7 answers

Number theory in Physics

As a Graduate Mathematics student, my interest lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications of Number theory to physics. I have heard…
C.S.
  • 1,029
67
votes
7 answers

Fourier transform of the Coulomb potential

When trying to find the Fourier transform of the Coulomb potential $$V(\mathbf{r})=-\frac{e^2}{r}$$ one is faced with the problem that the resulting integral is divergent. Usually, it is then argued to introduce a screening factor $e^{-\mu r}$ and…
Emerson
  • 1,377
66
votes
7 answers

Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, which in general have no mathematical meaning (at…
MBN
  • 3,875
64
votes
4 answers

Rigorous underpinnings of infinitesimals in physics

Just as background, I should say I am a mathematics grad student who is trying to learn some physics. I've been reading "The Theoretical Minimum" by Susskind and Hrabovsky and on page 134, they introduce infinitesimal transformations. Here's the…
Brian Klatt
  • 923
61
votes
4 answers

Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of possible basis states be the set of…
Lagerbaer
  • 15,136
  • 4
  • 77
  • 83
1
2 3
…
99 100