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.

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Chemical potentials for $D$-brane bound states

This question is about a mathematical subtlety arising in the computation of the partition function of a supersymmetric ensemble of some lower dimensional $D$-branes attached to a stack of higher ...
2k views

Do all Noether theorems have a common mathematical structure?

I know that there are Noether theorems in classical mechanics, electrodynamics, quantum mechanics and even quantum field theory and since this are theories with different underlying formalisms, if was ...
272 views

What are good non-paraxial gaussian-beam-like solutions of the Helmholtz equation?

I am playing around with some optics manipulations and I am looking for beams of light which are roughly gaussian in nature but which go beyond the paraxial regime and which include non-paraxial ...
400 views

Spectral decomposition vs Taylor Expansion

This question and the comments and answers it received encouraged me to ask this question, although I know that there will be some people who think that this belongs in the math forum. But I think ...
10k views

Constructing Lagrangian from the Hamiltonian

Given the Lagrangian $L$ for a system, we can construct the Hamiltonian $H$ using the definition $H=\sum\limits_{i}p_i\dot{q}_i-L$ where $p_i=\frac{\partial L}{\partial \dot{q}_i}$. Therefore, to ...
24 views

Does microcausality plus the time-slice property imply local primitive causality?

In quantum field theory, observables are associated with regions of spacetime. One of the basic principles of relativistic quantum field theory is microcausality, which says that observables ...
76 views

Axiomatic Quantum Theory

Is there any practical advantage/disadvantage between using the axioms for the Hilbert Space formulation as opposed to the C* Algebra formulation of Quantum Theory? If not, then is it possible to ...
682 views

Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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Intuitively what's the relationship between forces and connections?

In Einstein's General Relativity we relate the effects of gravity with the curvature of the Levi-Civita connection on the spacetime manifold. Also, when we get the electromagnetic tensor $F = dA$ ...
62 views

Trying to understand how to connect the most general concept of a function to real world? [closed]

I'm a beginner wrapping my head around how general a definition a "function" really is when connected to the real world, please help. I am trying to connect the mathematical definition of a ...
34 views

Is there a systematic way to construct a SUSY theory?

For the sake of simplicity, I am considering a 0+0d scalar field theory with multiple bosonic and fermionic fields/variables. The fields are coupled together up to a certain order (say 4) with ...
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Number of bras and kets

My quantum mechanics teacher told us during the class that there were many more "bra" than "kets", but I confess that I don't quite understand this. Indeed, in quantum mechanics, ...
39 views

What does the Hausdorff-Young inequality tell us?

The Hausdorff-Young Inequality relates the size of a function and its Fourier coefficients. What is meant the by "the size of a function"?
222 views

Allowed anyons for Chern-Simons at level $k.$

Ref.1. proves that the allowed representations of Chern-Simons $\mathrm{SU}(2)_k$ are those with dimension $$\dim(R)\le k+1\tag{7.53}$$ Question: Is the generalisation of $(7.53)$ to arbitrary $N$ ...
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Orthogonality of two randomly chosen velocity vectors in the kinetic theory of gas and the relative velocity

I was looking for the average value of the relative velocity of ideal gas molecules in the kinetic theory. The following is from this article. The vector notation is not mathematically rigorous, just ...
2k views

Does Hestenes Zitterbewegung Explain why complex numbers appear in QM?

This question may fit better in the discussion of "Why Complex variables are required by QM?", but it also relates to the extent to which arguments by Hestenes are accepted in mainstream physics and ...
4k views

Electromagnetism for mathematicians

I am trying to find a book on electromagnetism for mathematicians (so it has to be rigorous). Preferably a book that extensively uses Stoke's theorem for Maxwell's equations (unlike other books that ...
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Convergence of $c^* Ac$ in second quantization

Let $A$ denote a bounded operator on a complex separable Hilbert space $\mathscr{H}$. Let $\mathscr{F} = \bigoplus \mathscr{F}_N$ be the Fock space generated by $\mathscr{H}$ where $\mathscr{F}_N$ is ...
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Dirac delta equalities in physics

Earlier I asked this question on the Math Exchange but I'm looking for a physics point of view. How do you interpret an equation like $$x^n \delta(x) = 0, \qquad n\in \mathbb{N},$$ around $x=0$? Why ...
84 views

Confusion about the dimension of a Hilbert Space in Quantum Mechanics [duplicate]

In Quantum Mechanics, the quantum state of the physical system lives in an infinite-dimensional Hilbert space and can be written in terms of two different bases, the position basis (uncountably ...
228 views

Can one force the octupole moments of a charge distribution (neutral and with vanishing dipole moment) to vanish using a suitable translation?

In a previous question, I noted that if you have a charge distribution with nonzero charge, then it is possible to choose an origin (at the centre of charge) which makes its dipole moment vanish, and ...
45 views

What equation should I use if I am estimating the distance of a rocket's landing point to the point it was launched from?

I am trying to figure out how to estimate how far (in meters) that a solid fuel model rocket will land from its launching point. To do this, I have figured out I will need to estimate the maximum ...
111 views

Does one ever need infinitely many cohomologies?

In a theory containing gauge fields or higher-form gauge fields, if the background spacetime is a complicated manifold, a nice way to represent the configuration of the gauge field mathematically is ...