# 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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### Mathematically Rigorous Introduction to the Standard Model [duplicate]

I am looking for textbooks, lecture notes, lecture videos on a rigorous introduction to the standard model of elementary particles. I'd prefer to not be referred to monographs for an introduction as ...
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### Mathematically Rigorous Introductory Resources for Condensed Matter Physics

I am looking for textbooks, lecture notes, lecture videos on rigorous introductions to condensed matter physics. I'd prefer to not be referred to monographs for an introduction as they tend to be ...
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### How do I self-study physics at the undergrad level? [closed]

I'm a new physics undergrad worried that I won't be able to learn everything I want at the university I'm going to. Basically the Institute I'm going to is applied sciences focused, and all electives ...
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### On the Bogoliubov-de Gennes (BdG) equation

I'm a graduate student majoring in mathematics, in particular nonlinear PDEs. So I know very little about physics, including quantum mechanics. I'm interested in the Bogoliubov-de Gennes (BdG) ...
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### Compactification in String Theory and Compactification in Topology are they the same thing?

In topology, there is a concept of compactification which is defined as follows. A space $Z$ is a compactification of $X$ if $Z$ is compact Hausdorff and there exists an embedding $j:X \rightarrow Z$ ...
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### Doubt on the continuity factor of Dyson mega-spheres

I) Dyson Mega-Spheres In a nice and cool recent paper, $$, the authors constructed another interresting solution of general relativity; they constructed a thin-shell around a star: a dyson sphere ...
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### In what sense is string theory not expected to be a QFT?

This question came to mind while reading about Weinberg's folk theorem that any quantum theory that is Poincare covariant and satisfies cluster decomposition will look like a quantum field theory at ...
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### Intuition for the differences between two notions of quantum ergodicity: One given by weak-* convergence and one by pseudodifferential operators

Consider the two notions of quantum ergodicity of the Laplacian operator $\Delta$. (Phase space): $\Delta$ is said to be quantum ergodic (in the phase space) in a compact Riemannian manifold if there ...
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### Mathematical equivalent of Fundamental nature of charge [closed]

How to mathematically represent the fact that electric charge is a fundamental quantity? i.e. that it cannot be explained in terms of other things, for example, the normal force can be explained as ...
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### Whats is a large fields problem in RG?

I was advised on MO to link this question and reproduce it here, so here it goes. I was reading Constructive Renormalization Group by V. Rivasseau and I got some points which I would like to clarify. ...
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### Quantum Particle in a Fractal Box

I was thinking about particle in a 2D box the other day, and I realize that it shapes actually affect its energy and wavefunction. Therefore I thought to myself, what if a particle is inside a fractal ...
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### Resources on Post-Einsteinian Results in GR

What are some good books, lecture notes, articles, etc. that can be used as introduction to the landscape of major results in general relativity since Einstein? In terms of the timeline, I'm thinking ...
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### How was the minimal model with a boundary related to the D brane?

Quote my advisor: The D brane was the boundary of the CFT However, in the development of the rational CFT, such as the minimal model, the D brane was not realized. Thus, when the boundary CFT was ...
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### Green's function existence vs explicit description

Are there examples in physics where the mere existence of a Green's function on some domain (for some PDE) has useful applications? Or is it true that in literally all applications of Green's ...
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### Contractivity of trace distance in infinite dimensions

The trace distance is heavily used in physical applications and is defined being half of the trace norm $T(\rho, \sigma) := \frac{1}{2} Tr\left[\sqrt{(\rho-\sigma)^{\dagger}(\rho-\sigma)}\right]$. It ...
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### Interacting QFT construction on curved spacetime

As far as I can tell, most of the concrete models considered in (rigorous) QFT on curved spacetime are either free or perturbative. In fact the only construction of an interacting QFT on curved ...
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### Euler equation of motion for fluids

I was seeing some proofs of Euler equation of motion for fluids online and most of the videos drew this figure in which they consider infinitesimal cylindrical element. My question:- Now it mentions ...
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