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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Holonomic constraints as a limit of the motion under potential
In Mathematical Methods of Classical Mechanics, Arnold states the following theorem without proof in pages 75-76:
Let $\gamma$ be a smooth plane curve, and let $q_1, q_2$ be local coordinates where
$...
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(Time-)Orientability in the Language of Fiber Bundles
I'm currently studying spin geometry through Hamilton's book Mathematical Gauge Theory. At a given point, Hamilton considers a pseudo-Riemannian manifold, which I'll take to be Lorentzian in $d=3+1$ ...
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Azimuthal coordinate operator: Hermition or not? Self-adjoint or not?
I am told that the azimuthal coordinate operator $\hat{\phi}$ is not self-adjoint. I am told this by people who I am sure know much more about this stuff than I do. To my unsophisticated mind, "...
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Einstein's gravity Lagrangian invariance under the change of differential structure
I came across an article claiming the appearance of singularities in the energy-momentum tensor $T_{\mu \nu}$ as a result of changing the differential structure:
I wonder what symmetry or current (in ...
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Why are light rays expressed or generally shown as a sine wave? [duplicate]
Whether it be a YouTube video or book lights rays i.e(the visible specturm,uv rays) are expressed as a sine wave. Why is it so?
What is the plot of its against? Why does it oscillate? Why does it ...
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Limit for big system size of Fokker-Planck eigenfunctions
I am learning how to use diagonalization methods applied to Fokker-Planck equations with Gardiner's book and these notes. The idea is to find the probability density, $ P[X_t\in[x,x+dx]]=\rho_t \, dx$,...
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What does it mean for classical mechanics to be based on the category of sets?
It is quite common[1][2] in the study of physics in the context of category theory to say that one of the fundamental difference between classical mechanics and quantum mechanics is that classical ...
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The limit of time evolution operator
Through reading Nenciu's rigorous proof on the Adiabatic Theorem and Gell-Mann-Low Theorem, I found:
Since the limit $t_0\to-\infty$ does not exist for $U(t,t_0,\epsilon)$, in order to make use of ...
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Is integral of energy-momentum tensor in QFT over a region $R$ self-adjoint?
Consider a quantum field theory in flat 1+1D spacetime for simplicity. Let $T_{\mu\nu}$ be the conserved symmetric stress tensor. One writes operators by integrating the tensor over the whole space, ...
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Mathematical explanation of the extinction paradox
I am trying to learn properly about scattering. For this I was pointed to Wave Propagation and Scattering in Random Media by Ishimaru.
I got a bit stuck in section 2-2 General properties of the Cross ...
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Analytical continuation as regularization in Quantum Field Theory, the remaining questions
There is an old question posted (Regularization) which did not get an answer, about the validation of analytic continuation as regularization. It did get some discussion in the comments, referring to ...
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Mathematical references for gauge theory in condensed matter physics
I am currently trying to go through some literature on the classification of symmetry protected topological phases. Primarily, I am interested in the classical of topological phases using mathematical ...
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Why are these unbounded operators (essentially) self-adjoint?
Can anyone provide exact mathematical reasoning as to why the following fundamental unbounded symmetric operators are essentially self-adjoint? I.e. on, their natural domains, they admit a unique ...
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Use of mathematical structure on physics [closed]
I want resources for studying in detail the connection between the mathematical structures of physical theories and said physical theories.
For example, i know what a Hilbert space or a principal ...
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Charge Density Of A Conducting Strip
I am currently doing a project which requires me to figure out the charge density of a strip. Assume that the strip is isolated in a vacuum.
Assume the strip is 1 dimensional, kind of like a rod. What ...
