# 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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### Gauge-invariance of Lagrangians

I am rereading David Bleecker's Gauge Theory and Variational Principles, and I have realized I don't understand something. The offending part is in 3.3 (page 50-52), however I am reproducing the ...
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### Physical meaning of theorem

This is the image of theorem from V.I Arnold's Mathematical method of mechanics. I understood the example given in text. But I want to know what is physical meaning of example? Can anybody help?
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### Taking a trace using a continuous spectrum of eigenstates

This may be a simple question, but I have not been able to find an adequate discussion in any source that quite answers it. In many cases in quantum mechanics, traces are evaluated using the ...
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### Proving a Mathematical hypothesis using Physics [closed]

I've asked the question below on mathexchange here about 2 weeks ago. while I did not satisfied with the comments and answer there specially because the lack of examples and references that I was ...
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### Is there a function which is square integrable and doesn't tend to zero at infinity but it belongs in the domain of the momentum operator?

Is there a function which is square integrable and doesn't tend to zero at infinity but it belongs in the domain of the momentum operator? There are some counterexample for functions that are square-...
(I) Electric field at a point on positive $x$-axis: Let us consider Cartesian coordinate system with infinitely large circular plane at $y$-$z$ plane. Let $P$ be any point where we want to measure $\... 1answer 40 views ### Additive constant in Hamilton-Jacobi theory? In Hamilton-Jacobi theory Hamilton's principal function S is a function of n+1 constants , But we take one of the n+1 constants as an additive constant . I don't get this step? 0answers 49 views ### Have fractional order differential models been explored as an alternative to standard gravitational field theory? Since Einstein introduced his field equations and general theory of relativity, experimental evidence, at least on the cosmic scale has repeatedly supported the theory. Nevertheless, many seeking to ... 1answer 81 views ### Auxiliary Grassmann variables in supergeometry I was reading on super geometry and how it is used to model fermions and supersymmetry in classical field theory. In texts like [1] or [2] the authors introduced auxiliary Grassmann odd variables to ... 2answers 377 views ### Commutator expectation value in quantum mechanics Suppose$A$and$B$are operators,$A$is Hermitian,$B$anti-hermitian, and their commutator is the identity, i.e. $$[A, B] = I \, .$$ Denoting the eigenvectors of$A$as$\lvert a \rangle$, so that$...
I am working on the calculation of the deformation of a circular elastic sheet with radius $R=1.2~m$ when a plate with mass $M$ and radius $r_0 = 4~cm$ is sitting in the center of the sheet. I used ...