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        Questions tagged [mp.mathematical-physics]

        Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

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        Is Witten's Proof of the Positive Mass Theorem Rigorous?

        I noticed that the only official reason given for awarding Edward Witten the Fields Medal was his 1981 proof of the positive mass theorem with spinors, so I was assuming that the proof was fully ...
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        86 views

        Conjecture for a certain Cauchy-type determinant

        Given the Cauchy-like matrix $$ \mathbf X_M(q) = \left[ \frac{2}{\pi} \frac{ \Gamma\!\left(m - \frac{1}{2} \right)\Gamma\!\left(n + \frac{1}{2} \right) }{ \Gamma(m)\,\Gamma(n) } \frac{m-\frac{3}{4}} {\...
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        48 views

        What is the best book to learn about the wave equation? [on hold]

        I'm looking for a book that teaches the wave equation and how to solve it for more advanced cases than the basic one (infinite/half infinite string, standing waves etc) What book would you recommend ...
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        64 views

        Surfaces extending modified geodesic paths

        What happens if the usual geodesic equation on an n-manifold is directly modified from a source dimension 1 space (giving a path) to a dimension 2 space (giving a surface). I suspect that this gives a ...
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        votes
        1answer
        153 views

        Definition of a Dirac operator

        So it seems that a Dirac operator acting on spinors on $\psi=\psi(\mathfrak{su}(2),\mathbb{C}^2)$ can be written in this case simply as: $D=\sum_{i,j} E_{ij}\otimes e_{ji}$, where $E_{ij}$ are ...
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        1answer
        78 views

        Localization of solutions for time-dependent Schroedinger equation

        I've been playing around with numerical solutions to the Schroedinger equation and I came across something that feels very natural, but I was not able to prove it with the math I know. The ...
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        74 views

        Decomposition of the group of Bogoliubov transformations

        Consider the fermion Fock space $\mathcal{F}=\bigoplus_{k\ge 0}\bigwedge^k\mathfrak{h}$ of some finite-dimensional 1-particle Hilbert space $\mathfrak{h}$. The group $\mathrm{Bog}(\mathcal{F})$ of ...
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        1answer
        89 views

        Non-isolated ground state of a Schrödinger operator

        Question. Does there exist a dimension $d \in \mathbb{N}$ and a measurable function $V: \mathbb{R}^d \to [0,\infty)$ such that the smallest spectral value $\lambda$ of the Schr?dinger operator $-\...
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        239 views

        Applications of flat submanifolds to other fields of mathematics

        Developable surfaces in $\mathbb{R}^{3}$ have lots of applications outside geometry (e.g., cartography, architecture, manufacturing). I am a curious about potential or actual applications to other ...
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        81 views

        Geometric meaning of residue constraints

        $\DeclareMathOperator\Res{Res}$I have been reading Kontsevich and Soibelman's "Airy structures and symplectic geometry of topological recursion" (https://arxiv.org/abs/1701.09137) and am having ...
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        314 views

        Do any finite predictions of Quantum Mechanics depend on the set theoretic axioms used?

        I was wondering if any of the finite predictions of Quantum Mechanics depend on what set theoretic axioms are used. We will say that Quantum Mechanics makes a finite prediction about an experiment if,...
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        60 views

        On an approach on the Hilbert-Polya Conjecture suggested by Schumayer and Hutchison

        In their expository paper, ''Physics of the Riemann Hypothesis arxiv.org/abs/1101.3116v1'', Hutchison and Schumayer suggested the following approach on the Hilbert Polya conjecture, via quantisation ...
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        1answer
        275 views

        Kontsevich Formality sign convention

        Since my question is related to sign convention, I want to define everything from the very beginning. $T_{poly}^k(M)=\Gamma(\wedge^{k+1} TM)$ are the multi vector fields with shifted degree and with ...
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        78 views

        $T\bar{T}$ deformation: Stress-energy momentum tensor deformed in CFT and in QFT for various $d$-dimensions

        The $T\bar{T}$ deformation is based on the original work of Zamolochikov [1] explored deformations of two-dimensional conformal field theories (CFT) by an operator that is quadratic in the stress-...
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        114 views

        How to choose phase to give a desired Fourier transform

        Cross posted from MSE. I have a mathematical problem arising from a physics application, which I feel must have been solved before, but I don't know the terminology associated with it. I am looking ...

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