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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.

      16
      votes
      1answer
      821 views

      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 ...
      4
      votes
      0answers
      96 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}} {\...
      0
      votes
      0answers
      49 views

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

      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 ...
      1
      vote
      0answers
      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 ...
      5
      votes
      1answer
      154 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 ...
      1
      vote
      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 ...
      4
      votes
      0answers
      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 ...
      2
      votes
      2answers
      122 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 $-\...
      3
      votes
      2answers
      241 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 ...
      1
      vote
      1answer
      116 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 ...
      6
      votes
      1answer
      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,...
      0
      votes
      0answers
      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 ...
      7
      votes
      1answer
      276 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 ...
      4
      votes
      0answers
      79 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-...
      5
      votes
      0answers
      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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