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.
2,244 questions
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Can a gauge field over $R^n$, with finite Yang-Mills action, be extended to a gauge field over $S^n$?
Consider a vector bundle $E$ with compact structure group $G$ over $\mathbb{R}^n$, and a smooth connection $D$ in this bundle compatible with the structure group. Denoting the curvature of this ...
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Does Bungert–Slepčev rigidity imply Γ-convergence to Laplacian in relational graph frameworks? [closed]
Consider quasi-uniform point clouds in \mathbb{R}^3 with symmetric positive weights w_{ij}^\ell normalized as \sum_j w_{ij}^\ell = O(\ell^{-2}). Bungert–Slepčev (2025) prove rigidity: finite non-...
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Elimination of an unknown function from an overdetermined system of partial differential equations
This question arose from quantum physics research (e.g., Quantum Rep. 2022, 4(4), 486-508)
I have an overdetermined system of partial differential equations for five real unknown functions of four ...
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Staying away from points/minimizing potential energy
Let $x_1,\dotsc,x_n$ be points on $\mathbb{R}/\mathbb{Z}$. Write $\|x-y\|$ for the distance between two points $x,y$ in $\mathbb{R}/\mathbb{Z}$. Let $V$ be one of the following functions $V_j:\mathbb{...
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Can we write the Einstein tensor as exterior derivatives of differential forms?
In general relativity textbooks a conserved quantity is a tensor $J^\mu$ that satisfies $\nabla_\mu J^\mu=0$ (with $\nabla$ the Levi Civita connexion associated to a metric $g$). One can also write ...
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Necessary and sufficient conditions for a closed differential form to be the pullback of a volume form?
Considering $\alpha$ a $k$-form on a manifold $X$, $\text{dim}\,X=n> k$, when can we say that $\alpha$ is the pullback of a volume form ? (ie there exists a map $\phi : X\rightarrow Y$ with $Y$ ...
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Patterns in group cohomology for Abelian groups [duplicate]
Let $G=\bigoplus_{i=1}^k \mathbb{Z}_{N_i}$ be a generic finite Abelian group. Then by equations (113)–(115) of Wan, Wang, and He - Twisted Gauge Theory Model of Topological Phases in Three Dimensions, ...
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Is $ H= (-\Delta)^{\alpha/2} + (X^2)^{\beta/2}$, $\frac{1}{\alpha}+\frac{1}{\beta} = 1$ a quantum harmonic oscillator?
Consider the operator (on $\mathbb{R}$)
$$ H_{\alpha} = (-\Delta)^{\alpha/2} + (X^2)^{\beta/2} \quad\text{with}\quad \frac{1}{\alpha}+\frac{1}{\beta} = 1,\quad\text{and}\quad \omega_{\alpha} =\frac{\...
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Strategy for solving ODEs with non-smooth or generalized rate functions?
Non-smooth (generalized) rate functions in ODEs
How do you typically solve differential equations in which the generalized rate function (meaning that it is a generalized function that may or may not ...
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Rigorous definition of euclidean perturbative path integral quantisation of gauge theories
I am trying to understand Witten's localisation argument for topologically twisted theories, specifically $\mathcal{N} = 4$ $d = 4$ Super-Yang-Mills Theory. Since there is in general no Lebesgue ...
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Compound distribution from stochastic timelike foliation
In a two-dimensional Minkowski spacetime patch with light-cone coordinates $(U,V)\in(0,1)^2$, consider the timelike foliation defined by
$$
V(U)=e^{s/\ln U},\qquad s>0
$$
Randomizing the global ...
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Asymptotics of the projection on the kernel of the coboundary operator on infinite cubical lattice
Consider the infinite cubical lattice $\mathbb{Z}^d \subset \mathbb{R}^d$ as a polyhedral cell complex and write $C^k_{(2)}(\mathbb{Z}^d)$ for the Hilbert space of real oriented $\ell_2$ $k$-cochains ...
- 617
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Continuous spectrum of Dirac’s Hamiltonian for hydrogen atom
Consider the Dirac equation for an electron in the hydrogen atom. What is the continuous spectrum of the Hamiltonian?
A reference would be helpful.
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Characterization of phase transition using Gibbs states
I am far from being an expert on the theory of Gibbs measures, but I know there is a criteria for phase transitions using uniqueness of infinite-volume Gibbs states. This goes roughly as follows. We ...
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Dualizability in physics and the cobordism hypothesis
This is a physically motivated question, cross-posted from PhySE. Apologies in advance if there are inaccuracies in my formulation.
A fundamental observation is that objects representing physical ...
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