# 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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### What classifies gaugings?

Gauging a global symmetry $G$ introduces several free parameters to the theory. For example, In $d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ...
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### Why can't $i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?

In the time-dependent Schrodinger equation, $H\Psi = i\hbar\frac{\partial}{\partial t}\Psi,$ the Hamiltonian operator is given by $$\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V.$$ Why can't we ...
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### System in Lieb and Yngvason's paper [closed]

I'm reading The Physics and Mathematics of the Second Law of Thermodynamics and have a question. In A. Basic concepts 1. Systems and their state spaces, the term system is formally introduced and one ...
218 views

### The use of Helmholtz decomposition

Examining the article on Wikipedia Helmholtz decomposition, compatible with the explanations of the book Introduction to Electrodynamics $4^{\mathrm{th}}$ edition David J. Griffiths §1.6 the theory of ...
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### Inertial Forces while analysing forces on a Piston in a Slider - Crank Mechanism? [on hold]

I get that we are analysing the Piston in a Non - Inertial Frame of Reference, but the point of my question is that according to D'Alemberts Principle, whenever an Inertial Force comes in the line of ...
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### How to prove that orthochronous Lorentz transformations $O^+(1,3)$ form a group?

Orthochronous Lorentz transform are Lorentz transforms that satisfy the conditions (sign convention of Minkowskian metric $+---$) $$\Lambda^0{}_0 \geq +1.$$ How to prove they form a subgroup of ...
78 views

### Orthochronous indefinite orthogonal group $O^+(m, n)$ form a group

My question is based on Qmechanic's answer here which proves that $O^+(m, 1)$ forms a group -- that if two Lorentz transformations have positive time-time co-ordinate, so does their product. The key ...
54 views

### Is there a commonly accepted definition of a quantum phase definition for a finite lattice/set of particles?

As noted by Sachev, and in a previous question, https://www.physicsoverflow.org/41602/, there cannot be quantum phase transitions for finite systems (with bounded local Hilbert space dimension). The ...
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### Proper path integral of a field theory

I have been trying to find out the sweet middle ground of describing path integration of field theories, in between the physicist way and the mathematician way, but it seems hard to find something ...
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### Why are only functions discussed in physics and not relations? [closed]

Why are only functions discussed in physics and not relations?
278 views

### Why use a particular regularization for $\int_0^\infty \mathrm{d}x\,e^{i p x}$?

There are many badly defined integrals in physics. I want to discuss one of them which I see very often. $$\int_0^\infty \mathrm{d}x\,e^{i p x}$$ I have seen this integral in many physical problems. ...
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### Hopf Algebras in Quantum Groups

In the theory of quantum groups Hopf algebras arise via the Fourier transform: A third point of view is that Hopf algebras are the next simplest category after Abelian groups admitting Fourier ...
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### Can one test an octonionic interpretation for a quantum-information conjecture, apparently valid in the real, complex and quaternionic settings?

For the values $\alpha = \frac{1}{2},1, 2$, corresponding to real, complex and quaternionic scenarios, the formulas (https://arxiv.org/abs/1301.6617, eqs. (1)-(3)) \label{Hou1} P_1(\...
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### Operators that act on the edge of a quantum spin chain with periodic boundaries

Consider a quantum spin chain of length $N$. Each site/spin has the local Hilbert space $\mathbb{C}^d$ and so for the whole chain the Hilbert space is $(\mathbb{C}^d)^{\otimes N}$. Now for periodic ...
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### Is it there any theory or model in theoretical physics that is akin to Tegmark's Mathematical Universe Hypothesis?

Physicist Max Tegmark proposed a hypothesis that asserts that all mathematical structures do exist as universes. (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) But this hypothesis ...
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### Completeness condition involving continuum states

Consider a potential $V(x)$ in 1d. Suppose that $V(|x| > a )= 0$ for some positive $a$. We then know that the hamiltonian $H = - \frac{\partial^2}{\partial x^2 } + V(x)$ has non-normalizable or ...
Let $(M,g)$ be a globally hyperbolic spacetime. Let $\Sigma$ be a Cauchy surface in $(M,g)$. In this paper, page 9, Lemma A.1, the author says that if we take $D = J^{-}(\Sigma)\setminus \Sigma$ then \$...