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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Domain of sum of momentum operators
This is a repost from MathStackExchange (https://math.stackexchange.com/q/4840786/) where however no solution has been found so far.
Given the tensor product of Hilbert spaces $\otimes_{i \in \mathcal{...
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What is the Hilbert dimension of a Fock space?
Quantum field theory in curved spacetimes is often described in the algebraic approach, which consists of describing observables as elements of a certain $*$-algebra. To recover the notion of a ...
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Real algebraic formulation of quantum mechanics?
In a deterministic classical theory we describe the positions and velocities of particles using real numbers.
In a non-deterministic classical theory we describe the positions and velocities of ...
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On the $\ast$ map in the Osterwalder-Schrader axioms
I'm studying "A Mathematical Introduction to Conformal Field Theory" by Schottenloher and there is one point on the Osterwalder-Schrader axioms that I am a bit confused about. They are ...
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Quantum mechanics and derivative operators
EDITED POST
Suppose we have a classical problem where the Hamiltonian is defined as:
$$H = c\frac{p^2}{x}$$
This Hamiltonian emerges in the context of Hamiltonian 1D cosmology, where we define $x= a(t)...
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How to derive the probability distribution of reduced density matrix eigenvalues for randomly chosen pure states in Page's theorem?
Motivation
I am trying to reproduce the proof in Page's theorem as conjectured in the seminal paper Average Entropy of a Subsystem by Don N. Page. It is crucial in various resolutions of black hole ...
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What is the physical meaning of self-adjoint operator extension?
What does it mean that there isn't any extension of a certain operator in a given domain? Does it imply that I can't apply that operator in that domain, and so that I can't measure some observables (...
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Mathematical objects on crystal meltings and their relation to particle physics
I am a mathematician interested in analytic number theory, and I found the paper Dimers and Amoebae
, which shows how many mathematical objects like the Mahler measure, the Ronkin function and the ...
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Equivalent definition of Hawking quasi-local mass
I actually asked the following question at MathSE but didn't receive any response. My question is really about why the definition (2) below can be derived from the definition (1). Specifically, I don'...
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References for Exterior Differential Systems for physicists
Many problems in classical mechanics, classical and quantum field theory among others require the study of systems of partial differential equations where questions like existence and uniqueness ...
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Physical motivation for the definition of Spin structure
I'm pretty confused about the motivations behind defining a spin structure on a manifold. Let me explain.
In quantum mechanics, particles are represented by irreducible unitary projective ...
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Hertzian Dipole: Why is there no longer a phase shift at $\frac\lambda2$? [closed]
Today we learned about the Hertzian Dipole. Out teacher told us that the length of the wire connecting the two capacitor plates is $l=\frac\lambda2$. He also stated that there is a no more phase shift ...
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Newtonian generalisation of binomial theorem for commuting operators
Suppose $\hat{A}$ and $\hat{B}$ are commuting operators on some Hilbert space, $[\hat{A},\hat{B}]=0$, chosen suitably to ensure operators $1/\hat{A}$, $1/\hat{B}$ and $\hat{A}/\hat{B}$ are suitably ...
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How can motion along a spiral curve conclude in a finite time, but have infinite turns around the origin?
The first question of the book "200 puzzling problems in physics" has 3 point objects forming a triangle(equal sides), and they start moving towards one another - A always moves towards B, B ...
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On the existence of ground state for a free particle
Given a free particle, the ground state of the system is the eigenstate with zero momentum. However, we also know that momentum operator does not have proper eigenstates, but rather it's spectrum is ...
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