# Tagged Questions

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 ...

62 views

### How can I show that inversion is continuously connected to a reflection?

From Ex 3.1 in the TASI lectures on the conformal bootstrap: http://arxiv.org/abs/1602.07982 the problem is the inversion map (with Euclidean signature) $$I\colon x^\mu \mapsto \frac{x^\mu}{x^2}$$ ...
231 views

### Path dependent phase in quantum mechanics

In elementary treatments of quantum mechanics, we are taught that the wavefunction of a single particle is complex valued ($\Psi : \mathbb{R}^3 \to \mathbb{C}$). In particular, the wavefunction has a ...
35 views

### Objective time derivative that is no Lie derivative

I am trying to understand the notion of "Objectivity" and "Objective Time Derivatives" (invariance of rheological equations under arbitrary time dependent rotations and translations) in Continuum ...
80 views

### Exotic differentiable structures in physics

When reading a bit on exotic spheres and exotic $\mathbb{R}^4$'s, I came across some papers of Carl H. Brans and Torsten Asselmeyer-Maluga: "Exotic differentiable structures and general relativity" (...
55 views

1k views

### Why is a Hermitian operator a “quantum random variable”?

To me, as a stupid mathematician, a random variable is a measurable function from some probability space $(\Omega, \sigma, \mu)$ to $(\Bbb{R}, B(\Bbb{R}))$. This makes sense. You have outcomes, events,...
1k views

### Does the axiom of choice appear to be “true” in the context of physics?

I have been wondering about the axiom of choice and how it relates to physics. In particular, I was wondering how many (if any) experimentally-verified physical theories require axiom of choice (or ...
810 views

55 views

134 views

### How to properly use Perturbation Theory in classical systems?

Context: If we consider a particle in upwards motion near the Earth's surface and acted by a quadratic drag we get the non-linear eom: $$\frac{dv}{dt}=-g-\frac{b}{m}v^2.$$ We can solve it ...
3k views

### Spherical wave as sum of plane waves

How can we do this computation? $\iiint_{R^3} \frac{e^{ik'r}}{r} e^{ik_1x+k_2y+k_3z}dx dy dz$ where $r=\sqrt{x^2+y^2+z^2}$ ? I think we must use distributions... Physically, it's equivalent to ...
3k views

### Negative probabilities in quantum physics

Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
225 views

### Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
205 views

### How to make rigorous the idea of a continuous complete set?

In Quantum Mechanics, when using Dirac's formalism one of its features is the expansion of state vectors into continuous basis of eigenvectors of unbounded self-adjoint operators. Let $\mathcal{H}$ be ...
75 views