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Background Lagrangian mechanics on $\mathbb R^n$ is usually defined by picking a Lagrangian function $L: {\rm T}\mathbb R^n \to \mathbb R$, where ${\rm T}\mathbb R^n = \mathbb R^{2n}$ is the tangent …

This question is closely related to another one I asked recently, and may be thought of as a warm-up to that one. Consider $\mathbb R^n$ with its usual metric, and pick a one-form $b$ and a function …

Background Consider an electron with mass $1$ moving in $\mathbb R^n$ in under the influence of a static electromagnetic field. Up to identifying vector fields with differential forms, Maxwell's equ …

Recall the following theorem (c.f. LC Evans, M Zworski, "Lectures on semiclassical analysis", Theorem 3.15, depending on the version): Theorem: Let $\varphi: \mathbb R^n \to \mathbb R$ be smooth and …

There is a folk — I can't call it a theorem — "fact" that the mathematical relationship between Complex and Tropical geometry is analogous to the physical relationship between Quantum and Classical me …

Toeplitz operators provide a natural language with which to do geometric quantization. I don't want to really understand them, and I don't need them in full generality. I'm looking for some referenc …

I have a fairly specific question. My intuition says the answer is "yes", but there is a natural generalizations in which I take out all the "physics", and then I think the answer is "no". Edit num …

I'm going to ask a very vague question, and then give specifics for the version I particularly care about. I'm interested in answers at all levels of vagueness. At the most vague version, I am in th …

This question is very closely related to another one I just asked. The general question is to what extent there is a theory of differential equations for smooth correspondences (between a smooth mani …

The question I will ask makes sense in much more generality, but I will leave the translation to the experts, since I'm only looking for a special case (and it would not surprise me if the answer does …

I'm looking for either a few precise mathematical statements about Wiener integrals, or a reference where I can find them. Background The Wiener integral is an analytic tool to define certain "integ …

The notion of vertex algebra, like any reasonable algebraic notion, makes sense inside any (sufficiently linear) symmetric monoidal category. The standard pictures of the operator product, however, su …

In "Quantum field theory and the Jones polynomial" (Comm. Math. Phys. 1989 vol. 121 (3) pp. 351-399), Witten writes: A representation Ri of a group G should be seen as a quantum object. This repr …

In his 2004 paper Conformal Field Theory and Torsion Elements of the Bloch Group, Nahm explains a physical argument due to Kadem, Klassen, McCoy, and Melzer for the following remarkable identity. Let …

The notion of "supersymmetry" that I am aware of proceeds as follows. One fixes a spacetime $\mathbb R^n$ and signature; I will write $\mathrm{SO}(n)$ for the corresponding group of orthogonal transf …