As I understand it, Lions and DiPerna demonstrated existence and uniqueness for the Boltzmann equation. Moreover, this paper claims that Appropriately scaled families of DiPe …

Background Suppose we have a finite-dimensional Hilbert space $H = \mathbb{C}^s$ (for a natural number s) and we construct the symmetric (or bosonic) Fock space built from it: $$F …

I am wondering if there is any mathematical (or physical, besides the fact that classical quantum mechanics uses complex numbers) justification for why the complexified (1,3) Cliff …

Hello, I don't know if this is a good place for exposing my problem but I'll try... I have a gauge theory with action: $S=\int\;dt L=\int d^4 x \;\epsilon^{\mu\nu\rho\sigma} B_{\ …

I am confused regarding supermanifolds. Suppose I consider R^(1,2) (1 "bosonic", 2 "fermionic"), This map (x,a,b) -> (x+ab, a,b) (a,b are fermionic) is supposed to be a morphism of …

Physicists use the "Atiyah-Bott formula" for path "integrals" (for instance the supersymmetric proof of the Atiyah-Singer index theorem. Is there some way to make atleast some of t …

Max Koecher (in, for example, The Minnesota Notes on Jordan Algebras and Their Applications (new edition: Springer Lecture Notes in Mathematics number 1710, 1999)), defined a domai …

I'm in the process of understanding the heat equation proof of the Atiyah-Singer Index Theorem for Dirac Operators on a spin manifold using Getzler scaling. I'm attending a masters …

What's the current state of Yang Mills Mass Gap question, is there any place that does this problem? Especially I want to know if there is any progress (out of that mentioned in th …

In this question, Orbicular made the following comment to Feb7 and my own answers; Please keep in mind that - even though it is stated very often - noncommutative geometry does …

Well, this is an awkward question and I don't know if it is mathematical enough for MO (I'm sorry if not) but I'll try it: What observations in the coordinate system centered in my …

In standard calculus it is a well known fact that left-point and mid-point Riemann sums do become equal in the limit. When it comes to stochastic integration this is no longer the …

My undergraduate advisor said something very interesting to me the other day; it was something like "not knowing quantum mechanics is like never having heard a symphony." I've bee …

In his answer to this question, Scott Carnahan mentions "mirror symmetry mod p". What is that? (Some kind of) Gromov-Witten invariants can be defined for varieties over fields ot …

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 d …