10
votes
1answer
176 views
Why don’t existence and uniqueness for the Boltzmann equation imply the same for Navier-Stokes?
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 …
8
votes
1answer
124 views
Spectral theory for self-adjoint field operators on a symmetric Fock space
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 …
5
votes
3answers
223 views
Clifford Algebra in Dirac Equation
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 …
2
votes
1answer
208 views
Deriving symmetries of a Gauge theory
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_{\ …
3
votes
3answers
110 views
Morphisms of supermanifolds
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 …
9
votes
1answer
221 views
Path integrals, localisation
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 …
4
votes
2answers
229 views
Proof that domains of positivity of symmetric nondegenerate bilinear forms are self-dual cones?
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 …
12
votes
2answers
285 views
Why is the harmonic oscillator so important? (pure viewpoint sought). How to motivate its role in Getzler’s work on Atiyah-Singer?
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 …
2
votes
1answer
254 views
What’s the current state of Yang Mills Mass Gap question?
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 …
13
votes
4answers
576 views
The ‘real’ use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics
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 …
8
votes
6answers
704 views
How can I conclude that I live in a solar system?
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 …
9
votes
2answers
205 views
Convergence and non-convergence of left-point and mid-point Riemann sums
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 …
23
votes
32answers
3k views
Where does a math person go to learn quantum mechanics?
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 …
12
votes
5answers
1k views
Mirror symmetry mod p?! … Physics mod p?!
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 …
9
votes
1answer
188 views
Which functions are Wiener-integrable?
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 …
