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12
votes
2answers
829 views

Literature on fractal properties of quasicrystals

At the seminar where the talk was about quasicrystals, I mentioned that some results on their properties remind the fractals. The person who gave the talk was not too fluent in a rigor mathematics ...
2
votes
1answer
200 views

What determine whether the dynamical equations are tensor equations or vector equations?

Newton's 2nd law which is central to Newtonian dynamics, is a vector equation $\sum\textbf{F}_{external}=m\textbf{a}$ Same with Maxwell's equations in the covariant form. On the other hand, ...
1
vote
2answers
909 views

Inverted Harmonic oscillator

what are the energies of the inverted Harmonic oscillator? $$ H=p^{2}-\omega^{2}x^{2} $$ since the eigenfunctions of this operator do not belong to any $ L^{2}(R)$ space I believe that the spectrum ...
5
votes
2answers
609 views

Are there 'higher order moments' in physics?

This may be a rather noob question but please let me clarify: I'm struggling to understand the use of the word 'moments' w.r.t., probability distributions. It seems after some research and poking ...
10
votes
1answer
191 views

Characters of $\widehat{\mathfrak{su}}(2)_k$ and WZW coset construction

I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine ...
15
votes
1answer
174 views

Miura transform for W-algebras of exceptional type

Miura transform for W-algebras of classical types can be found in e.g. Sec. 6.3.3 of Bouwknegt-Schoutens. Is there a similar explicit Miura transform for W-algebras of exceptional types, say, E6? It's ...
6
votes
4answers
958 views

Is QFT mathematically self-consistent?

After recently going through a short program of self-study in quantum mechanics, I was surprised to find a quote attributed to Feynman essentially saying he was extremely bothered by the computational ...
5
votes
3answers
1k views

Can Laplace's equation be solved using Fourier transform instead of Fourier series?

Sorry for the long text, but I am unable to make my question more compact. Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not ...
9
votes
0answers
457 views

Classical mechanics: Generating function of lagrangian submanifold

I have a short question regarding the geometrical interpretation of the Hamilton-Jacobi-equation. One has the geometric version of $H \circ dS = E$ as an lagrangian submanifold $L=im(dS)$, which is ...
3
votes
2answers
301 views

Why higher frequencies in Fourier series are more suppressed than lower frequencies?

One can expand any periodic function in sines and cosines. When calculating the coefficients $a_0$, $a_n$, and $b_n$ one find that $a_1>a_2>...>a_n>...$, similarly for $b_n$. Is there an ...
15
votes
2answers
474 views

Generalized Complex Geometry and Theoretical Physics

I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
8
votes
2answers
277 views

Are there rigorous constructions of the path integral for lattice QFT on an infinite lattice?

Lattice QFT on a finite lattice* is a completely well defined mathematical object. This is because the path integral is an ordinary finite-dimensional integral. However, if the lattice is infinite, ...
15
votes
6answers
603 views

Which QFTs were rigorously constructed?

Which QFTs have mathematically rigorous constructions a la AQFT? I understand there are many such constructions in 2D, in particular 2D CFT has been extensively studied mathematically. But even in 2D ...
5
votes
1answer
44 views

Scaling solutions in context of Denef - Moore

My question is based on the paper Split states, entropy enigma, holes, halos. What are the scaling solutions discussed on page 49 of the paper ? It is stated that the equations ${\sum_{j, i\neq ...
8
votes
3answers
142 views

Does the complex 3-sphere have a complex structure modulus?

This question has a flavor which is more mathematical than physical, however it is about a mathematical physics article and I suspect my misunderstanding occurs because the precise mathematical ...
10
votes
1answer
380 views

Chern-Simons theory

In Witten's paper on QFT and the Jones polynomial, he quantizes the Chern-Simons Lagrangian on $\Sigma\times \mathbb{R}^1$ for two case: (1) $\Sigma$ has no marked points (i.e., no Wilson loops) and ...
10
votes
3answers
172 views

Physical interpretation to the category of CFTs

This question comes from reading Andre's question where I wandered whether that question even makes sense physically. In mathematics, VOAs form a category, does this category as a whole have a ...
11
votes
8answers
780 views

Mathematical Universe Hypothesis

What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc. I ...
13
votes
2answers
417 views

Topological twists of SUSY gauge theory

Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this theory has 3 ...
3
votes
2answers
863 views

Does Hestenes Zitterbewegung Explain why complex numbers appear in QM?

This question may fit better in the discussion of "Why Complex variables are required by QM?", but it also relates to the extent to which arguments by Hestenes are accepted in mainstream physics and ...
1
vote
1answer
291 views

Mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states

What is the mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states, independent of any specific physical theory.
26
votes
11answers
2k 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 ...
49
votes
11answers
8k views

Quantum Field Theory from a mathematical point of view

I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view. Are there any good books or other reference ...
4
votes
2answers
219 views

Physics talk with an emphasis on Mathematics [closed]

I have to give a 10 minute physics talk that have to involve a fair bit of mathematics -- i.e. not just qualitative/handwaving material to some undergrads. I have wasted the last 3 hours looking for ...
5
votes
1answer
258 views

How Exactly Does Linear Regge Trajectories Imply Stability?

(for a more muddled version, see physics.stackexchange: http://physics.stackexchange.com/questions/14020/whats-with-mandelstams-argument-that-only-linear-regge-trajectories-are-stable) There is a ...
13
votes
1answer
113 views

Instanton Moduli Space with a Surface Operator

I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator. Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are ...
13
votes
5answers
305 views

Other processes than formal power series expansions in quantum field theory calculations

I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e. , what dynamical systems ...
6
votes
0answers
45 views

What is the importance of studying degeneration on $M_g$

Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$. It seems to be important in physics to study ...
9
votes
5answers
338 views

Where do theta functions and canonical Green functions appear in physics

In the beginning of Section 5 in his article, Wentworth mentions a result of Bost and proves it using the spin-1 bosonization formula. This result provides a link between theta functions, canonical ...
8
votes
1answer
53 views

Sub and super multiplicativity of norms for understanding non-locality

In relation to various problems in understanding entanglement and non-locality, I have come across the following mathematical problem. It is most concise by far to state in its most mathematical form ...
11
votes
1answer
112 views

Metric interpretation of self-adjoint extensions?

I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...
2
votes
2answers
378 views

p-adic quantum mechanic [closed]

i got a degree on physics so my question is ?as a physicist could i learn P-adic analysis or p-adci quantum mechanics ?? is there any good book on the subject ? as an introductory level How the ...
1
vote
0answers
210 views

What does it mean for a phase space trajectory to be “long” and “stable”?

What does it mean for a phase space trajectory to be "long" and "stable"? I understand the concept of a trajectory in phase space but not how these adjectives can be applied to one. Thanks.
10
votes
2answers
58 views

Extensions of DHR superselection theory to long range forces

For Haag-Kastler nets $M(O)$ of von-Neumann algebras $M$ indexed by open bounded subsets $O$ of the Minkowski space in AQFT (algebraic quantum field theory) the DHR (Doplicher-Haag-Roberts) ...
15
votes
1answer
1k views

Onsager's Regression Hypothesis, Explained and Demonstrated

Onsager's 1931 regression hypothesis asserts that “…the average regression of fluctuations will obey the same laws as the corresponding macroscopic irreversible process". (Here is the links to ...
2
votes
0answers
440 views

Heat equation and Bessel's function [closed]

Could someone please explain why if the time-independent heat equation can, via changing of variables, take the form of Bessel's equation that the $\sqrt\lambda$ should take the values of the zeros of ...
61
votes
6answers
3k views

The Role of Rigor

The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
2
votes
1answer
172 views

Probablistic problems in physics?

So I have an opportunity to do math research with a probabilist. I would like to propose to him a project that relates to physics, as it would be a good way to learn about another field. What are some ...
22
votes
4answers
4k views

Mathematically-oriented Treatment of General Relativity

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ...
13
votes
3answers
203 views

Status of local gauge invariance in axiomatic quantum field theory

In his recent review... Sergio Doplicher, The principle of locality: Effectiveness, fate, and challenges, J. Math. Phys. 51, 015218 (2010), doi ...Sergio Doplicher mentions an important open ...
15
votes
4answers
825 views

What is a good introduction to integrable models in physics?

I would be interested in a good mathematician-friendly introduction to integrable models in physics, either a book or expository article. Related MathOverflow question: what-is-an-integrable-system.
12
votes
0answers
402 views

Hypersingular Boundary Operator in Physics

This has been a question I've been asking myself for quite some time now. Is there a physical Interpretation of the Hypersingular Boundary Operator? First, let me give some motivation why I think ...
0
votes
1answer
150 views

Use of escort distribution in nonextensive stat. mech

In some of the articles which I read recently, I happen to see the following statement. In Nonextensive statistical physics, it is inappropriate to use the original distribution $P=(p_i)$ ...
19
votes
5answers
3k views

What do theoretical physicists need from computer scientists?

I recently co-authored a paper (not online yet unfortunately) with some chemists that essentially provided answers to the question, "What do chemists need from computer scientists?" This included the ...
4
votes
1answer
315 views

Propagators from integral representations of Green`s functions

I'm working on an article about propagators from int. representations of Green`s functions for several N-dimensional potential(all this is done in an N-dimensional Euclidian space). Potentials like ...
20
votes
2answers
119 views

Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
15
votes
4answers
83 views

Why can't noncontextual ontological theories have stronger correlations than commutative theories?

EDIT: I found both answers to my question to be unsatisfactory. But I think this is because the question itself is unsatisfactory, so I reworded it in order to allow a good answer. One take on ...
22
votes
1answer
496 views

Mermin-Wagner theorem in the presence of hard-core interactions

It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core ...
16
votes
6answers
956 views

Applications of delay differential equations

Being interested in the mathematical theory, I was wondering if there are up-to-date, nontrivial models/theories where delay differential equations play a role (PDE-s, or more general functional ...
6
votes
1answer
219 views

Nonextensive statistical mechanics

I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times ...