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23
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0answers
478 views

Linear sigma models and integrable systems

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow I have already difficulties in penetrating the literature... I'd highly appreciate any ...
11
votes
0answers
65 views

Minimal strings and topological strings

In http://arxiv.org/abs/hep-th/0206255 Dijkgraaf and Vafa showed that the closed string partition function of the topological B-model on a Calabi-Yau of the form $uv-H(x,y)=0$ coincides with the free ...
11
votes
0answers
364 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 ...
9
votes
0answers
175 views

Can Lee-Yang zeros theorem account for triple point phase transition?

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost bocome standard ingredient of any comprehensive statistical mechanics textbook. If the volume tends to infinity, ...
9
votes
0answers
199 views

What is Motivic mathematics and how is it used in physics?

In a few videos I've seen where he discusses the new approach to calculating the super Yang Mills scattering amplitudes, Nima Arkani-Hamed sometimes alludes to the use of Motivic methods as being ...
8
votes
0answers
167 views

p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)

I am going to ask a question, at the end below, on whether anyone has tried to make more explicit what should be a close relation between p-adic string theory and the refinement of the superstring ...
8
votes
0answers
330 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 ...
7
votes
0answers
144 views

The Integral Trick and An Equality in Nakajima's Lecture

In Nekrasov et al's series papers MNS, they calculate such kinds of integral $$ \frac{E_1 E_2}{N(2\pi i)^N(E_1+E_2) }\oint d\phi_1 \wedge d\phi_2\wedge \ldots\wedge d\phi_N \prod_{i<N} (-\phi_i) ...
7
votes
0answers
137 views

Electric potential of a spheroidal gaussian

I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form $$ ...
7
votes
0answers
478 views

String theory from a mathematical point of view

I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
6
votes
0answers
238 views

Proof for the completeness of eigenfunctions of a self-adjoint operator

I always heard the eigenfunctions of a self-adjoint operator form a complete basis. Where can I find a proof in infinite dimension space? Presumably readable for physicists.
6
votes
0answers
113 views

Quantization as a functor

Can anyone give an mathematical elaboration of the following statement: Quantization is a functor carrying the category of Hilbert space and linear maps to that of Symplectic manifolds satisfying ...
6
votes
0answers
191 views

Physical interpretation: weighted eigenvalues of the Laplacian with a potential

I'm a mathematician with only the basic knowledge of Physics, so my question may be trivial: in this case, mercy me. :-) Let $\Omega \subseteq \mathbb{R}^N$ be a domain and let $V,m:\Omega \to ...
6
votes
0answers
40 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 ...
6
votes
0answers
247 views

1-form formulation of quantized electromagnetism

In a perpetual round of reformulations, I've put quantized electromagnetism into a 1-form notation. I'm looking for references that do anything similar, both to avoid reinventing the wheel and perhaps ...
5
votes
0answers
49 views

Any examples of commensurable subgroups appearing in physics?

I am a mathematician. I am studying and working on Hecke pairs which I am going to give the related definitions in the following. But first let me explain what I am looking for to learn by asking this ...
5
votes
0answers
131 views

Understanding the intermediate field method for the $\phi^4$ interaction

In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to ...
5
votes
0answers
150 views

Noether currents for the BRST tranformation of Yang-Mills fields

The Lagrangian of the Yang-Mills fields is given by $$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ ...
5
votes
0answers
102 views

Finding symmetry of a part of an equation, given the group transformation property of another part

I am reading this paper on Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to ...
5
votes
0answers
211 views

7 sphere, is there any physical interpretation of exotic spheres?

Basically an exotic sphere is topologically a sphere, but doesn't look like a one. Or more accurately: homeomorphic but not diffeomorphic to the standard Euclidean n-sphere The first exotic ...
5
votes
0answers
98 views

What can quantum adiabatic computation provably accomplish?

Let's say I have a quantum adiabatic computer in a black-box that works perfectly, doesn't suffer from decoherence/noise problems, etc. Are there any proven bounds for an adiabatic algorithm that ...
4
votes
0answers
44 views

Intuitively what's the relationship between forces and connections?

In Einstein's General Relativity we relate the effects of gravity with the curvature of the Levi-Civita connection on the spacetime manifold. Also, when we get the electromagnetic tensor $F = dA$ ...
4
votes
0answers
55 views

Self-adjointness

I know I have posted this question before some time ago. But no one could help so I decided to put my problem in another background. The Schrödinger equation of a free scalar field is given by ...
4
votes
0answers
117 views

Topological Quantum Field Theories

I've asked this on Math.SE, but with no avail. So, I decided to ask it here. I was wondering about the following after reading the Wikipedia article on TQFTs. It is said that TQFTs have vanishing ...
4
votes
0answers
79 views

Coleman-Mandula theorem in mathematical language

Every supersymmetry text starts off mentioning the Coleman-Mandula theorem. Often it is introduced using rather colloquial terminology. I was wondering if anyone knew a precise mathematical ...
4
votes
0answers
71 views

Transport theorem derivation question

I am trying to rigorously go through some fluid mechanics proofs and theorems. I am currently going through a proof related to the transport theorem and I am having trouble with a step. The steps in ...
4
votes
0answers
100 views

Noether current for the Lagrangian without Lorentz invariance

I am reading an article by Watanabe & Murayama. It gives a proof on the counting of Nambu–Goldstone bosons without Lorentz invariance. I am trying to derive all the equations to get a better ...
4
votes
0answers
190 views

What are endomorphism bundle valued $p$-forms and exterior covariant derivatives and their use in Chern-Simons theory?

Chern-Simons Forms appears in several places in physics for examples, Fractional Quantum Hall Effect, response of Topological Insulator, invariant of knot, electromagnetism in 2+1 space-time, ...
4
votes
0answers
84 views

Cauchy Problem for Boltzmann Equations

One of the first profound analysis about the solutions of the Boltzmann Equation was given by DiPerna and Lions in the late 1980s. You can find one of their main papers here: ...
4
votes
0answers
122 views

Question about the HVZ theorem

In this paper1 the authors cite the HVZ theorem2 saying that it follows from the method used by M. Reed & B. Simon without modifications; I don't really understand this point. Is there anyone who ...
4
votes
0answers
118 views

K3 gravitational instanton

Could you please recommend a sufficiently elementary introduction to K3 gravitational instanton in general relativity and the problem of finding its explicit form? Under 'sufficiently elementary' I ...
3
votes
0answers
75 views

Physical significance of Taylor and Maclaurin series - What is the significance of defining a Maclaurin series in Mathematical Physics?

In physics, usually Taylor series is used to express a quantity which keep changes with coordinate. For example the potential energy of a molecule changes with coordinate, so we express the potential ...
3
votes
0answers
49 views

Research problems in application of Lie groups to differential equations

Are there any open problems in physics involving Lie groups and differential equations for a phd theses. Some applications are say, Noether's theorem in classical or quantum field theory. But I am ...
3
votes
0answers
47 views

How many unequivalent Seifert surfaces appear in a AdS/CFT extension?

When introducing the 't Hooft diagrams from Feynman diagrams on a torus has there been a classification in terms of knots and Seifert surfaces?
3
votes
0answers
88 views

Geometric quantization AND nuclear physics

Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. Geometric quantization is one formalization of the notion ...
3
votes
0answers
73 views

On the Geroch's argument

During the study of Geroch's argument to prove positive mass theorem, I faced a problem explained below: Suppose $(M,g_{\mu \nu})$ is a four dimensional Lorentzian Manifold and $\Sigma$ is a ...
3
votes
0answers
73 views

explicit matrix elements for a representation decomposed into subgroup by branching rules

I'm looking for a way to construct a representation for a simple Lie group such that one particular subgroup is manifest. I learned the branching rules from Cahn, Georgi and Slansky, but I'm still not ...
3
votes
0answers
102 views

Isospin and Hypercharge of the SU(2) bps monopole embedding

I am reading the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups - Weinberg, Erick J . In appendix C of this paper the author states, that the solution ...
3
votes
0answers
105 views

Asymptotic limit of the two kink solution of the sine-gordon equation

I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as: ...
3
votes
0answers
73 views

Divergence calculation of a lie algebra valued quantity having spinor indices

I am reading this paper by E. Weinberg - Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups. I am having a problem with a calculation. I don't have much experience ...
2
votes
0answers
24 views

Some question about symplectic transformation

I read Arnold's book Mathematical Methods of Classical Mechanics and come across with three problems in page 229. 1.Let $\lambda$ and $\bar{\lambda}$ be simple (multiplicity 1) eigenvalues of a ...
2
votes
0answers
77 views

Solving the Schrodinger equation with appropriate symmetry

In the paper Markov Fields by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger ...
2
votes
0answers
31 views

Lie algebra and BPS stats

i would know what is a charges Lattice and the relationship between it and roots lattice ? and if there is relationship between mutation of quiver and weyl group? and how the PBS stats correspond ...
2
votes
0answers
33 views

Solutions of PDEs in different coordinate systems

Suppose we have a PDE, for example the Helmholtz paraxial equation: $$ \nabla_\perp^2A+2ik\frac{\partial A}{\partial z}=0 $$ Solutions depend on the coordinate system we are using, i.e. we obtain ...
2
votes
0answers
34 views

Are there any systems in physics which can only be formulated as an integral equation?

My question is are there any systems in physics that can only be formulated as an integral equation? Or do all integral equations have an equivalent differential equation?
2
votes
0answers
63 views

Is the algebra of a differential equation invariant under transformation?

I've found that the algebra of this differential equation $$\frac{d^2y}{dz^2}-(3z^2+\gamma)\frac{dy}{dz}+(cz+\alpha)y=0$$ is in $sl(2)$ because it is possible to use the generators of the $sl(2)$ ...
2
votes
0answers
56 views

Understanding the algebra associated with an implicit potential

In the paper here(page 7-8) the authors make a claim that the Natanzon potential (an implicit potential) follows an $SO(2,2)$ algebra. This potential defined as : $$ U(z(r)) = ...
2
votes
0answers
81 views

Does the success of canonical quantization guarantee the path integral works too?

If the canonical quantization approach to a field theory is successful, is it a good indicator that the path integral will work as well? Furthermore, can the success of a particular quantization ...
2
votes
0answers
64 views

A question about polarization in quantum mechanics

We start our question we a definition A subbundle $P\subset TM^{\mathbf{C}}$ of the complexified tangent bundle is called a complex polarization if \ $P$ is Lagrangian P involutive dim$P\cap\bar ...
2
votes
0answers
100 views

Mathematical form of chemical potential difference and entropy production

I'm trying to understand the form of the 'force' which drives chemical reactions, ie. the difference in chemical potential, also sometimes called the 'affinity'. $$\Delta \mu = - kT ln ...