Questions tagged [mathematical-physics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

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20 views

SUSY and free Majorana field theory

Given a free Majorana field theory in $D$ spacetime dimension. Say $D=2$ to $10$. Question: Which $D$ spacetime dimension,do we have a free Majorana field theory with Majorana spinor in the real ...
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D-brane, and SUSY charges

The following results summarize the relation between orientifold and D-brane, and SUSY charge $$ \begin{array}{l||c|c|c|c|c|c}\text{orientifold} &\text{O4} & \text{O3} & \text{O2} &\...
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String theory allows chiral gauge coupling

In Polchinski String Vol 1: Chiral gauge couplings. The gauge interactions in nature are parity asymmetric (chiral). This has been a stumbling block for a number of previous unifying ideas: they ...
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Supersymmetry $\mathcal{N}$ constrained by spacetime dimensions $D$

Given some spacetime dimensions $D$, are there only certain allowed supersymmetry charge nunbers $\mathcal{N}$? What are the relations of $\mathcal{N}$ and $D$ for the following cases: When the ...
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Does one ever need infinitely many cohomologies?

In a theory containing gauge fields or higher-form gauge fields, if the background spacetime is a complicated manifold, a nice way to represent the configuration of the gauge field mathematically is ...
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How is topology related to physics?

Topology has many occurences in physics like topological insulators, topological quantum computing etc. But what is confusing me is that topology is this mathematical theory that studies the behaviour ...
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1answer
18 views

Permissible Electrostatic Potential

Let us consider a $1D$ real function $V(x)$. When is this a classical electrostatic potential? My take on the problem: $V(x)$ must be differentiable everywhere. In fact, we should be able to ...
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Time derivative of path ordered monodromy matrix

I am currently gettting familiar with integrably systems and came the following statement in my literature: $U=U(x,\lambda,t)$ some matrix (Lax component) we define $$T(\lambda,t) = \mathcal{P} \exp \...
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Resonant and non-resonant tori density in non-degenerate system

I'm following the discussion on the page 290 of Mathematical Methods of Classical Mechanics by V. I. Arnol'd (you can download it here), and I've encountered the fact that in a nondegenerate system, ...
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Is Hermann Weyl's book “Space, Time, Matter” (1923) on General Relativity still relevant? [closed]

I really liked Hermann Weyl's mathematical books and would like to get accustomed to general relativity from his perspective, but wonder if it's still relevant after almost 100 (!) years? Can book be ...
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If you can simulate logic with math, and simulate math with logic, what came first? [closed]

If you can simulate logic with math and simulate math with logic, which came first? if 2 + 2 = 4 it is made up of logical rules. but an if-else can also be simulated by math. In other words, is the ...
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Supersymmetry v.s. BRST symmetry: QFT examples

Questions: Can any expert contrast the differences and similarities of Supersymmetry (SUSY) v.s. BRST (global) symmetry? (Question 1) What are the RULES and CRITERIA that having one symmetry implies ...
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Treating the delta potential in a Schroedinger equation in 1D

It is a standard problem in quantum mechanics. For the equation $$ -\psi'' + g \delta(x) \psi = E \psi ,$$ we integrate from $-\epsilon$ to $+\epsilon$ and thus get the boundary condition $$ g \psi(0) ...
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WHY BRST formulation works: Conditions imposed on QFT to find (how many) BRST parameters

question: WHY BRST formulation works? In more details: What are the conditions we need to impose on QFT to find the BRST (global) symmetry? Why can we demand the BRST parameter $\epsilon$ directly ...
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Which Osterwalder-Schrader axiom does a tree-level QFT violate?

(I think this question is really about any truncation of the perturbation series, but I want to avoid having to think hard, so I'll talk about tree-level only to ask the question.) Let's start with ...
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Issue in asymptotic expansion of Bogoliubov coefficients in Hawking 1975 paper

$p_{\omega}^{(2)}$ is given by $$\frac{1}{\sqrt{2\pi\omega}}\frac{1}{r}P_{\omega}^-\exp{\Bigg(-i\frac{\omega}{\kappa}}\bigg(\log\Big(\frac{v_0-v}{CD}\Big)\bigg)\Bigg)$$ this expression is valid for $...
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What is the analogue for symplectic structure in case of spin variables?

According to some (e.g. Haroche and Raimond in Exploring the quantum: atoms, cavities and photons), the quantum world consists (mainly) of spins and harmonic oscillators. For harmonic oscillators (i.e....
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Translationally invariant Gibbs state

In Velenik's Statistical Mechanics of Lattice Systems, Exercise 6.22 claims that if $\pi =\{ \pi_\Lambda:\Lambda \Subset\mathbb{Z}^d\}$ is a translationally invariant specification with nonempty Gibbs ...
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49 views

2D Ising model and FK-percolation

Consider the 2D Ising model on the finite lattice $\Lambda$ with $+$ boundary conditions, i.e., all spins outside of $\Lambda$ are $=+1$. Let $\mathscr{E}_\Lambda^b$ denote the edges in $\Lambda$ and ...
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Why is the local density of states related to the retarded Green function?

Consider a Hamiltonian $H$ acting on the single-particle Hilbert space $\mathscr{H}$ representing lattice sites, i.e., $|r\rangle$ forms an orthonormal basis of $\mathscr{H}$ where $r$ ranges over ...
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Are Chern-Simons theories classified by bordism groups?

For a long time it was thought that anomalies for a group $G$ were classified by $H^n(BG)$, although it is now understood that they are in fact classified by $\Omega^n(BG)$. On the other hand, ...
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Understanding the Issues of the Feynman Path Integral

Let us assume we live on Euclidean $\mathbb{R}^d$ and consider the normalized partition function \begin{equation} \begin{aligned} Z : D &\to \mathbb{R} \\ J &\mapsto \frac{\int \exp \left[ -S \...
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Why are Lagrangians linear in $\dot{q}$ so ubiquitous? Gauge theory, Berry phase, Dirac Equation, and more

It seems to me that we encounter first-order equations of motion in some very special situations in physics. It is not clear to me what the connection is, and I am hoping to get some insight into what ...
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Problems with this alternative definition of dual space in QM?

This question came up during discussions with my friends in QM, and they asked me this question I couldn't answer. Mathematically, the dual vector space $V^*$ of a vector space $V$ is defined as the ...
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References for topological strings on supermanifolds

This question concerns topological string theory. It was known sice its outset, that the BRST-cohomology ("the ring of observables") of the weakly coupled B-model topological string on a ...
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How to calculate resolution given sampling rate/size?

In a research paper documenting the analog to digital conversion process of an experiment’s radio receiver, the following is written: The station consists of 10 channels. Each channel writes 1 ...
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56 views

Effect of spectral flow on representations of a CFT

In this paper titled Spectral flow and conformal blocks in $AdS_3$ the authors states (See paragraph 2 on page 2), For WZNW models based on compact Lie groups, the spectral flow maps primary states ...
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1answer
54 views

Amount of heat emitted from the Sun by radiation

Supposing that the condition of humidity and the temperature are the same. Concretely if in one place on Earth there is the same humidity, temperature, it is more hot in the first part of the summer ...
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103 views

Why is the sequence of limits $\lim\limits_{V\to\infty}\lim\limits_{B\to 0}m(B,V)$ when reversed does not give the same result?

For spontaneous magnetization $m$ in a sample of volume $V$, what do the limiting operations $$ \lim\limits_{V\to\infty}\lim\limits_{B\to 0}m(B,V)=0,\\ \lim\limits_{B\to 0}\lim\limits_{V\to\infty}m(B,...
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What is known about the density of states of the Anderson model?

This question was posted a week ago on MathOverflow without an answer: https://mathoverflow.net/questions/369156/what-is-known-about-the-density-of-states-for-the-anderson-model The Anderson Model is ...
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Inferring angle of source?

Given the relative distance of 3 radio antennae, I want to infer an incident angle for some radio source seen by all 3 antennae, which I know to be on the ground. All I know is the relative locations ...
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A rigorous definition of operator exponential in QM?

In the Quantum Mechanics course I took, we defined the operator exponential simply as $$ \mathrm{e}^{\hat A} = \sum_{n=0}^\infty \frac{1}{n!} \hat A^n \: . $$ This is probably a good definition for ...
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What Operator is the Superconformal Index Counting?

Given a differential operator $\mathcal{D}$ with adjoint $\mathcal{D}^\dagger$, the index of $\mathcal{D}$ is usually defined (mathematically) by $$\text{ind }\mathcal{D}=\dim\ker\mathcal{D}-\dim\ker\...
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What is best book on self-adjoint extensions?

I need to understand self-adjoint extensions in quantum mechanics to solve some problems of scattering and bound states in Aharonov-Bohm potentials. There are some referencies that present the math ...
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60 views

Motivation and advantage of C$^*$-algebra formulation of quantum statistical mechanics

I am studying C$^*$-algebras and the formulation of quantum statistical mechanics by them, mostly from the book by Bratteli and Robinson Operator Algebras and Quantum Statistical Mechanics. I could ...
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83 views

If $\nabla\times\nabla\times\mathbf{F}$ = 0, then what can we conclude about $\nabla\times \mathbf{F} $, where $\mathbf{F}$ is a vector field? [closed]

If $\nabla\times\nabla\times \mathbf{F} = 0$, then can we say that $\nabla\times \mathbf{F} = 0$? If yes, then how to prove it?
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Physical interpretation of TFTs

1. Defining TFTs Let $n$ be a positive integer and $\mathbb k$ be a field. In my lecture I was introduced to TFTs using the following definition going back to Atiyah (around 1988): A $n$-dimensional, ...
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Hopf algebras vs Fusion categories for topological order

Disclaimer: Before I begin with the question I want to warn that some people would argue that it is a math question and not a physics question. However, it finds it origins in the study of topological ...
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28 views

Spin frame bundle and Orthogonal frame bundle

I was trying to understand the ACTIVE transformation (rotation) of spin states in terms of group action on orthogonal frame bundle. As we know, there exist a lie group homomorphism $ \rho : {\rm Spin}...
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302 views

Approaching physics using ordinary analysis rather than nonstandard analysis

As far as I know, in physics, calculus is approached using nonstandard analysis in which $dx$, $dy$, etc. (infinitesimals) are treated as fixed, extremely small quantities rather than the standard ...
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Correspondence between mathematician's and physicist's vertex operator algebra (VOA)

I have some conceptual doubts to clear up, in terms of piecing together what we learn of a vertex operator algebra (VOA) in conformal field theory, and how it is defined by a mathematician, say from ...
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Constitutive relations and strain energy in finite strain viscoelastic solid mechanics

I'm an applied math graduate student, and my research is straying into hyperviscoelastic models of materials. I've had trouble finding an answer to this question I have about the mathematical theory ...
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37 views

Physical significance of iterating spherical bessel functions with itself

When solving the Schrodinger equation for a nucleus, e.g. infinite spherical well problem, the eigenfunctions are of the form $\Psi(r,θ,ϕ)=R(r)Y_{l,m}(θ,ϕ)$, where the $Y_{l,m}$'s are the usual ...
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Mathematical vs Theoretical Physics [closed]

I'm pursuing a MSc in Mathematical Physics, but I wanted to know whether it is relatable with the Theoretical Physics domain. I know the difference between those too, but I do not want to limit myself ...
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Can branes in string theory be described by different systems of mathematics or logic?

Mathematically, in string theory, branes can be described using the notion of a category and the mathematical category theory says that logic can change from one category to another. We can build ...
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Suppose I give you $2^N$ functions that are eigenvectors of a fermionic $H$. How do I determine which function describes which spin configuration?

Consider the hamiltonian $$ H = - \frac{1}{2} \nabla^2 + V. $$ The potential $V : (\mathbb{R^3})^N \to \mathbb{R}$ is symmetric, so for each eigenvalue, there is an antisymmetric eigenvector. There is ...
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What is the solid angle $d\Omega$ in radiative transfer?

The Wikipedia article for radiative transfer gives the following definition: In terms of the spectral radiance, $I_{\nu }$, the energy flowing across an area element of area $da$, located at $\mathbf{...
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Difference between stationary and non-stationary radiative transfer?

I am currently studying radiative transfer. In researching this subject, I found that there is stationary radiative transfer and non-stationary radiative transfer. However, it is not clear what the ...
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1answer
47 views

Solution set: Mathetmatical Methods For Physics [closed]

Recently, I had a good start with H.W. Wyld on mathematical methods for Physics and now looking forward to ask whether is there any solutions available for the problems given at the end of each ...
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47 views

Physics that calls for deeply nested Lie/Poisson brackets

I've been scouring physics for non-associative situations, particularly where study of quasigroups and loops might come in handy (they always seem to be left out). The poisson and lie brackets form a ...

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