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18
votes
5answers
1k views

Companion to theoretical physics for working mathematicians

In the Princeton Companion to Mathematics one reads that even pure mathematicians should know some theoretical physics and applied mathematics. What are some well-organized comprehensive companions to ...
8
votes
2answers
277 views

What is the BRST-anti-BRST formalism?

What is the BRST-anti-BRST formalism? Is the Sp(2) doublet the ghost, antighost pair? Introductory accounts of this subject seem to be hard to find. I would appreciate a reference for someone who ...
1
vote
0answers
51 views

Interpretation for a condition in fluid dynamics

I have been working with some mathematical models in biology and fluid mechanics. My problem is about the interpretation of a condition that I found for a vector representing the velocity of a fluid. ...
24
votes
2answers
1k views

When exactly and why matrix multiplication became a part of undergraduate curriculum?

The story about Heisenberg inventing matrices and matrix multiplication in 1925 is very well known and well documented. Few weeks later Born and Jordan picked this and recognized the matrix ...
0
votes
1answer
57 views

A hyperbolic partial differential equation (wave-like) with variable-dependent coefficient and possibly singular in one variable

First, I beg your pardon since the title of the question is a bit confusing I guess. I'm working on a physical equation of the wave-like form. Explicitly, it reads ...
-2
votes
1answer
88 views

What are the formula of representation of quasicrystals and the law or mechanism of the formation [closed]

I vaguely recall that formula of representation of quasicrystals is relevant to tiling plane,and tiling plane without period is relevant to recursiveness, and do not know the mechanism or physics ...
4
votes
1answer
176 views

Sites for seeking possible collaborations

As a material scientist, I have recently constructed algorithms for solving ground state of arbitrary cluster interactions models and prepared publications in the field of physics and material ...
2
votes
2answers
242 views

Gauge-theoretic formulation of Maxwell equations [duplicate]

Does any one know how to write the Maxwell equations as an equation on a principal $U(1)$-bundle? In Freed & Uhlenbeck's Instantons and Four manifolds, the authors claim that the Maxwell ...
3
votes
1answer
396 views

Helmholtz equation Poynting vector integral

The Maxwell's equation for harmonic time dependent field in vacuum is \begin{align} \nabla \times B + i\omega E &= 0\\ \nabla \times E - i\omega B &= 0 \\ \nabla \cdot B &= 0 \\ \nabla ...
6
votes
5answers
2k views

Optical methods for number theory?

I found a paper: 'A New Method of Finding the Distribution of Prime Number', saying We stack discs and annuluses with certain rules then turn on the light to illuminate. The projection of ...
4
votes
2answers
236 views

Analytic solution of a system of linear, hyperbolic, first order, partial differential equations

In a try to solve a physical problem, I've faced a system of first-order partial differential equations of the form ...
0
votes
0answers
90 views

Geometric interpretation of table with permutations and inversions

Let $T(n,k)$ is the number of permutations of numbers $1, ..., n$ and each of the permutations has $k$ inversions. We can consider a table for $T(n,k)$ for some $n$ and $k$. For eg. $n=1,...,6$, ...
2
votes
0answers
83 views

Diffusion equation on mixing of diffusing particles

I am trying to study mixing of diffusing particles like it was done by E. Ben-Naim On the Mixing of Diffusing Particles. The picture below shows the idea how permutations and inversion numbers reflect ...
71
votes
2answers
106k views

Perfectly centered break of a perfectly aligned pool ball rack

Imagine the beginning of a game of pool, you have 16 balls, 15 of them in a triangle <| and 1 of them being the cue ball off to the left of that triangle. Imagine that the rack (the 15 balls in a ...
11
votes
4answers
944 views

Can the equation of motion with friction be written as Euler-Lagrange equation, and does it have a quantum version?

My (non-expert) impression is that many physically important equations of motion can be obtained as Euler-Lagrange equations. For example in quantum fields theories and in quantum mechanics quantum ...
3
votes
1answer
303 views

A particular contour integral

Mathoverflow, I'd like to carry out the following integral, $$f(t) = \int_{- \infty}^{\infty}\frac{-i\Omega e^{i \Omega t}}{1-\sqrt{-i\Omega}\coth(\sqrt{-i\Omega})} d\Omega.$$ Here's what I've ...
3
votes
1answer
330 views

Path integrals for stochastic equations

Does there exist a rigorous mathematical proof for path integral representations given in the physics literature? See for example http://arxiv.org/abs/hep-ph/9912209v1 For imaginary time rigorous ...
2
votes
0answers
86 views

The condition of maximality in branching rules of $SO$ group representations

Let the highest weight of a $SO(2n+1)$ representation be given as $(m_1,m_2,...,m_n)$ ($m_1\geq m_2 \geq .. \geq m_n \geq 0$) and the highest weight of a $SO(2n)$ representation be $(s_1,s_2,...,s_n)$ ...
4
votes
1answer
321 views

About using the character formula for $SO(2n)$.

I have known of the following equation for characters of a $SO(2n)$ representation with highest weights $(h_1,...,h_n)$ and for $(t_1,t_2,..,t_n,t_1^{-1},t_2^{-1},..,t_n^{-1})$ being the eigenvalues ...
3
votes
0answers
266 views

In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play? [closed]

I've asked this question on Physics.SE but was advised to ask it here. Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is ...
7
votes
1answer
373 views

A question on chiral rings and geometry of the vacuum bundle

I am reading "Mirror Symmetry" by Hori et al, and have a question on Chap.17 (Chiral rings and geometry of the vacuum bundle). On p.425 the authors say Consider the path-integral on the ...
15
votes
3answers
487 views

An algebraic approach to the thermodynamic limit $N\rightarrow\infty$?

In physics one studies quite often the thermodynamic limit or what we call the $N\rightarrow \infty$ behavior of a system of $N\rightarrow\infty$ particles. This is of particular relevance in the ...
8
votes
1answer
404 views

Dimensional regularization in odd dimensions

I am not quite sure that my question below is appropriate for this site, probably it should be addressed to the physical commutity. But I hope that some (mathematical) physicists do attend MO. I have ...
3
votes
0answers
109 views

What is the relationship between complex time singularities and UV fixed points?

In this paper it is described how the turbulent kinetic energy spectrum and the flatness (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of ...
23
votes
6answers
4k views

Explanations for mathematicians, about the falsifiability (or not) of string theory [closed]

Like many other mathematicians, I think string theory very attractive. This theory has wonderfully influenced many new topics in mathematics (I myself have worked on one of them), but it's not the ...
2
votes
1answer
694 views

Derivation of Bessel functions

I am writing a summary on a work on Fluid Dynamics that develops irrotational flow states that appear to interact amongst each other according to the equations of Electromagnetism ...
1
vote
1answer
595 views

What is the “fundamental theorem of invariant theory” ?

The basic question I guess can be formulated as - given two integers $N_f$ and $N_c$ what are the ways in which the fundamental and the anti-fundamental representations of $U(N_f)$ be combined to get ...
9
votes
3answers
832 views

Is there an observer dependent mathematics? [closed]

Is there any field of mathematics that deals with the role of the observer? E.g., some formulation in which a set is changed, in some unspecified way, when it is observed? Or maybe some philosophy of ...
3
votes
1answer
130 views

Three body problem with point interactions

I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials). Is ...
0
votes
2answers
459 views

Deriving the Mercator projection algorithm

The standard model of Mercator projection shows a cylinder wrapped around a spherical earth eg Wiki. Many sites describe the resulting square map like this: "...spherical Mercator maps use an extent ...
2
votes
2answers
304 views

Translation of an article

I need to read this article "On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups" authors:G.Zhislin, A. ...
3
votes
1answer
242 views

Solvable models in quantum mechanics

Is there anyone who studied on the book "Solvable Models In Quantum Mechanics" by Albeverio? I don't succed in understanding the proof of page 116 about the eigenvalues of the Hamiltonian with point ...
1
vote
1answer
324 views

Proof of generalized Cauchy formula

I would like to know if there is a proof for the identity used in the superconformal index of 4d ${\cal N}=2$ gauge theory. In the paper by Rastelli el al, it was discovered that Eq. (10) is equal to ...
11
votes
2answers
597 views

What do correlation functions compute in CFT?

I would like to understand what correlation functions compute in Conformal Field Theory in mathematics. Let me begin with basic definitions. We define a free boson field $\phi(z)$ as a formal power ...
5
votes
2answers
436 views

Permuting Racked Pool Balls with a Single Break

Given reasonable physical assumptions (on friction, collisions, etc.), would it be possible to "break" in a pool game such that when all the balls come to rest, the only difference is that the racked ...
0
votes
1answer
97 views

orthotropic materials solution of boundary value problems

What are the methods or approaches for the analytical solutions of boundary value problems in the theory of elasticity for orthotropic materials?
5
votes
2answers
946 views

Homotopy $\pi_4(SU(2))=Z_2$

I am a physics student, recently I read a paper using Homotopy $\pi_4(SU(2))=Z_2$, I guess mathematicians have some visualization or explanation of this result. So I come here ask for help. ...
4
votes
1answer
460 views

Impact of LHC on math ? [closed]

LHC (Large Hadron Collider) "... remains one of the largest and most complex experimental facilities ever built". May be it is even the most complex project in humankind's history(?). Such projects ...
1
vote
1answer
417 views

David Hilbert on Complex Multiplication [closed]

I have tried vainly to understand the significance of the following statement attributed to David Hilbert: The theory of complex multiplication is not only the most beautiful part of mathematics ...
1
vote
0answers
267 views

Distribution of random vectors

Two positive numbers $\alpha$ and $\beta$ are given. We are going to describe a process of choosing a random vector on the unit sphere $S$ in $\mathbb R^3$ (given by $x^2+y^2+z^2=1$). A vector $u\in ...
2
votes
4answers
532 views

Higgs mechanism from a deformation quantization point of view

Is it possible to describe the Higgs mechanism from a deformation quantization point of view? How would one do it? Are there aspects of the Higgs mechanism and Higgs particle which one may see clearer ...
6
votes
2answers
695 views

Quantum mechanics basics [closed]

Hello. I'm thinking about where does the basic quantum mechanics things comes from. I mean the forms of operators and a Shroedinger equation. The more intuitive explanation is better. To get forms of ...
0
votes
1answer
328 views

Why is the physical space equivalent to $\mathbb{R}^3$ [closed]

I am trying to understand what would be the logical reasons behind our assumption that our physical space is equivalent to $\mathbb{R}^3$ or 'physical straight line' is equivalent to $\mathbb{R}$. ...
7
votes
1answer
2k views

What is the current state of the mathematics of Higgs fields?

Topical. I know there are good mathematical theories in which "Higgs" is used, in a geometrical sense. Would someone care to explain? To clarify, I'd like to know about Higgs bundles on Riemann ...
0
votes
1answer
283 views

How the spin value is related to mathematical nature of the field?

Fields are one of the following: scalars, vectors, spinors or some Lie algebra elements, right? And it's often said that scalars are spin-0 and vectors are spin-1. So, what's idea of correspondence ...
3
votes
3answers
605 views

Best book for learning sensor fusion, specifically regarding IMU and GPS integration.

I have posted this in MathOverflow because the subject is primarily Math related. I have a requirement of building an Inertial Measurement Unit (IMU) from the following sensors: Accelerometer ...
1
vote
0answers
227 views

Bosonic String Theory

I would like clarification of 26 dimensional Bosonic String Theory. A definition would be, that this is free bosons compactified on a torus and orbifolded by a 2-point reflection group (or ...
9
votes
1answer
980 views

Self-tightening knot

Is there a way, for some finite L>1, to tie two pieces of rope together, such that any finite force is not enough to pull them apart? The type of rope I have in mind is something like cylindrical ...
0
votes
0answers
215 views

Simple question on the foundations of spin foam formalism

To make it simple, take the spin foam formalism of ($SU(2)$) 3D gravity. My question is about the choice of the data that will replace the (smoothly defined) fields $e$ (the triad) and $\omega$ (the ...
4
votes
1answer
710 views

Minimize Energy for Charge Distributions

I am considering [positive] charge distributions $\rho:M\rightarrow\mathbb{R}_+$ (nonnegative reals) with unit charge $\int_M\rho=1$ for convenience. Here $M$ is a nice-enough region, say a ...