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3
votes
1answer
88 views

Two point function of a free scalar field in Euclidean space-time

This question was previously asked here http://physics.stackexchange.com/questions/251927/two-point-function-of-a-free-massless-scalar-field-in-euclidean-space-time though I did not get there an ...
3
votes
1answer
403 views

origin of analogy “primes as the atoms of number theory/ arithmetic”

a math student recently challenged me on the old comparison/ analogy of prime numbers to "the atoms of number theory or arithmetic" and then was wondering the origin of the phrase. where does this ...
2
votes
0answers
44 views

Conserved quantities for the Cauchy momentum equation

I apologize if this question is too elementary for mathoverflow; I asked it (unsuccessfully) on MATH.SE first. As a bit of background: one way to study the mechanics of deformation of a continuous ...
22
votes
6answers
2k views

Number theory and physics

I was following some lectures by Edward Frenkel about Langlands correspondence. He was describing some analogies between number theory and theoretical physics (Mirror symmetry). At some point ( my ...
88
votes
26answers
19k views

A soft introduction to physics for mathematicians who don't know the first thing about physics

There have been similar questions on mathoverflow, but the answers always gave some advanced introduction to the mathematics of quantum field theory, or string theory and so forth. While those may be ...
8
votes
2answers
1k 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. ...
0
votes
0answers
63 views

Looking for A. J. Tolland's exposition of non-renormalizability [duplicate]

In the MathOverFlow thread "Mathematical explanation of the failure to quantize gravity naively" there are references to "A.J. Tolland's very nice exposition of nonrenormalizability". However, ...
1
vote
0answers
76 views

On Different Ways of Proving Isoperimetric Inequalities [closed]

Update: Thanks to Douglas Zare's comment, My previous questions in this thread turned out to be equivalent to the Isoperimetric problem. Thus I edited my question to make it a bit different. ...
8
votes
1answer
432 views

Mathematics of Chiral Rings

Let $A$ be a graded vector space, and suppose that two commuting differentials $d_1$ and $d_2$ of degree +1 act on $A$, such that $A$ equipped with either is a chain complex. We now construct $C(A)$, ...
5
votes
1answer
125 views

Generating Functional for the Dirac Field, equivalence of expressions

As with the Klein-Gordon field, we can alternatively derive the Feynman rules with the free Dirac theory by means of a generating functional. In analogy with the scalar field theory where $Z[J]$ is ...
0
votes
1answer
66 views

Computational Physics or Pure Math Modules for Theoretical Physics [closed]

I'm beginning my university course in Theoretical Physics next week and we have been asked to choose our modules. We have compulsory modules in Physics, Vector Algebra and Dynamics. But we also have ...
14
votes
5answers
2k 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 ...
4
votes
0answers
247 views

Unusual generalization of the law of large numbers

I have seen in physical literature an example of application of a very unusual form of the law of large numbers. I would like to understand how legitimate is the use of it, whether there are ...
14
votes
3answers
2k views

Applications of set theory in physics

In the introduction of the paper "Links between physics and set theory", the following quote of Eris Chric is stated: "Set theory perhaps is too important to be left just to ...
4
votes
1answer
142 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. ...
4
votes
1answer
163 views

reference for higher spin - not gravitational nor stringy

Other than the papers of Berends, Burgers and van Dam, are there any papers that study the general case of deforming a free field theory with higher spin fields to be interactive?
8
votes
0answers
95 views

Approximation of the effective resistance on Cayley graph

Let $\Gamma$ be a finitely generated group, and denote by $G$ the Cayley graph of $\Gamma$. Denote by $d_R$ the resistance distance metric on this graph. The resistance distance metric between the ...
33
votes
7answers
4k 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 ...
15
votes
5answers
3k views

Flux through a Mobius strip

A friend of mine asked me what is the flux of the electric field (or any vector field like $$ \vec r=(x,y,z)\mapsto \frac{\vec r}{|r|^3} $$ where $|r|=(x^2+y^2+z^2)^{1/2}$) through a Mobius strip. It ...
8
votes
2answers
446 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 ...
26
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
100 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 ...
3
votes
3answers
1k views

Mathematical definition of running [closed]

This will be a tad hard to explain, so bear with me. Taking into account only the legs what would be an accurate definition of the position of the upper legs, lower legs and feet with respect to time? ...
3
votes
1answer
484 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 ...
-2
votes
1answer
102 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
194 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 ...
4
votes
2answers
408 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 ...
1
vote
0answers
3k views

What is the geometric meaning of the third derivative of a function at a point? [closed]

What is the geometric meaning of the third derivative of a function at a point? This question is now asked on the sister site: ...
4
votes
2answers
3k views

Something like mathoverflow in other sciences [closed]

Are the sites similar to mathoverflow in other sciences related to mathematics? statistics, computer science, physics, economics, etc? Let me explain what I mean by "similar": those are sites devoted ...
7
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
544 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
107 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
104 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 ...
79
votes
2answers
109k 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 ...
12
votes
9answers
2k views

Newton equations, second order equation and (im)possible motions

I am am currently studying Newtonian mechanics from a conceptional and axiomatic point of view. Now, if I am not mistaken, one (but surely not all) statement of Newtons second law about nature is, ...
26
votes
3answers
2k views

How can simple physical “proofs” of mathematical facts be made rigorous?

Mark Levi's The Mathematical Mechanic is a book of examples of how physical reasoning can be used to solve mathematical problems; another couple of examples is in this blog post at Concrete Nonsense. ...
3
votes
1answer
375 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 ...
83
votes
3answers
6k views

Has the Lie group E8 really been detected experimentally?

A few months ago there were several math talks about how the Lie group E8 had been detected in some physics experiment. I recently looked up the original paper where this was announced, "Quantum ...
3
votes
1answer
415 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 ...
4
votes
1answer
363 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 ...
2
votes
0answers
97 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 $(s_1,s_2,...,s_n)$ ...
0
votes
2answers
683 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 ...
3
votes
0answers
347 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
420 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
531 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
646 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
118 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 ...
25
votes
6answers
5k 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
1k 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 ...
2
votes
1answer
802 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 ...