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 The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics ...

learn more… | top users | synonyms

2
votes
1answer
199 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
2
votes
1answer
111 views

Causality and operationalism: from sets and functions to monads

When working in a laboratory, the most basic behaviour is to turn a knob or dial and then see a transformation of some data output. An example is increasing a magnetic field and seeing Zeeman ...
1
vote
1answer
31 views

Formula relating sum of values of a function to its integral

I came across the above formula in some quantum mechanics lecture notes explaining the Casimir effect. Anyone seen it before if so could you please tell me its 'name'. B refers to the Bernoulli ...
1
vote
1answer
230 views

What is the relationship between completeness of wave functions and completeness of Hilbert space?

In the lecture, my prof said that completeness means that any wave function can be constructed using an infinite number of "other" basis wave functions. This is very intuitive since this is nothing ...
-1
votes
1answer
88 views

What kind mathematical Transformation is this?

$$\int f(\alpha)e^{\alpha^*y-z|\alpha|^2}\pi^{-1}~\mathrm d^2\alpha~=~z^{-1}f(z^{-1}y)$$ I am doing the problem of finding Wigner function for fock states given by the exercise problem from ...
13
votes
0answers
469 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 ...
10
votes
0answers
172 views

Reading differential forms

When, usually in text of physics or concerning thermodynamical aspects of chemistry, I find notations such as$$\mathrm{d}f=g\,\mathrm{d}t$$ I always interpretate it as $\frac{\mathrm{d}f(t)}{\mathrm{d}...
9
votes
0answers
67 views

Experimental Hopf fibrations

Recently I read a paper where the authors experimentally constructed a Hopf fibration - that is, they created a quantum system where the nematic vector field of the system had a non-zero Hopf ...
4
votes
0answers
53 views

Solutions of nonlinear systems invariant wrt. perturbations (looking for applications)

I want to ask if the following purely mathematical problem (that I'm working on) might have some applications to physics. The problem in a nutshell: describe properties of solution sets of real ...
4
votes
0answers
145 views

Recent missed opportunities à la Freeman Dyson

There is an excellent paper by Freeman Dyson from 1972 (here) and therein the author cites old talks by Hilbert (here) and Minkowski (chapter 2 here) speaking about similar topics, namely how ...
3
votes
0answers
55 views

Scalar product of torsional forms - how are the standard identities modified?

It is known that for any smooth, orientable, compact manifold $X$ without boundary and $\alpha \in \Omega^{r}(X), \beta \in \Omega^{r-1}(X)$ it holds \begin{equation} (d\beta,\alpha)= (\beta, d^{\...
3
votes
0answers
259 views

What are the topics of string theory that are comprehensible with only a mathematical background on Manifolds and Algebraic Topology?

What are the topics of string theory that are comprehensible with only a mathematical background on manifolds and algebraic topology? Also, I have read only the first four chapters in Peskin & ...
3
votes
0answers
856 views

How do I derive the critical temperature for bose condensation in two dimensions?

In class we derived the 3D case, but there's a step I don't understand: $$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...
2
votes
0answers
108 views

Convert discrete sum to principal integral

I'm studying IQHE beginning with Laughlin's famous gauge argument. I referred to his Nobel Lecture, in which he mentioned a paper that enlightened him. It is Phys.Rev.B.23.5632(1981) which talked ...
2
votes
0answers
102 views

Questions about closed forms and cycles

I read the section closed forms and cycles in Arnold's Mathematical Methods of Classical Mechanics (page 196-200), but the problems in this section is too difficult to solve in the way following the ...
2
votes
0answers
264 views

Modeling Syringes e.g. with the ideal gas law

Gentlemen I have a similar yet very practical problem that might provide further insight. I'm trying to model a moving plunger in a syringe (something like a piston in a cylinder). At time zero the ...
2
votes
0answers
162 views

On “the geometry of free fall and light propagation” paper by Ehlers

In the paper The geometry of free fall and light propagation by Ehlers and his colleagues (Gen. Relativ. Gravit. 44 no. 6, pp. 1587–1609 (2012)), I reach to an axiom which says: There exists a ...
2
votes
0answers
312 views

How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?

Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
2
votes
0answers
392 views

A solvable model for the finite rectangular potential well with a bump in the middle

A well known example in quantum mechanics is that of a finite rectangular potential well with a rectangular bump in the middle. I guess this closely approximates the "umbrella" effect of the $NH_3$ ...
2
votes
0answers
373 views

A question about Dirac operator

The Dirac operator at 2 dimension can be written as $$ D=\sum_{k=1,2}\sigma^{k}D_{k}=\left( \begin{array}{cc} 0 & \partial_{x}-i\partial_{y}-i(A_x-iA_y)\\ \partial_{x}+i\partial_{y}-i(A_x+...
1
vote
0answers
61 views

Why is this differential added instead of subtracted?

I was looking at a derivation of the Barometric formula which reads like this: Consider a flat disc of air of mass $\mathrm{d}m$ at distance $h$ above the ground of mass $\mathrm{d}m$ and ...
1
vote
0answers
42 views

Given a dimension of a known object in the image, how can we calculate the dimension of other objects in the same image ?

The question considers a very specific scenario in which we have an image with let us say, two rectangle objects. We know width and height of one object. How can we calculate the dimensions of the ...
1
vote
0answers
31 views

Mathieu equation and instabilities

Consider the Mathieu equation $$ \tag 1 y'' + (A -2q\cos(2t))y = 0, $$ How does it provide instabilities for small $q << 1, A > q$? I don't understand this because as the result of ...
1
vote
0answers
87 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
1
vote
0answers
55 views

Gauge invariance and non-commuting second derivatives

I'm currently doing a homework assignment in relativistic quantum mechanics, and one of the problems involves proving the gauge invariance of a particular lagrangian. The problem is really quite ...
1
vote
0answers
62 views

Solving inhomogeneous Stokes equation

I want to solve the Stokes inhomogeneous equation, i.e. $$\nabla^2 \vec v -\nabla P = \vec f(r,\theta)$$ $$\nabla\cdot\vec v=0$$ where $\vec f$ is irrotational, i.e. $\partial_y f_x - \partial_x ...
1
vote
0answers
57 views

Simple math used for physics

I read the book "Analysis 1" by Harro Heuser about calculus and it several interesting chapters about applications of mathematics for physics. For example there was one part of the chapter, which ...
1
vote
0answers
54 views

Translation symmetry and Cauchy products

I often meet the following situation: $$\sum\limits_{n=0} ^\infty \sum\limits_{k=0} ^n f(k)g(n-k)=\sum\limits_{p=0} ^\infty \sum\limits_{q=0}^\infty f(p)g(q)$$ While intuitively this is very clear ...
1
vote
0answers
242 views

How simplify functional derivatives (in path integrals) with mathematica?

Are there any packages that can simplify functional derivatives in path integrals? For instance the expression (integrate over, $x,y,z,u,v,r,s$): $$\int\delta_{J_{A}^x}\delta_{J_{B}^x}\delta_{J_{B}^...
1
vote
0answers
111 views

Periodic sequence with exponentially increasing period?

I have to develop a physical model for a certain type of biological oscillation that can be built upon periodic sequences. From earlier questions I know that any periodic sequence (containing $0$s ...
1
vote
0answers
49 views

Ascertaining a mathematical equality to derive a partition function

we have an equation like this: $$\mathcal N(x)=\sum_{q=1}^\infty (\psi(x,q) \log(q)) \qquad (1)$$ while $\psi(x)$ is the function for some oscillations (may contain complex part), $x\in \Bbb R$ and $...
0
votes
0answers
61 views

How to Solve this Integral

I am currently doing a problem in Quantum optics, specifically the problem of finding Wigner Function for Number states or Fock states. I am actually did the problem in a different way and found that ...
0
votes
0answers
23 views

Mathieu equation nonstable solutions

This israther mathematical question, but it is connected with some physics. Let's have Mathieu equation: $$ \tag 1 y''(t)+ (a -2q\cos(2t))y(t) = 0 $$ Suppose domain of parameters $a, q$ values, where $...