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 ...

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1answer
219 views

Resources for theory of distributions (generalized functions) for physicists

I am looking for tutorials, articles or books containing theory of distributions in context of mathematical physics. Please suggest.
2
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1answer
103 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 ...
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1answer
34 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 ...
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1answer
51 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 ...
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0answers
295 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 ...
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0answers
583 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 ...
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0answers
41 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 ...
3
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0answers
95 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
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0answers
51 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, ...
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0answers
209 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 & ...
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0answers
716 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
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0answers
93 views

The implications of Gödel's Second Incompleteness Theorem on Theoretical Physics models

Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics? I work partially in Quantum Information Theory ...
2
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0answers
92 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
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0answers
170 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
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0answers
130 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
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0answers
249 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
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0answers
314 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
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0answers
359 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)\\ ...
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0answers
49 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 ...
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0answers
33 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 ...
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0answers
48 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 ...
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0answers
99 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 ...
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0answers
47 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 ...
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0answers
31 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 ...
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0answers
41 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 ...
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0answers
31 views

Quantum mechanics and distribution law in mathematical logics

Recently I've heard that quantum mechanics can be formulated by starting from the rejection of distribution law in mathematical logic: $a$ and $(b$ or $c)$= $(a$ and $b)$ or $(a$ and $c)$. Did ...
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0answers
140 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, $x,y,z,u,v,r,s$): ...
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0answers
77 views

Current density in phase space

I have a question which arises from looking at the impact free Boltzmann equation. Let $(\vec{x},\vec{v})$ be a vector in our phase space $\Gamma^N = \mathbb{R}^{6N}$. The dynamics of a state are ...