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11
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2answers
452 views

Are derivations of physical laws less important than the laws themselves? [closed]

The proportionality between the kinetic energy of gas molecules and temperature is a well-known result. This is usually shown by considering a cubical box containing an ideal gas, and postulating that ...
4
votes
0answers
62 views

Axiomatic QFT: Time-slice Axiom vs Transformation Properties

I am studying Wightman axioms and Haag–Kastler axioms for QFT from Haag's book "Local Quantum Physics". In both axiomatic frameworks, he introduces the "Time-slice Axiom" (axiom G) as "There should ...
1
vote
1answer
42 views

generating function method for expectation values of operator products

Many times in quantum physics we face a problem of calculating expectation values of normal product operators. Assume we have a two level system with creation and annihilation operators $\hat{a}$ and ...
4
votes
2answers
105 views

Where the time-dependent wavefunction $\Psi(\vec{x},t)$ lies?

Supose $\vec{x}=(x,y,z)\in \mathbb{R}^3$. The state of a physical system is described by the function $\Psi(\vec{x},t)$, where it must satisfy $$\int_{\mathbb{R}^3} ...
0
votes
2answers
39 views

Question about limit cycles and linear systems

In here http://users.isy.liu.se/en/rt/claal20/SysBio2015/Notes_SysBio_2015_partC.pdf it says: A limit cycle is however an intrinsically nonlinear concept: a linear system cannot have a limit ...
5
votes
2answers
442 views

Proof of Ampère's law from the Biot-Savart law for tridimensional current distributions

Let us assume the validity of the Biot-Savart law for a tridimensional distribution of current:$$\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\int_V ...
5
votes
0answers
98 views

Uniqueness of solution in newtonian mechanics

Recently I came across the problem of Norton's dome. I thought of two questions, for which I found no answer. Does there exist a newtonian initial value problem, where the total force on each body ...
5
votes
1answer
82 views

Can I *always* decompose a normalizable function into the discrete Hydrogen spectrum?

This question has been bothering me for a while now: can one reconstruct an arbitrary (normalizable) function $\phi(\mathbf r)$ in $\mathbb R^3$, with only the discrete set of Hydrogen wavefunctions ...
3
votes
1answer
122 views

Number theoretic loophole allows alternative definition of entropy?

A bit about the post I apologize for the title. I know it sounds crazy but I could not think of an alternative one which was relevant. I know this is "wild idea" but please read the entire post. ...
2
votes
2answers
68 views

Variant of the Sokhotski–Plemelj theorem

I am aware of the Sokhotski–Plemelj theorem (I have also heard people referring to it as the "Dirac identity") which states that in the limit $\eta\rightarrow 0^+$ $$\frac{1}{x\pm i\eta}=\mathcal ...
2
votes
1answer
86 views

Conservation of momentum in infinite square well

This is inspired by Griffiths QM section 2.2, on the infinite square well, which is about how far I've gotten (so, sorry if this is addressed later in the book). For any given starting wavefunction, ...
3
votes
1answer
78 views

Semi-infinite forms?

I am reading Vafa's paper 'Topological Mirros and Quantum Strings'. In this paper, the author says the Hilbert Space of a fermionic string theory corresponds to the space of semi-infinite forms on the ...
3
votes
1answer
48 views

Do all equillibrium points of a discrete mapping show up on the bifurcation diagram?

The question in the title is perhaps vaguely posed, so I'll include the concrete example which is bugging me. Suppose we have a mapping given by $$N_{t+1}=N_t\cdot ...
0
votes
0answers
50 views

Tension in string

In the derivation of the 1d linear wave equation for small amplitude waves on 1d string, they said at the end that if the density $\rho(x)$ is assumed to be constant, then the Tension $T(t)$ would ...
1
vote
0answers
55 views

Physics : Formula involving density, Mass, temperature and pressure [closed]

A set of dryers has a mass 40kg and density of 16kg/m3 at temperature of 40°C under the pressure 760mmHg. At what temperature will the mass be 50kg with density 20kg/m3 under a pressure of 700mmHg
2
votes
1answer
79 views

What does unphyisical quantity mean? [closed]

I was reading this Terry Tao article and almost near the end he says "the terms involving infinity do not make particularly rigorous sense, but would be considered orthogonal to the application at ...
1
vote
1answer
55 views

response function and Fourier transform

A response function defined as the kernel of the following integral: $\rho(t) = \int_{-\infty}^t \chi(t,t') E(t')dt'$ (1), where $\chi(t,t')$ is the response function. Physically, it relates ...
1
vote
0answers
46 views

About Green's function in spherical coordinates

Here is a self-contained part of the content from one paper I am currently reading. But there is one point I can't understand. Though there will be some equations, they are easy to follow. In $d$ ...
2
votes
1answer
111 views

Derivation of Schwarzschild metric using the full machinery of differential geometry [closed]

How would one derive the Schwarzschild metric using the full machinery of differential geometry, using the component approach as little as possible? Something along these lines: Begin with a manifold ...
2
votes
1answer
71 views

A question about the uniqueness of Riesz representation theorem

I am sorry this question may be too math related. However, I come from physics background and I would like to ask for an physicist's explanation. As far as I know, the Riesz representation theorem ...
6
votes
0answers
110 views

Canonical second quantization vs canonical quantization with multisymplectic form in AQFT

First of all, I'm a mathematician that knows less than the basics of QFT, so forgive me if this question is trivial. Please, keep in my mind that my background in physics is very poor. 1) The usual ...
4
votes
2answers
113 views

Radial quantum number for infinite circular well

For completeness, I will sketch the solution of a particle in an infinite circular well first and then get to my question. I apologize in advance since the introduction is standard undergraduate ...
4
votes
0answers
117 views

Mathematics of Surface Divergence and Surface Curl

While studying electrodynamics I found two functions - Surface Divergence and Surface Curl - that seem to condense the formulas for superficial discontinuities of the electric and magnetic fields ...
2
votes
1answer
58 views

Physic explanation of some property of heat equation? [closed]

When I compute the heat equation, I found that gross of heat do not change,it is same as our real world.But as I know , the heat equation is found according to the way of heat conduction. Why the ...
1
vote
1answer
136 views

Why is the logarithm of the number of all possible states of a system differentiable?

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$ Where $\Omega$ is the number of all accessible states (ways) for the system. $ ...
0
votes
1answer
56 views

Spectrum of Laplacian on one hemisphere

as is well-known, the spectrum of the Laplace operator on $S^2$, computed via $-\Delta f=\lambda f$, is positive and discrete. What happens to the spectrum if we just take one hemisphere into ...
0
votes
0answers
33 views

The change in time of a concentration in a fluid can be described by Reynolds' theorem. Is that the whole story?

Let $d\in\left\{2,3\right\}$ and $\Omega_t\subseteq\mathbb R^d$ be the bounded set occupied by a fluid at time $t\ge 0$. Moreover, let $\eta_t:\Omega_t\to[0,\infty)$ be the concentration of imaginary ...
0
votes
0answers
69 views

Are there applications of $L_p$ spaces in quantum mechanics?

In quantum mechanics, there a lot of emphasis on $L^2$ spaces since Hilbert spaces describe states in quantum mechanics, so we have $$ \langle \psi | \psi \rangle = \int |\psi^2(x)|\, dx$$ Even ...
3
votes
0answers
45 views

Proof that fixed points of a null field are zero

Suppose we have a scalar field $V$ (which can be acoustic pressure, or a scalar electric potential) that is a solution of the wave equation $$\Box V(x,y,z,t) = 0$$ I am wondering if a fixed ...
19
votes
1answer
362 views

What, to a physicist, are instantons and the Donaldson invariants?

I study gauge theory from a mathematical perspective. To me, one of the most fundamental ideas is the notion of an instanton on a 4-manifold. To be precise, I have a Riemannian 4-manifold and a ...
1
vote
0answers
50 views

Is time-1 map of a Hamiltonian vector field on a cylinder always twist?

I have a one degree of freedom analytic Hamiltonian $H(q,p)$ defined on a semi-infinite cylinder, i.e. $(q,p) \in \mathbb{T} \times \mathbb{R}^{+}$, such that all level sets $H(q,p)=c$ are closed ...
1
vote
1answer
46 views

Angular momentum partial components of a $k$-dependent pairing potential

I am going over this review on pairing in unconventional superconductors :http://arxiv.org/abs/1305.4609v3 which on page 21 states that for a "regular" function $U(\theta)$, partial components $U_l$ ...
0
votes
0answers
37 views

Expansion of comparator

Currently I am working on Pesking Schroeder Section 15.1 and trying to understand the expansion given in (15.5), which is $$ U(x+\epsilon n, x) = 1 - i\,e\,\epsilon\,n^{\mu}\,A_{\mu}(x)+O(\epsilon^2) ...
12
votes
1answer
1k views

Equation of a torus

In the recent paper http://arxiv.org/abs/1509.03612, page 37. They say that a torus can be described by the equation $$y^2=x(z-x)(1-x)$$ where $x$ is a coordinate on the base $\mathbb{P}_1$. Could ...
2
votes
1answer
63 views

Maxwell Boltzmann distribution: Going from momentum to energy

I am learning about the Maxwell Boltzmann distribution, and am trying to convert the equation from momentum into energy, but I'm stuck on changing $d^n p$ into $dE$. I have the equation: $$ ...
1
vote
1answer
50 views

Optics Diffraction Grating Plot

I was unsure whether to post this in physics stackexchange or mathematica stackexchange, so I posted it in both. I'm trying make an intensity plot for a diffraction grating that contains 100 ...
2
votes
1answer
118 views

In the algebraic formulation of Quantum Mechanics, how do probability amplitudes naturally arise?

In the algebraic formulation of quantum mechanics, consider $\mathcal{B}(\mathcal{H})$ as the set of all bounded operators on $\mathcal{H}$ (with involution, norm, etc.), which form a C*-algebra $C$. ...
13
votes
4answers
847 views

Can momentum have a complex expectation value?

I'm making examples of wave functions to incorporate in a QM exam. I came up with the following wave function, which gives me some troubles: $$\psi(x,0) = \begin{cases} A(a-x), & -a \leq x \leq ...
1
vote
0answers
72 views

Experiments to resolve dillema between continuity and discrete

Which experiments/experimental methods are suggested to resolve an alternative about the structure of our universe space and time - is it continuous or is it discrete in a very small scale, especially ...
2
votes
1answer
47 views

Time dependent electric field: Mathematical expansion for local electric field

In many articles and books I see that local electric field is expanded as $$\vec E_0(\vec r(t)) = \vec E_0(\vec R_0) − (\vec a(t) \cdot \nabla) \vec E_0(\vec R_0) \cos(\Omega t) + \ldots $$ For ...
1
vote
1answer
182 views

Understanding Noether's theorem rigorously

I've known about Noether's theorem for some time and reading some things about it recently I've realised I haven't completely understood it. In that case I've been trying to understand a more rigorous ...
2
votes
1answer
78 views

How do we take the limit of this quantum operation?

I am wondering how to take the following limit: \begin{align} L= \lim_{\tau \to \infty} \frac{1}{\tau} \int_{-\tau/2}^{\tau/2} dy \, \left(1 - \frac{1}{\sqrt{ \pi} \sigma } ...
1
vote
0answers
127 views

Cones with deficit angle 2$\pi$ and euler characteristics

I've managed to confuse myself with cones and deficit angles. Let's consider a conical defect in 2 dimensions. So the metric is the usual one in polar coordinates, $$ ds^2 = dr^2 + r^2 d\phi^2,$$ ...
1
vote
0answers
90 views

What are the implications of integrating the Poisson bracket? [closed]

Reading Ref. 1 I admit I am a little lost in some places. I was hoping that someone in this area could explain the basic premise of integrating the Lie bracket and further is it connected to nlab's ...
4
votes
0answers
87 views

Gromov-Witten invariants

I'm a mathematician studying Schubert calculus, and I'm out to compute the Gromov-Witten invariants of the complete flag manifold. Well, I actually already know how to compute them, but only in a way ...
9
votes
1answer
127 views

Resources for algebraic topology in condensed matter physics

I wanted to know if anyone had any good introductions on algebraic topology for the theoretical physicist? I am particularly interested in applications to condensed matter physics, but would be happy ...
1
vote
1answer
56 views

Are there Non-conformal maps encountered in Physics?

We always encounter Conformal maps in Physics, may be they are easier to study, but are there Non-Conformal transformations encountered in Physics anywhere? if they are encountered, where are they ...
3
votes
0answers
37 views

Action for solution of general nth order differential equation [duplicate]

Suppose I want to find solution to a general nth order differential equation. (If I am right about the logic then) one might say that the solution $y\equiv y(x)$ is that function for which the ...
5
votes
2answers
222 views

What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
2
votes
1answer
48 views

which is correct way to find error in degree of linear polarization?

I have a set of "degree of polarization (DOP)" values for a star. Assume there are 10 DOP values in the set. DOP is defined as square root of sum of squares of fractional Stokes parameters, namely q ...