"Mathematical physics consists of the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories." (from Journal of Mathematical Physics) This tag is intended for questions on methods used ...

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35 views

distribution of the product of a poisson and a bolzmann

What is the distribution of the product of two variables for which each of them has its own distribution(specifically one poisson and one bolzmann)? I found on wikipedia that for the sum of the two ...
3
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2answers
116 views

Obstruction to extending $G$-bundle to 4-dimensions in Chern-Simons theory

I am reading Dijkgraaf and Witten's paper on Chern-Simons and finite gauge groups and something they have written about the obstruction to extending the bundle to the 4-manifold confuses me. My ...
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1answer
34 views

Compute the curl

Given that $\vec{\nabla}.{\vec{m}}=0$, and the vectors be in $\mathbb{R}^3$ I am trying to show that $$\vec{\nabla}\times \frac{r^2}{2}\vec{r}\times\vec{m}=(\vec{m}.\vec{r})\vec{r}-2r^2\vec{m}$$ I ...
3
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1answer
77 views

solving the $ \varepsilon_{ijk}\varepsilon_{lmn}$(Levi Civita)

How can I solve this : $ \varepsilon_{ijk}\varepsilon_{lmn}=??$ I know that It can be solve with 2 determinants but I don't know how.and I don't what are the determinants!
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1answer
166 views

Operator curl and gradient

Operator curl $\nabla$ x$(\cdot)$ (x is cross product) working on a $ C^1$ vector field and operator gradient $\nabla(\cdot)$ working on scalar fields. And results of these operators is vector ...
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34 views

Intuition behind a braid operator which is also a solution for Yang-Baxter equation

I am going through this paper, 'Quantum entanglement and topological entanglement' by Louis H Kauffman and Samuel J Lomonaco Jr published in New Journal of Physics 4 (2002). It started with ...
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2answers
999 views

can an electric field exist at a point where the electrical potential there is zero?

can an electric field exist at a point where the electrical potential there is zero? 0 v=integral of E.dl
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1answer
38 views

Periodicity on System of Equations

$$ y(t) = \begin{bmatrix} cos\sqrt\omega & -sin\sqrt3\omega & 0 & 0 \\ sin\sqrt3\omega & cos\sqrt3\omega & 0 & 0 \\ 0 & 0 & cos\omega & -sin\omega \\ 0 & 0 ...
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1answer
65 views

Reference request for Lorentz group and unitary representations

More precisely, I often read or listen that Lorentz group has not (non trivial) unitary finite dimensional irreducible representations because it is not compact. Now, I know that the "converse" part ...
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2answers
20 views

if $v$ is a member of $H$ and $v$ is not a member of $M$ then $u$ is member of $K$. How is this possible?

Let $(V,K)$ and $u,v$ is a member of $V$. Suppose that $M$ is a subset of $V$ is a subspace of $V$ with basis $B_m=\{m_1,...,m_r\}$ with $r$ less than and equal to $n$. Let $H$ be a subspace spanned ...
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119 views

If $f(x,y,t):= u(r) \cos ( \omega t)$, use the multivariable chain rule to obtain an ODE for $u$ from the PDE for $f$.

Let $f(x,y,t) :=u(r)\cos \omega t$, where $r= \sqrt{x^2 +y^2}$. Physics tells us the following: For $f(x,y,t)$ to describe a vibrating membrane, with $f(x,y,t)$ telling how high the mem- brane is ...
3
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1answer
110 views

$\mathbb{RP}^3$ is homeomorphic to the solid ball with antipodal points identified

I am reading the book Application of Path integrals by Schulman, which has a chapter on applications of homotopy theory to path integrals. In that he says we can geometrically describe $SO(3)$ by a ...
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1answer
78 views

Trouble in proving that $\|x\|_p = \max|x_j|$

We define p-norm in this way: $\|x\|_p = \{\sum ^N_j_=_1|x_j|^p\}^ {1\over p}$ We know that It change to $\|x\|_p = \max|x_j| $ when $ p \to \infty $ How can I prove this ?
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24 views

Do partial derivatives of recurrence relations exist? And what do they mean?

I have a recurrence relation that represents the amount of radio active tracer adsorbed by hands after a series of $n$ contacts with a surface. Thus: $$Y_i=\sigma_i+\beta_iY_{i-1}$$ Where $i=1..n$, ...
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2answers
798 views

Commutator of $x$ and $p^2$

I have a question: If I have to find the commutator $[x, p^2]$ (with $p= {h\over i}{d \over dx} $) the right answer is: $[x,p^2]=x p^2 - p^2x = x p^2 -pxp + pxp - p^2x = [x,p]p + p[x,p] = 2hip$ But ...
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2answers
236 views

Finding speed with only distance [closed]

Excellent human jumpers can leap straight up to a height of 110cm off the ground To reach this height, with what speed would a person need to leave the ground? How do I solve this question when no ...
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1answer
250 views

Find the position equation from this velocity equation

Find the position equation from this velocity equation $$\displaystyle \frac{dr}{dt} = v_{t}\sqrt{1-e^{-v_{t}t}},$$ where $t$= time and $v_t$= constant I'm wondering if there's a way to solve this ...
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0answers
58 views

The equvalence of the virtual work and the Hamiltonian equations

I am reading Whittaker's Analytical Dynamics. This is chapter 10 *Hamiltonian Systems&. Paragraph 109 is Hamiltonian Systems & Their integral invariants. Whittaker starts with the Lagrangian ...
4
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1answer
89 views

What does this dynamic system represent for?

I know systems like $$\frac{dx}{dt}=Sx$$ where $S$ is a symmetric matrix admit a solution that dialates along eigendirection of $S$. And systems like $$\frac{dx}{dt}=Ax$$ where $A$ is a ...
2
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1answer
90 views

holomorphic vector field on Fano Kähler-Einstein manifold

Let M be a compact Fano Kähler-Einstein manifold, V is a holomorphic (1,0) vector field. Fano conditions tells that $V=\nabla^{1,0} f$ for some smooth complex valued function.By Matsushima theorem, ...
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2answers
66 views

Motivation for introducing von Neumann algebra in addition to $C^*$algebra

Observables are self-adjoint elements of a $C^*$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^*$algebra can always be ...
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1answer
72 views

Computing The Fourier Sine Series.

Compute the Fourier Sine series of the odd function: $f(x) = x^3 - 4x, -2 \leq x \leq 2 $. (Periodically extended with period 4) I know how to compute this of course where: $b_n = ...
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1answer
113 views

Can 0 be an eigenvalue?

Let $-\Delta $ be the positive Laplacian and consider the operator $$ -\Delta + V $$ on $L^2(\mathbb{R}^3)$ with domain the Sobolev space $W^{2,2}(\mathbb{R}^3)$. Here $V:\mathbb{R}^3\to \mathbb{R}$ ...
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101 views

Find the Euler-Lagrange equation of $F=p(x)y'^2-q(x)y^2+2f(x)y$

The question statement: obtain the Euler-Lagrange equations associated with extremizing $\int_a^b F\, dx$. Our F is $$F=p(x)y'^2 -q(x)y^2 +2f(x)y$$ I haven't used the EL equations for some time, ...
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3answers
215 views

Why does the Method of Successive Approximations for a Differential Equation work?

Time dependent perturbation theory in quantum mechanics is often derived using the Method of Successive Approximations for a Differential Equation. I have not seen an explanation or a more rigorous ...
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0answers
68 views

Meaning of quasiperiodicity in classical KAM

I'm learning about the classical KAM theorem, and I can't quite infer precisely what the term "quasi-periodic solution" means in the theorem's statement. I'm reading the following introductory note: ...
2
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1answer
231 views

Lie algebras and physics

I often hear physicists talk about Lie algebras and their representation theory, but most of the time hardly understand them because my knowledge of physics is very limited. Does anyone know of any ...
5
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1answer
165 views

Physical interpretation of $q$-deformation

I am currently reading the paper Quantum Group Particles and Non-Archimedean Geometry by Volovich and Aref'eva. Here they discuss the difference between $q$-deformation and $\hslash$-deformation. In a ...
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1answer
71 views

What is 'target manifold'?

I saw in a lecture about O(3) sigma model something about 'target manifold', but I do not know what is it. Is there any book I could learn about that?
3
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1answer
107 views

Series of modified Bessel functions

There is a known identity to evaluate a sum of the form $$\sum_{n\geq1} \rho^n I_n(\omega) $$ Where $\rho>0$, $\omega >0$ and $I_n$ is the modified Bessel function of the first kind. ??? ...
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22 views

Determination if ODE is self-adjoint using $ \mathrm L $

According to Arfken 6th edition. Mathematical Methods for Physicists: second-order ODEs corresponding to linear, second-order differential operators of the general form $$ \mathcal Lu(x) = p_0 (x) ...
2
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1answer
158 views

Looking for recommendations on textbooks for self study in a few subjects

I'm a first year graduate student in physics who picked up both an undergraduate degree in math and physics. However, in getting the math degree there were a few courses I either didn't take or ...
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49 views

Evaluating a particular infinite sum (over Matsubara frequencies)

In condensed matter physics, one often runs into sums over Matsubara frequencies. I know the way to evaluate these is to interpret the sum as an integral over some function with infinite number of ...
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100 views

Passing the singularities .

I need some information or detail with example to the following statements. Circumvent the singularity by a contour inside the wave-guide. Circumvent the singularity by a contour outside the ...
14
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1answer
208 views

Legendre Transformation of a Lagrangian in Classical Mechanics

I have some questions about the Legendre Transformation of a Lagrangian in Classical Mechanics to the Hamiltonian: We start with a Lagrangian $L(q,\dot{q})=\frac{\langle \dot{q} , \dot{q}\rangle }{2} ...
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1answer
79 views

What are the structure constants for the algebra of quaternions? Show this algebra is associative.

What are the structure constants for the algebra of quaternions? Show this algebra is associative. How can I find the structure constants? I know that for an algebra $\mathscr{A}$ and basis ...
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2answers
204 views

Easy way to find the streamlines

In a textbook, this problem appears: Find the streamlines of the vector field $\mathbf{F}=(x^2+y^2)^{-1}(-y\hat{x}+x\hat{y})$. The system we need to solve, I suppose, is: ...
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1answer
31 views

surjectivity of a linear transformation and spanning

Okay, we have that $\{|a_i\rangle\}_{i=1}^n$ is a set of vectors spanning a vector space $V$. Also, $T\in L(V,W)$ is surjective, where $L(V,W)$ is the set of linear transformations (functionals) from ...
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1answer
44 views

What do the equations on this gate mean or relate to?

These equations are on gates to the John Dalton building in Manchester UK: http://i.imgur.com/uXFQSfg.jpg Does anybody know what they mean or which work they ...
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147 views

How to write $SO(2n)$ characters in terms of rotation angles?

Say one is working in a representation of $SO(2n)$ such that it has the highest weights $(h_1,...,h_n)$. And let $\{H_i\}_{i=1}^{n}$ be a basis in the Cartan of $so(2n) = Lie(SO(2n))$. Now one says ...
2
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1answer
145 views

Solving the source free Maxwell equations for plane waves

I've been trying to solve the maxwell equations: $$\nabla\cdot\vec{D}=0,\quad \nabla\cdot\vec{B}=0$$ $$\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t},\quad \nabla\times\vec{H}=\frac{\partial ...
5
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1answer
139 views

Quotients of $S^{2n+1}$

Any sphere $S^{2n+1} = SO(2n+2)/SO(2n+1)$ can be thought to be given as the zero-set in $\mathbb{C}^{n+1}$ of the equation, $\sum_{i=1}^{n+1} \vert z_i \vert ^2 = 1$ Now say one wants to quotient it ...
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1answer
60 views

show $\sum_{i=1}^\infty a_i^{\ast}b_i$ is convergent using the Schwarz inequality

Question: Let $\{a_i\}_{i=1}^\infty$ and $\{b_i\}_{i=1}^\infty$ be in $\mathbb{C}^\infty$. Show $\sum_{i=1}^\infty a_i^{\ast}b_i$ is convergent, using in particular the Schwarz inequality. Attempt ...
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0answers
48 views

Taking the non-relativistic limit of a Lagrangian

This question has to do with question 1 on this sheet. I'm trying to self-learn QFT, please be patient with me! I have problem to get the exact form of the Lagrangian in the non-relativistic limit as ...
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1answer
120 views

Calculating the average force (mathematical physics)

I am trying to calculate the average force with regards to this question: Calculate the average force that USA gold medalist Allyson Felix (mass = $55.3$ kg, height = $168$ cm) exerted backwards on ...
3
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1answer
127 views

How do I calculate the following? (with answers)

Would anyone be able to help me calculate the following questions? I have the answers, I just want to understand the process. If you are able to give me any feedback, would you be able to write your ...
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2answers
229 views

Calculating the linear output force a threaded rod and nut would produce based on the input torque

I would like to calculate the amount of linear thrust a threaded rod combined with a rotationally static nut would be able to produce based on the rotary force applied to the rod. The information ...
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1answer
70 views

Nonlinear solution condition and graphical representation

The solution of a nonlinear solitary wave equation can be written as $$\phi(x) = \pm v \tanh\left[\frac{m}{ \sqrt 2} (x-x_0)\right]$$ where the plus and minus refer to the kink and antikink ...
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1answer
69 views

Need help with boundary conditions of a differential equation.

QUESTION: A particle $A$ is moving along the $X$ axis at a constant horizontal velocity $u\hat{i}$. Another particle $B$ is moving such that its velocity vector always points towards the particle ...
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64 views

Geometric or physical meaning of a defective matrix

I've been reading wikipedia pag of Jordan canonical form, which induces matrices that does not have eigenbasis, i.e. defective matrices. The physical and geometric meaning of normal matrices are ...