"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 ...

learn more… | top users | synonyms (1)

1
vote
0answers
18 views

Constructive weights to resum Feynman graphs

In Rivasseau's and Wang's "How to Resum Feynman Graphs", the weights of a spanning tree corresponding to a connected graph are defined as $$w(G,T) = \frac{N(G,T)}{|E|!},$$ where $N(G,T)$ is the ...
1
vote
1answer
105 views

Expectation value quantum mechanics momentum operator

What is the random variable that belongs to the expectation value of momentum in quantum mechanics. Or in general: Is there any way we can define the expectation values that occur in quantum mechanics ...
2
votes
3answers
197 views

What do physicists mean with this bra-ket notation?

In Quantum mechanics we said that $\langle x'|\psi \rangle = \psi(x)$, where $\langle \phi|\psi \rangle $ is the dot product in $L^2(\mathbb{C})$. I found out, that this is true, if you set x' to ...
12
votes
2answers
494 views

Mathematically rigorous text on classical electrodynamics.

Is there any textbook (preferably not written by a physicist) on classical electrodynamics which gives a rigorous (by the standards of pure mathematics) treatment of (a part of) the topics found in ...
1
vote
1answer
175 views

Navier-Stokes equations in tensorial form on a general coordinate system

How to write the classical Navier-Stokes equations in tensorial form on a general coordinate system? Any references?
4
votes
1answer
125 views

Linear Algebra in curved space

We know that Euclidean geometry and Newtonian Physics are special cases that only work in a flat space-time. Got to thinking about linear algebra and matrices. Is linear-algebra a special subset of ...
3
votes
1answer
118 views

Boundary Value Problem with Robin condition

How to solve the problem: $\left(3\right)$ \begin{cases} u_{tt}-a^{2}u_{xx}=f\left(x,t\right)\\ u_{x}\left(0,t\right)-h_{0}u\left(0,t\right)=g_{0}\left(t\right)\\ ...
0
votes
2answers
105 views

Why does something constant have a parabolic shape?

Consider an object dropped from a certain position, and the only force is acceleration due to gravity. The object accelerates the same throughout the free fall; not speeding up or slowing down. So ...
1
vote
2answers
121 views

Why is acceleration $\frac{1}{2}at^2$ halved when finding final height (distance)?

The final distance of an object dropped from a certain height is: $$S_f=S_0-\frac{1}{2}at^2,$$ $S_f=$ Final distance $S_0=$ Initial height from which the object was dropped $a=$ acceleration due ...
1
vote
0answers
76 views

Transpose of an operator $T$

How can I prove that a transpose operator is a basis-dependent? Is it true that I define transpose operator in this way: $ A^T= \Sigma_{i,j} \langle e_j|A|e_i\rangle$?
2
votes
2answers
63 views

Application of representation theory

I often read that one can use representation theory in the field of quantum physics or for the analysis of symmetries in physics or chemistry. Unfortunately I coundn't find a concrete example for ...
5
votes
1answer
130 views

Physical Meaning of Symplectic Vector Fields

The mathematics of symplectic (as well as Hamiltonian) vector fields is something that has been quite clear to me for some time, but recently I have been thinking much more about what certain ...
0
votes
1answer
501 views

Showing Jacobi identity for Poisson Bracket

We were given the following problem: show that $[A,[B,C]] + [B,[C,A]] + [C,[A,B]] = 0$ where $[A,[B,C]]$ et cetera are Poisson brackets. As I understand it this is a poisson bracket (where ...
1
vote
0answers
47 views

Isn't This New Relativistic Formulation of NS-Equations, Solution of Navier-Stokes Existence and smoothness problem?

Estakhr Material-Geodesic Equation is a new type of geodesic equation, with new and relevant degrees of freedom, that describes the behavior of a fluid for large times, this new approach to solving ...
3
votes
1answer
89 views

motivating the conservation of symplectic area by way of general (coordinate) covariance

I'm trying to motivate why a symplectic structure captures exactly the right structure one needs to do classical mechanics. The easiest part of this story goes like this: we need a procedure for ...
0
votes
4answers
86 views

Regression analysis for non linear function

I am trying to model a problem with damped sine wave, $f(x) = a\sin(bx)\exp(-cx)$. I want to find optimum $a,b,c$ for my data. Can anyone please shed some light on this?
0
votes
0answers
64 views

Representing real function as integral over trigonometric functions

Since one can clearly express any function g(x) as integral from 0 to infinity of A(k)cos(kx)dk + integral from 0 to infinity of B(k)sin(kx)dk, how would G(k) relate to A(k) and B(k)? In other words, ...
2
votes
1answer
67 views

Examples of manifolds foliated by $S^2$

I have come across the Frobenius theorem in my study of GR, which for the special case of $S^2$ roughly means, that every point of a manifold with spherical symmetry can be foliated by spheres. I know ...
0
votes
1answer
103 views

Quantum Mechanics-Question [closed]

I'm a 3rd year student of a Mathematic School and i'm looking what to follow after i'm done with my undergratuate studies. I'm interested in following two paths: 1)Pure Mathematics (I know that i can ...
4
votes
2answers
77 views

Solving $\int_{-\infty}^{\infty}\frac{x^2e^x}{(1+e^x)^2}dx$

I am attempting to use residues to solve $\int_{-\infty}^{\infty}\frac{x^2e^x}{(1+e^x)^2}dx$; the answer is $\frac{\pi^2}{3}$. I have tried to split $\frac{x^2e^x}{(1+e^x)^2}$ into two parts ...
1
vote
1answer
49 views

Non-square tensors?

I learnt tensor algebra for physics and I never saw a non-square (or non-cubic...) tensor. But, from a mathematical point of view, do non-square tensors exist? And if so, are they used in some area in ...
2
votes
0answers
109 views

Solutions of Laplace's Equation/Landau & Lifschitz Fluid Mechanics

in Fluid Mechanics by Landau and Lifschitz (a fairly well-known book - I'm just mentioning it for those who might have it) they are discussing "As we know, Laplace's equation has a solution l/r, ...
1
vote
0answers
32 views

Need help with Placherel's Theorem

We know that the law of conservation of energy dictates that the energy carried by a waveform in the time domain must equal the energy contained in its power spectrum in the frequency domain. How ...
1
vote
1answer
88 views

Indices Contraction in Minkowski Spacetime

Why is it that $$\partial_\mu\partial^\mu=\partial_t^2-\nabla^2$$ (this I believe is called the D'Alembert operator.) but $$\partial_\mu j^\mu=\dot{j^0}+\nabla\cdot \vec j?$$ Why is there a minus on ...
1
vote
1answer
40 views

Strange factor multiplying the fermionic part in the NS mass-squared operator?

In the Neveu-Schwarz sector, the worldsheet fermions can be expanded as $$ \psi^I(\tau,\sigma) \sim \sum\limits_{r\in Z+1/2}b_r^Ie^{-ir(\tau-\sigma)} $$ and the total mass squared operator can then ...
0
votes
1answer
99 views

Needing Further Explanation of Knudsen's Cosine LAw

I'm reading over a paper by R. Feres and G. Yablonsky titled Knudsen's Cosine Law and Random Billiards, and I can't get around how they don't show directly how Knudsen's Cosine Law was derived. I'm ...
0
votes
1answer
34 views

Finding the change in radius that induces an $11\%$ drop in gravitational force between two bodies.

How come differentials only estimate the answer and don't give an exact answer that you might get when you calculate the real figure using other methods? Example: Let $F = Gm_1m_2/r^2$ Let $r=8$. ...
5
votes
0answers
91 views

Percolation and number of phases in the 2D Ising model.

Update. As my previous figure had conceptual mistakes I decided to change the picture to another, more instructive After a long time I came back to try to understand an article on the Ising ...
4
votes
0answers
100 views

Dimensional Regularization

I am studying a bit of theoretical physics (QFT and string theory), and I obviously stumbled upon dimensional regularization. I have been told that this technique has in fact a solid mathematical ...
1
vote
0answers
184 views

The Hanging Chain Problem, checking if I am right

I am trying to make sure I approached this problem correctly. It's a hanging chain. I'm told by a classmate that the physics doesn't make sense, but it's a really a math problem, so that I guess is ...
0
votes
0answers
71 views

Scale Factors via Ellipsoidal Coordinate System Scale Factors

In Morse & Feshbach (P512 - 514) they show how 10 different orthogonal coordinate systems (mentioned on this page) are derivable from the confocal ellipsoidal coordinate system $(\eta,\mu,\nu)$ by ...
4
votes
1answer
254 views

How to analyze the asymptotic behaviour of this integral function?

Based on the asymptotic analysis of correlation functions at large distence in Physics, now I get a math question. Let the function $$f(x)=\int_{-1}^{1}\sqrt{1-k^2}e^{ikx}dk.$$ Without working out ...
1
vote
0answers
22 views

Covariant form of a tensor.

I understand why stress-energy tensor for a comoving observer at rest relative to the fluid is diag$\{\rho, -P,-P,-P\}$ How does this lead to the generalized covariant form, often quoted in ...
1
vote
1answer
155 views

Non-commuting projection operators on a Hilbert space

Let $H$ be a separable Hilbert space. Can you provide an example of 3 orthogonal projection operators which are mutually non-commuting?
0
votes
1answer
77 views

Deformations of complex structures and Deformations in quantum algebra

I am a bit confused about the meaning of the word "Deformation". For one, as in Wikipedia, it seems to refer to fixing a compact surface and varying the complex structure. For another, as in ...
0
votes
1answer
51 views

Suppose that $\int _0^1 f(x)v(x)=0$ for every $v \in C^{\infty}([0,1])$ for which $v'(0)=v(1/2)=0$. Show that $f(x)=0$ for all $x\in [0,1]$.

Suppose that $\int _0^1 f(x)v(x)=0$ for every $v \in C^{\infty}([0,1])$ for which $v'(0)=v(1/2)=0$. Show that $f(x)=0$ for all $x\in [0,1]$.Suggestion: take u to be the suitable cut off version of ...
1
vote
1answer
48 views

Finding the kernel , the image and the rank of $[A\ A]$ for an invertible $A$

Let $A$ be an invertible matrix of order $n$. What are the kernel, the image, and the rank of the matrix $\begin{bmatrix} A & A \end{bmatrix}$ (of order $n \times 2n$)?
6
votes
1answer
357 views

Why can algebraic geometry be applied into theoretical physics?

It is to be said at the outset that I do not have much familiarity with physics beyond what is in a semi-popular book; say, the Feynman Lectures Vol 1 and 2. As I progressed in math graduate school ...
0
votes
0answers
161 views

What is the Dirac mass on measure space?

I am reading the book "Lectures on Stochastic Analysis." But I know seldom about measure space. I meet with a symbol which the author call Dirac mass(in 9.3 of this book). Let E be a measurable space, ...
1
vote
1answer
149 views

What really Navier-Stokes existence smoothness problem is?

Can any one explain to me (without using mathematical equations) that what is Navier-Stokes existence smoothness problem. I read a lot about Navier Stokes existence smoothness problem, but I still can ...
2
votes
0answers
40 views

Fock Subspaces and Weight Vectors

I've got an assignment due in a few hours, and I'm at a complete loss as to how to even start it, really. I haven't encountered any Dirac notation before, so I'm having a lot of trouble attempting the ...
0
votes
0answers
33 views

Viscosity of a ball with known deceleration

For a metal ball going through a liquid with initial horizontal speed u, mass m and radius r and viscosity resistance constant C1, I found: ...
5
votes
0answers
47 views

Deconvolution of distribution of diffraction reflexes

I'm a chemist stuck in a mathematical problem. Please bear with me as I'm trying to express myself in Math language. Let me explain in short terms the experimental method I'm using: X-ray ...
0
votes
0answers
43 views

Equations of motion for a block

I am looking for a very simplified derivation of the equations of motion (rotational and translational) for a block with a body fixed frame. I need to compare the EOMs for a system when the center ...
0
votes
1answer
37 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
votes
2answers
119 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 ...
1
vote
1answer
36 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
votes
1answer
81 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!
1
vote
1answer
186 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 ...
0
votes
0answers
36 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 ...