Questions tagged [mathematical-physics]

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. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

Filter by
Sorted by
Tagged with
0
votes
1answer
38 views

Can branes in string theory be described by different systems of mathematics or logic?

Mathematically, in string theory, branes can be described using the notion of a category and the mathematical category theory says that logic can change from one category to another. We can build ...
0
votes
0answers
23 views

Complex Analysis [migrated]

There is a small formula for finding definite integral by complex analysis methos : If $f(x)$ containes cosine and sine functions along with polynomial functions then $f(x)$ can be treated as a real ...
1
vote
1answer
44 views

Suppose I give you $2^N$ functions that are eigenvectors of a fermionic $H$. How do I determine which function describes which spin configuration?

Consider the hamiltonian $$ H = - \frac{1}{2} \nabla^2 + V. $$ The potential $V : (\mathbb{R^3})^N \to \mathbb{R}$ is symmetric, so for each eigenvalue, there is an antisymmetric eigenvector. There is ...
-3
votes
2answers
37 views

What is the solid angle $d\Omega$ in radiative transfer?

The Wikipedia article for radiative transfer gives the following definition: In terms of the spectral radiance, $I_{\nu }$, the energy flowing across an area element of area $da$, located at $\mathbf{...
0
votes
1answer
31 views

Difference between stationary and non-stationary radiative transfer?

I am currently studying radiative transfer. In researching this subject, I found that there is stationary radiative transfer and non-stationary radiative transfer. However, it is not clear what the ...
1
vote
1answer
42 views

Solution set: Mathetmatical Methods For Physics [closed]

Recently, I had a good start with H.W. Wyld on mathematical methods for Physics and now looking forward to ask whether is there any solutions available for the problems given at the end of each ...
0
votes
0answers
41 views

Physics that calls for deeply nested Lie/Poisson brackets

I've been scouring physics for non-associative situations, particularly where study of quasigroups and loops might come in handy (they always seem to be left out). The poisson and lie brackets form a ...
0
votes
0answers
16 views

Converting altazimuth coordinates to a vector to determine a baseline vector?

I know the equatorial coordinates of a “beam” pointing from an Earth-based observer toward some distant star. I have converted those coordinates to altazimuth coordinates for that observer and a ...
3
votes
3answers
142 views

Why is the Legendre transformation the correct way to change variables from $(q,\dot{q},t)\to (q,p,t)$?

I always found Legendre transformation kind of mysterious. Given a Lagrangian $L(q,\dot{q},t)$, we can define a new function, the Hamiltonian, $$H(q,p,t)=p\dot{q}(p)-L(q,\dot{q}(q,p,t),t)$$ where $p=\...
0
votes
1answer
70 views

Query regarding $L^{2}$ functions

Given that a wave-function $\psi$ can be written as the superposition of plane waves where $\mathbf k$ is the wave vector (3D) and $g({\mathbf k})$ is a complex fn, must be sufficiently regular to ...
3
votes
0answers
36 views

How can we prove that a non-linear equation of motion for a classical scalar field satisfies causality?

Let $\phi$ be a classical scalar field in $1+D$-dimensional spacetime with coordinates $(t,\vec x)$, and consder the equation of motion $$ \newcommand{\pl}{\partial} (\pl_t^2-\nabla^2)\phi+m^2\phi+ g\...
3
votes
1answer
188 views

Does entanglement of a bipartite PPT state $\rho$ imply entanglement of $\rho + \rho^{\Gamma}$?

Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
3
votes
1answer
38 views

Must a field approach one of its vacua to have finite energy?

I'm reading these Cornell lectures on solitons (link doesn't work right now, but it just worked yesterday), and I can't seem to prove what I thought would be a simple analysis exercise. Namely, ...
1
vote
0answers
31 views

On the definition of a stationary process

I have come across various ways one refers to a process as stationary and cannot seem to get the equivalency and the level of rigor in each of them: According to Stochastic processes in physics and ...
1
vote
0answers
27 views

Intuitive Understanding of Mathematical Proof of Quantum Hall

I'm curious about the proof of the existence of a quantum Hall effect, which has recently come up because of the 40$^{\mathrm{th}}$ anniversary of the QHE problem. In particular, the paper says [The ...
2
votes
1answer
29 views

Basic doubt regarding Markov Processes

Take the Langevin equation for the position of a particle in Brownian motion. $$ m\frac{d^2x}{dt^2} = -\gamma\frac{dx}{dt} + \eta(t) $$ My professor wrote this as the following in the class: $$ \lim_{\...
0
votes
0answers
14 views

Why does this distribution function depend on time and not temperature?

When reading Sterile neutrino hot, warm, and cold dark matter I came across the following momentum distribution function for a neutrino species $\alpha$: $$\tag{5.8} f(p,t) = \frac{1}{e^{E(p)/T + \...
0
votes
0answers
38 views

How to prove $\operatorname{div} \mathbf{A}=\operatorname{Div} \mathbf{A} \mathbf{F}^{-\mathrm{T}}$?

I recently focus on solid mechanics and I am reading Nonlinear Solid Mechanics A Continuum Approach for Engineering by Gerhard A. Holzapfel. However, I was confused by a mathematical formula eq(2.49), ...
0
votes
1answer
88 views

Are X and Y boson gauge mediator of X and Y gauge symmetry? With zero X and Y charge?

Recall that the electron carries U(1) gauge charge -1. the U(1) is gauged and mediated by the U(1) gauge boson which is the photon with zero U(1) gauge charge, thus $0$. Now let us take this ...
1
vote
0answers
29 views

What does it mean by conformal group act projectively and unitarily? [closed]

What does it mean by conformal group act projectively, unitarily, and projective unitarily?
5
votes
0answers
58 views

Lost reference: Kähler gravity in six dimensions and three dimensional $SL(2,\mathbb{C})$ Chern-Simons theory

I've noticed that several references take for a fact that by studying Kähler gravity on a Calabi-Yau threefold one can demostrate that any lagrangian submanifold embedded in the threefold posees three ...
0
votes
0answers
16 views

Bloch Component under Lorentz Condition

Suppose we have Gaussian state in the momentum representation $$ a(\textbf p) = (2\pi)^{-3/4}w^{3/2}exp(-\textbf{p}^2/2w^2) $$ and a state $$b(\textbf p) = K\text{sinh}(\frac{\alpha}{2}) q_z a(\...
2
votes
2answers
143 views

Physics interpretation of Sobolev space

What is the physics interpretation of Sobolev space? $H^{s,p}:=\left\{u\in L^p(\mathbb{R}^n):\mathcal{F}^{-1}((1+|\cdot|^2)^{s/2}\mathcal{F}(u))\in L^p(\mathbb{R}^n)\right\}$, $s\geq 0,\, 1<p<\...
1
vote
0answers
61 views

Measure of Feynman path integral

Feynman path integral for non-relativistic case is defined as: $$\int\mathcal{D}[x(t)]e^{iS/\hbar}$$ where $$\int \mathcal{D[x(t)]}=\lim_{N\rightarrow\infty}\Pi_{i=0}^{i=N}\bigg(\int_{-\infty}^{\infty}...
24
votes
11answers
5k views

Does it make sense to say that something is almost infinite? If yes, then why?

I remember hearing someone say "almost infinite" in this YouTube video. At 1:23, he says that "almost infinite" pieces of vertical lines are placed along $X$ length. As someone who ...
1
vote
0answers
33 views

What happened to positive energy theorem for $n\geq 8$?

I was flipping through Geometric Relativity by Dan A. Lee where on chapter $8$ the book proved spacetime positive energy theorem for $3\leq n <8$. What happened to positive energy theorem for $n\...
4
votes
0answers
51 views

Mean value of observable in non-normalizable state

If $|\psi\rangle$ is a normalizable state in the Hilbert space of a quantum system and if ${\cal O}$ is some observable we can always evaluate the mean value of ${\cal O}$ on the state $|\psi\rangle$ ...
5
votes
2answers
167 views

Questions about BRST formalism and BV formalism

This is from Pierre J. Clavier and Viet Dang Nguyen's paper Batalin-Vilkovisky formalism as a theory of integration for polyvectors. In section 2.3, it states: A symmetry is said to be open when it ...
0
votes
0answers
12 views

How are coefficients of equation of sideslip angle in the paper “A general Solution to the Aircraft Trim Problem” calculated?

I am sure many of you guys(Aerospace related) must have read the paper, "A General solution to the Aircraft Trim Problem" by Marco, Duke and Bernt. I am working with the turning of the Aircraft and I ...
3
votes
0answers
74 views

Physical and mathematical significance of the NS-2 brane

This question is about topological string theory and it was also posted in MathOverflow. The existence of a new brane called "an NS-2 brane" is predicted in (the second paragraph in the page ...
2
votes
3answers
200 views

Line integral of a point charge

I am trying to teach myself Electrodynamics through self-study of Griffiths' Introduction to Electrodynamics, and I am having difficulty with a calculation that involves a line integral of a point ...
1
vote
0answers
44 views

Expression for sum over paths

In an introductory lecture on the path integral formalism, I came across the following. Suppose that $\gamma$'s are paths such that a particle travelling along any of them reaches the position co-...
0
votes
0answers
34 views

What are infinitesimal formally? [duplicate]

Can any problem in physics involving infinitesimal be converted to a rigorous epsilon Delta argument? Say for example finding the moment of inertia of a continuous body? Another is what is the ...
2
votes
1answer
59 views

Can a null hypersurface be foliated by spacelike sections?

Let $(M,g)$ be a $d$-dimensional Lorentzian manifold and let $\Sigma \subset M$ be a null hypersurface, which therefore has dimension $(d-1)$. We know that its normal vector $k^\mu$ is null and since ...
0
votes
1answer
53 views

Index on a compact manifold

How can the integral of a topological term (like the Nieh-Yan term) on all of a compact manifold be nonzero whereas it's a total derivative and the manifold has no boundary? I assume the manifold can ...
0
votes
1answer
46 views

Difference between two derivative operator given in Jackson's book

As I was reading Jackson (3rd edition), On page 543 I see two different types of derivatives. they are given, (11.76) $$ {\partial^\alpha} {\equiv} \frac{\partial}{\partial x_\alpha} = (\frac{\...
1
vote
2answers
61 views

Can 'distance' be mathematically described as the convolution of velocity and time, in time domain?

I have phrased the question as such, to confirm that convolution of the two functions raises the dimensionality of the convolution product. So, if I do convolution of velocity and time, then the ...
1
vote
0answers
36 views

Interpretation of random matrix eigenvectors in physics

Random matrices may be used in physics to replace Hamiltonian of complex system, for instance in nuclear physics. Eigenvalues of these matrices are simply interpreted as the energy levels (even if we'...
0
votes
2answers
66 views

Linking the de Rham bundle/complex over spacetime to the gauge bundle

In some textbooks, the Maxwell equations are stated in a very simple mathematical form (up to multiplicative constants coming from the system of units being used): $$ \begin{array} \mbox{d}F =0, \\ \...
0
votes
1answer
48 views

Average quantity over Keplerian orbit

I have been working through some lecture notes and am quite confused on something. I am trying to understand how to average a quantity over an orbit (Keplerian) but I am struggling to get a clear idea ...
0
votes
0answers
24 views

Weight function in inner product

Until know I thought that the definition of the inner product between two functions $f(\vec{r})$ and $g(\vec{r})$ with the same domain $D:[a,b]$ was: $$\int_a^b f\cdot \overline{g} \cdot d\vec{r}$$ ...
0
votes
1answer
28 views

Angular velocity of a conic pendulum [closed]

Some year 12 circular motion questions for you. I have an experiment where an object of m mass is tied to a string of L length. Centripetal force (Fc) is known along with m and L. The object is spun ...
4
votes
1answer
69 views

What are some good references for field theory via functional analysis?

Many of the aspects of QFT are traditionally done in ways incompatible with a rigorous mathematical treatment, calling for a variety of tricks to fix essentially what was caused by unjustified ...
-1
votes
1answer
11 views

Relation between product and type of quantity?

In physics, whenever we have 3 quantities $A$, $B$ and $C$ related as $ A=BC $ where $B$ and $C$ are vector quantities and $ \theta $ is the angle between $B$ and $C$, if $A$ is proportional to $cos\...
3
votes
0answers
48 views

Taking the infinite-volume limit of a lattice fermion in different ways: does this give all unitarily inequivalent Hilbert-space representations?

When the quantum field theory of a free fermion field is formulated on a finite lattice, the Hilbert space is finite-dimensional. The "spectrum condition" that we normally require in QFT is ...
1
vote
0answers
95 views

Calculating exactly the divergent part of amplitudes to all loop order with DimReg

Suppose we have the $L$-loop amplitude of the form $$\mathcal{I}_L=\int \prod_{i=1}^L \frac{d^D q_i}{(2 \pi)^D} \frac{1}{q_i^2} \frac{1}{(p-\sum_{i=1}^L q_i)^2}.$$ Introducing Feynman parameters to ...
0
votes
0answers
34 views

Combinatorics identity for arbitrary value of Spin

I wanted to prove this identity for the general value of $\lambda$ $$ \sum_{n=0}^{\lambda-1} (-1)^n{\lambda-1 \choose n} {\partial^{\left(\lambda-1-n \right)}{\partial_-}^{\left(n \right)}}\left( \...
0
votes
1answer
45 views

Meaning of Kronecker Product in Partially Expanded Operators

I am studying operators in quantum mechanics and have reached confusion in the meaning of the Kronecker product of such operators. I am fairly lost so please excuse any errors in the following text. ...
1
vote
1answer
50 views

How can even there be a non-zero BMS vector field with zero asymptotic data?

Following the BMS approach, one spacetime $(M,g)$ is asymptotically flat when: We can find a Bondi gauge set of coordinates $(u,r,x^A)$ characterized by $$g_{rr}=g_{rA}=0,\quad \partial_r\det\left(\...
1
vote
1answer
54 views

Horn equation (wave propagation in an object with a circular cross-section)

I have a problem with finding eigenfrequencies for wave which propagate in an object with a circular cross-section. I don't know how to start. I'll be very grateful for solution and comment or ...

1
2 3 4 5
39