Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elementary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

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Lie Algebra Homomorphism for Fundamental Vector Field

This question is based on the exercise 10.1 (b) in "Geometry, Topology, and Physics" by Nakahara. Let $G\rightarrow P \rightarrow M$ be a principal bundle. Given an element of the Lie ...
75 views

What will happen if we change all the resistances in an infinite resistance ladder to their double value? [closed]

Let's have a circuit as below: Circuit 1 If the equivalent resistance of above circuit is $Z$ and if we have another circuit as below: Circuit 2 And if the equivalent resistance of above circuit is $R$...
47 views

Book on $SL(2,C)$

Is there a book, which treats $SL(2,C)$ in detail as a group, Lie group, its Lie algebra, geometry of its subgroups etc.? It is often seen as an example in Lie Algebra/Group books but it always ...
84 views

Why is the solution of the Klein-Gordon PDE a distribution?

I've also posted this question on physics SE in case it is more appropiate there. Consider the Klein-Gordon equation: $$(\square + m^2)\phi = (\partial_t^2 - \Delta + m^2)\phi = 0 \tag{1}$$ The ...
33 views

Help me with this math problem [closed]

Is there an exponential density that satisfies the following condition $p(x\le 2)= \frac{2}{3} p(x\le 3)$? If so, what is the value of delta?
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Definition of Feynman diagram

I'm reading Costello's book "Renormalization and effective field theories" (preliminary PDF, p. 35). I am stuck on his discussion of Feynman diagrams. He considers a finite-dimensional super ...
34 views

Applications of category theory in Computer Science and Mathematical Physics. [closed]

Could someone name some examples where we make use of category theory in Computer Science or Physics, specifically in Mathematical Physics?
37 views

odd function conclusion in D'Alembert's formula

here I have a particular question of D' Alembert's formula for the homogeneous wave equation in 1D: \begin{align}\frac{\partial^2 u}{\partial t^2} - C^{2}.\frac{\partial^2 u}{\partial x^2} =0\end{...
1 vote
64 views

Christoffel symbol on $T^*M$

I tried to prove the form of the Christoffel symbol on the contangent space given in the book "Elements of Noncommutative Geometry". The Christoffel symbols $\Gamma^k_{ij}$ of the Levi-...
20 views

Show that for associated Legendre function [closed]

Show that $P_n^m(-x)=(-1)^n(-1)^mP_n^m(x)$ I have tried to use the associated Legendre function. I also used Rodrigue's formula for $P_n^m$ and plug the value back in the associated Legendre function. ...
28 views

Doubt on the general solution of three dimensional Laplace equation in Fourierspace [closed]

I am finding difficulty in deriving the general solution of laplace equation in fourierspace. The result alone was presented in paper by Faxen 1921( onlinelibrary.wiley.com/doi/10.1002/andp....
4k views

Inhomogeneous heat equation with Fourier transform

Consider the heat equation $$\dfrac{\partial u}{\partial t}=\dfrac{\partial^2 u}{\partial x^2} +G(x,t).$$ with the condition $u(x,0)=f(x)$. When $G(x,t)=0$ it is quite easy to solve it using Fourier ...
233 views

Understanding's Wikipedia's definition of a spinor

I am trying to understand spinors from a mathematical view. I've seen similar questions on this website but I'm still unclear on what they are exactly. On Wikipedia they state: Although spinors can ...
1 vote
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1 vote
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Partition function of a QFT.

There is a YouTube lecture by Robert Dijkgraaf titled:"Introduction to Topological and Conformal Field Theory (1 of 2)." https://www.youtube.com/watch?v=jEEQO-tcyHc&t=2977s At one point ...
1 vote
72 views

Definition of $a_{0}$ - what is wrong with my calculations?

Consider the following problem, which was extracted from page 13 of these lecture notes. Consider $w$ to be radially symmetric ($w(x) = w(|x|)$), compactly supported and nonnegative. Let $f$ be ...
64 views

How is the Hodge star operator defined for vector-valued forms?

Let $M$ be an oriented Riemannian manifold of dimension $n$. For any $\omega \in \Omega^k(M)$, we define the Hodge star operator $\star$ of a $\omega$ as the unique $n-k$ form $\star\omega$ that ...
69 views

Discrepancy in Results with Self-Adjoint Operator on a Special Hilbert Space in 2D Geometric Algebra

I am exploring the behavior of multivectors in 2D geometric algebra, specifically examining the product $\mathbf{u}^\ddagger \mathbf{u}$, where $\mathbf{u}=a+xe_1+ye_2+be_{12}$ and its Clifford ...
1 vote
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1 vote
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How to calculate the length of the image of the curve $\Gamma$? [closed]

How to calculate the length of the image of the curve $\Gamma= \{z(t) :z (t) =at, t \in [0,1]\}$ under the mapping $w = z^n$, where $n \in \mathbb{N}, a \in \mathbb{C}$?
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What would be the new Equation of motion if the magnetic field's origin is shifted from the origin of a co-rotating spherical polar coordinates?

The equation of motions due to the dipole magnetic force of a planet in a frame corotating with the planet and origin at the centre of planet assumed to be sphere components wise are given as below: \...
38 views

Analytically solving PDEs on irregular domains in Physics

In many Physics courses you solve PDEs like heat or wave on square, circular, or spherical domains with separation of variables. Are there ways to solve PDEs and Boundary value problems on irregular ...
423 views

Magnetic field generated by a helix

Let $I$ be an electric current inside an infinite helix $H$ which is given by the following parametrization: $$H(t)=(\cos(t),\sin(t),t)\\t\in(-\infty,\infty)$$ Find the magnetic field $\vec{B}$ that ...
75 views

System of nonlinear first-order PDEs

The following system of nonlinear first-order PDEs describes the one-dimensional incompressible flow of an ideal fluid in an open long channel $$h_t+(hv)_x=0,$$ $$v_t+vv_x+gh_x=0,$$ where $h = h(x, t)$...
The algebra $\Gamma^\infty(\mathbb{C}l(M))$ is generated by $\Omega^1(M)$
I'm reading "Elements of Noncommutative Geometry" by Garcia-Bondía. There it was mentioned that the algebra $\Gamma^\infty(\mathbb{C}l(M))$ is generated by $\Omega^1(M)$. Here $\Omega^1(M)$ ...