# 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.

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64 views

### Piecewise solution to Euler-Lagrange equations in effective field theory

I would like to consider a background for a quantum field theory made up by connecting continuously two different solutions of the Euler Lagrange equations. The problem is one dimensional (let's call ...
35 views

### What is the best book to read for optimal mass transportation theory for students with physics background?

I need to read optimal mass transportation theory for my research. What is the best book to read. I am from physics background. How much mathematics and what sort of mathematics required prior to ...
117 views

### Does anyone know how to symmetrize $\gamma$-matrices?

I'm trying to construct the SO(5, 5) $\gamma$-matrices which are real and symmetric. Recently, I have 6 symmetric and 4 antisymmetric $\gamma$-matrices ($6_S + 4_A$ representation). How can I ...
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### What is the difference between real and complex instantons (mathemtically, and their physical significance), and connection to Wick rotation

I am struggling to understand the difference and physical significance between real and complex instantons- I think these are also sometimes called ghost instantons? There are also anti-instantons. ...
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### Prove that the electric field produce by a punctual charge is isotropic and radial

I would like to prove mathematically that the electric field produced by a punctual charge is isotropic and radial, i.e. $$\vec{E}(r,\phi,\theta)=E(r)\vec{e}_r\tag{1}$$ I think that this statement ...
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### Why is the singularity not taken into account?

In this article "Reflections on Maxwell’s Treatise", Section 4.2, it says: He replaces $\mathbf{m}$ with a volume element of magnetization $\mathbf{M}\ dV$ , integrates over $V$ , and lets the same ...
34 views

### Is the disposition of $1$s and $0$s when writing orthogonal ket vectors purely conventional?

If I want to define the basis in the form of $4$-vectors, how do I proceed to make sure they are orthonormal with one $1$ and three $0$ in each vector? Is it just by convention? Does it matter if I ...
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### For closed circuits, why can't we have more than one $f(r)$?

Force between current elements depends on a function of angles [$f(\eta, \theta, \theta^{\prime})$] and also on a function of distance between them [$f(r)$] . For closed circuits, there are more ...
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### References on deformation quantization

I'm looking for books or introductory review papers or lecture notes on the topic of deformation quantization. (And preferably, geometric quantization as well.) I'm mainly interested in the ...
49 views

### Is there a physical interpretation of the alternating property?

A map from a vector-space to its base field is called "alternating" if each vector with repeated elements is mapped to zero. I've read that symplectic geometry is an important representation of ...
191 views

### Quantized Banach Spaces

Reading the paper here, it mentions on the very first page that "The requirement of 'closed'-ness is imposed because we want to think of operator spaces as 'quantized (or non-commutative) Banach ...
177 views

### Regarding Ampere's Circuital Law

If I am to show that Ampere's Circuital law holds true for any arbitrary closed loop in a plane normal to the straight wire, with its validity already established for the closed loop being a circle of ...
97 views

### Integral of absolute value of spin angular momentum of $N$-body system

There are $N$ particles moving freely in a plane. Let $J(t)$ be the spin angular momentum of the system of particles about its center of mass. (even center of mass keeps changing with time as ...
136 views

### Does model theory in mathematics have any usefulness in the modeling of physical systems?

The term Model Theory in mathematics seems to have a somewhat precise definition here. Reading through that reference you'll largely see discussions strictly relating to mathematical concepts, but one ...
81 views

### A special path integral

May be $f(\vec{x}), \vec{g}(\vec{x})$ an arbitrary functions dependent on the coordinates $\vec{x}=(x,y,z)^T$. Defining the following function dependent on a 3-dimensional curve $\vec{\gamma(t)}$ ...
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### Does this Hamiltonian have point spectrum?

Consider such a Hamiltonian $$H = - \frac{1}{2} \frac{\partial^2}{\partial x^2} - F x + V(x) ,$$ with $F$ being some constant, and $V(x)= V(x+L)$ being some periodic potential. Does this ...
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### Can we avoid singularities by embedding the manifold on a bigger space, maybe Euclidean or Riemannian?

Can singularities be avoided by embedding Riemannian manifold on bigger space, or more specifically black hole singularities can be avoided or not by embedding in any other manifold. We don't have ...
132 views

### Symplectic Structure without predefined Hamiltonian

Here there is a link which has helped me understanding the relationship between symplectic geometry and classical mechanincs. In short, the symplectic form transforms the derivative of the Hamiltonian,...
127 views

### Do all the spacelike curve terminate at the spatial infinity $i_0$ in the Penrose Diagram of a Schwarzchild black hole?

Let's restrict to the radial direction, so the metric can be expressed as $ds^2=-(1-r_S/r)dt^2+(1-r_S/r)^{-1}dr^2$ with $r_S$ the Schwarzchild radius. Expressed in Kruskal coordinates, the metric is ...
477 views

### Robin boundary conditions for the heat equation

Consider a 3D channel with fluid or gas with walls $\Gamma_1$, inflow part $\Gamma_2$ and outflow part $\Gamma_3$. The temperature is described by the heat equation:  \frac{\partial T}{\partial t} -...
140 views

### Examples of application of detour matrices in physics?

Are there any good examples of application of detour matrices in physics?
87 views

### Charge and current density fields

The charge and current density fields in classical electromagnetism are scalar real number fields on space time manifold. But these fields diverge/become infinite in case of point charges, how is this ...