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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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49 views

Negative unity matrix not hermitian? (stabilizer formalism)

I read the section in the attached picture about the stabilizer formalism and was wondering about the last sentence in the pic. It says that all operators of the stabilizer group are hermitian, ...
26 views

conventional matrix notation for distance interval

Why matrix notation for distance interval is represented by this? $$g_{\mu \nu}\Delta X^{\mu}\Delta X^{\nu}=(\Delta X)^Tg (\Delta X)=\Delta X^{\mu}\Delta X^{\nu}g_{\mu \nu}$$ Could you explain ...
131 views

What is the meaning of “representation of the canonical commutation relation in the form of Heisenberg for symplectic locally convex space”?

What is the meaning of "representation of the canonical commutation relation in the form of Heisenberg for symplectic locally convex space"?
87 views

Post-measurement density matrix derivation

This is something standard, by I'm trying to redo this with spectral theory. Suppose we start with the usual postulates of quantum mechanics: States are unit rays on a separable Hilbert space. In ...
52 views

Position of a particle sliding down an arbitrary curve as a function of time

Given a curve in a frictionless environment with parameterization $\displaystyle \mathbf{r}(\theta)=x(\theta)\hat{\mathbf{i}}+y(\theta)\hat{\mathbf{j}}$ for $\theta\in[0,\theta_f]$, how can I find the ...
116 views

66 views

Motivating the Unintuitive Properties of Spinors

In the usual treatment of (Dirac) spinors, one usually starts with "factoring" the energy-momentum relation, deducing the properties of the $\gamma$ matrices by requiring the cross terms to cancel, ...
47 views

self-adjoint extension of the momentum operator in an infinitely deep potential

Theta parameter arises when calculating self adjoint extensions of the momentum operator of a particle in an infinnitely deep potential, what does this means physically?
34 views

What is the magic behind Sector Decomposition?

I have a question regarding Sector Decomposition, which is briefly introduced in this paper arXiv: 0803.4177. So far I played around with a toy example and applied the Sector Decomposition method to ...
302 views

109 views

Question about characteristics and classification of second-order PDEs

I know this question is quite maths-focused; however, it relates closely to numerical methods that are used to solve Physics problems (for example in Fluid Dynamics/CFD). I asked the same question ...
78 views

Joint Spectral Measure theorem

I want to gain an intuition to understand the joint spectral measure theorem. In the case that operators involved in this theorem have purely discrete spectrum, the theorem should be reduced to the ...
402 views

Weyl anomaly in 2d CFT (string theory lectures by D.Tong)

In his lectures on String Theory (http://www.damtp.cam.ac.uk/user/tong/string.html), Tong gives a proof of the Weyl anomaly, using equation $(4.36)$. It seems wrong to me. Here he uses the OPE ...
132 views

Chern-Simons and framing dependence$.$

According to ref.1, the correlation functions of a Chern-Simons theory are topological invariants, up to the so-called framing, that is, the trivialisation of $TM\oplus TM$. The origin of this framing ...
42 views

Finding the unit of Pressure/Volume

Me and my friend are trying to find the exact unit of Power=Pressure/Volume. We know that the unit has to be W(J/s) so we try from the equation above: (Kgm²/s³)=(N/A)/V The right side will be: (Kgm/s²)...
75 views

Inverse second derivative of a Legendre transformation

I'm trying to find the legendre transformation of $$f(x)=x^3$$ I have calculated it using the approach we learned in class: 1 - Find the derivative of function => $y(x) = f'(x)$ 2 - Take ...
89 views

Taylor Expansion of a Vector Field in Stokes Flow About a Sphere's Surface

So I am going through what could be a pretty simple identity: $\frac{1}{4 \pi a^2} \int_S \vec{u}(\vec{x}) dS=\vec{u}(\vec{0})+\frac{a^2}{6} \nabla^2\vec{u}(\vec{x})|_{\vec{x}=\vec{0}}$ where S is ...
63 views

Will the flux through an arbitrary closed surface be finite or infinite when a plane charge intersects the Gaussian surface?

Let's consider a closed Gaussian surface (in red). The white line and the white shaded part lies inside the Gaussian surface and the black line and the portion above it lies outside the Gaussian ...
89 views

Formal Connection Between Symmetry and Gauss's Law

In the standard undergraduate treatment of E&M, Gauss's Law is loosely stated as "the electric flux through a closed surface is proportional to the enclosed charge". Equivalently, in differential ...
70 views

Extensors in mathematics and in physics [closed]

Could someone explain in a simple but accurate manner what extensors are as mathematical entities and how they are used? How do extensors essentially differ from tensors? Are there or could there be ...
48 views

How to make sense of these zero frequency creation operators and corresponding states?

In quantum field theory a soft particle is a low energy particle. If I'm not mistaken one introduces a energy treshold $\Lambda$ and calls soft any particle with energy $\omega < \Lambda$. If \$a^\...