Questions tagged [invariants]

Question 1

I am studying turbulence more specifically properties of filtering operations given by $$ U(x, t) = \int_{\mathbb{R}^n} G(r, x) U(x-r, t) dr $$ with normalization condition $$ \int_{\mathbb{R}^n} G(r, ...

Question 2

So I've learnt that the Lagrangian is invariant under point transformations as well as under gauge transformations. Essentially meaning that if $$ \frac{d}{dt}\!\left(\frac{\partial L}{\partial \dot{q}...

Question 3

I encountered this - a rotating uniform charged ring could produce electric current and magnetic field. I myself find it shouldn’t be. The charges are uniformly distributed. Even so, the ring is ...

Question 4

Let $S_x$, $S_y$, and $S_z$ be the spin operators of a spin-$j$ particle, I noticed using MATLAB that no matter what irreducible representation I choose for $\frak{su}(2)$, I always find that $S_x^{2k}...

Question 5

Maybe a dumb question, but thinking about Drell-Yan, for example, you can detect the Z boson with the invariant mass of its dilepton decay products. However, do the incoming quark/anti-quark pair also ...

Question 6

I am studying turbulence and I came across the concept of isotropic tensors, that is tensor that are invariant under rotations and translations. After googling for a while the thing I found is that, ...

Question 7

Currently in my QFT lecture, we are learning about the renormalization. It was said that one-loop integrals in general can be reduced to scalar integrals, which are easier to solve. As an example I ...

Question 8

Regarding the electromagnetic field, a fundamental invariant is $E^2-B^2$. $E$ is the electric field, $B$ the magnetic field. Regarding the four-momentum of a particle, a fundamental invariant is $\...

Question 9

I'm probably just overthinking this, but here we go: Let $\gamma^\mu$ be the standard Dirac matrices defined by $\{\gamma^\mu,\gamma^\nu\}=2\eta^{\mu\nu}$, where $\eta^{\mu\nu}$ is the Minkowski ...

Question 10

In the chapter on Radiation by Moving charges by Jackson, it is stated that Larmor's formula $$P = \frac{2}{3} \frac{q^2}{4\pi \epsilon_0}\frac{\dot{v}^2}{c^3}$$can be generalized to a relativistic ...

Question 11

I read a book by Professor Liu Chuan. When talking about action principle, the author says: In classical mechamics, the true trajectory of a system is unique. Thus a trajectory obtained by action ...

Question 12

The relativity principle was first stated by Galileo as follows: Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, ...

Question 13

Could someone please lists the killing vectors for the FLRW metric with generic $K$ curvature? \begin{equation} ds^2 = -dt^2 + a(t)^2\left( \frac{dr^2}{1 - k r^2} + r^2 d\theta^2 + r^2 \sin\theta d\...

Question 14

The ground state of the toric code is written as $|\psi_g\rangle=\prod_v\left( \frac{1+A_v}{2} \right)|000...0\rangle$, where $A_v$ is the star operator (product of $\sigma^x$ operators on the edges ...

Question 15

When I was learning about the polarizations of massive and massless particles, I was told that for a massless particle its four-momentum is $p^{\mu}=(p,0,0,p)\;$ (in natural units), so the ...

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Questions tagged [invariants]

Reconciliation of filtering operation in turbulence

What exactly is meant by Invariance of the Lagrangian?

Is it correct for a rotating uniform charged ring to have current?

Sum of even powers of spin operators

For Detecting a Massive Boson via Its Decay Products, Do the Invariant Masses of the Particles That Produce It Have To Be Equal to Its Mass?

Isotropic tensor function

Understanding how to reduce tensor integrals to scalar integrals with the same number of external lines (renormalization)

Similarity of $E^2-B^2$ and $\mathscr{E}^2-p^2$

Constructing a Lorentz Scalar from Bilinear Covariants

Power as a Lorentz invariant (Jackson)

Why action is Lorentz invariant? [duplicate]

Does relativity=invariance? [closed]

Explicit FLRW Killing vector fields

Gauge invariant translational symmetry in the toric code

Wigner's little group: 4-momentum transformation of massive particles

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