# Questions tagged [invariants]

This tag is for questions relating to invariant, a property of a system which remains unchanged under some transformation. In physics, invariance is related to conservation laws.

327 questions
Filter by
Sorted by
Tagged with
26 views

### On finding a scalar function which leads to a covariant tensor by differentiation

I need to find a scalar (invariant) function $F$ that when differentiated, leads to a covariant tensor function $f$ with one live index as: $$\frac{\partial F}{\partial \dot x^k} = f_k$$ The ...
• 175
1 vote
35 views

### How to find Casimir operator eigenvalues of $SU(N)$? [closed]

The $[f1, f2, f3…fn]$ in the image represent the irreducible representations of $SU[n]$. How to find the irreducible representations of $SU[n]$ that conform to the form $[f1, f2...fn]$. Can you give ...
33 views

### Linearity of Amplitudes and Lorentz Frames

I know that this question may be a bit weird, but I decided to ask. Assume I have an amplitude, say in QED, which depends on a set of four-momenta $\{p_1,\ p_2,\ p_3,\ ...,\ p_n\}$. Further assume ...
• 3,992
34 views

### Relation bitween Mandelstam Variables in three-body final state

What is the relation between Mandelstam variables in the three body final state? There are 5 independent Mandelstam variables. What is the relationship between them?
• 11
48 views

### Mandelstams for $2\to 2\to 3$ process

2 initial particles become two other particles, from which one decays into 2. Let $p1$ and $p2$ be the momenta of the initial particles, $p3$ the momentum of the decaying particle, $p5$ and p6 the ...
1 vote
69 views

• 372
1 vote
103 views

### Challenging Cauchy's Stress Tensor: Objectivity and Generalization of Divergence Theorem

I'm investigating the limitations of the Cauchy stress tensor model in classical continuum mechanics, specifically focusing on its compliance with the principle of material frame indifference (MFI) ...
• 373
25 views

### How to show that $G_p=SO(D-1)$?

Let $G=SO(D-1,1)^{‎\uparrow‎}$ be the connected Lorentz group. Let $p$ be a timelike momentum with $p_0>0$. I want to show that $G_p=SO(D-1)$, the little group of $p=(M,0,\ldots,0)$ where $M>0$....
• 372
59 views

### Kretschmann Scalar for the FLRW Metric

I am trying to understand the Wikipedia definition of the Kretschmann scalar for a cosmological solution. The metric is given by the standard FLRW metric \begin{equation*} ds^2 = -dt^2 +a^2(t)\left(\...
• 1,611
71 views

477 views

### Speed of light postulate in special relativity in inertial vs. non-inertial frames

I'm trying to learn special relativity by myself. I've been following this series of videos, plus some other articles I've managed to find online. At this point I'm already quite far into the theory, ...
• 540
608 views

### Where does the negative signature case come from in the Pythagorean derivation of distances in spacetime?

I am reading Why does $E=mc^2$ (and why should we care?) by Brian Cox and Jeff Forshaw. I want to understand these three sentences (from page 76/77): Once we follow Occam and make these two ...
• 175
127 views

127 views

### Invariance and covariance [duplicate]

What exactly do we mean when we say that something is covariant? How is it different from being invariant? Am i right if I say that the word invariant is used when we're talking about a physical ...
• 140
1 vote