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# 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.

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### Rank of the Poincare group

There are two Casimirs of the Poincare group: $$C_1 = P^\mu P_\mu, \quad C_2 = W^\mu W_\mu$$ with the Pauli-Lubanski vector $W_\mu$. This implies the Poincare group has rank 2. Is there a way to ...
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### Difference between symmetry and invariance

I'm wondering what's the real difference between symmetry and invariance in Physics? I believe that sometimes the two words are given the same meaning and some other times they are used in a different ...
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### Does the Kosterlitz–Thouless transition connect phases with different topological quantum numbers?

The Kosterlitz-Thouless transition is often described as a "topological phase transition." I understand why it isn't a conventional Landau-symmetry-breaking phase transition: there is no local ...
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### Can GR be reformulated in terms of invariant observables?

Question So recently I was thinking about this: How many scalars are available in $4$ dimensions in General Relativity (without being redundant)? For example, with metric we can construct the ...
### Prove that $\mathbf{E}^2-\mathbf{B}^2$ and $\mathbf{E}\cdot\mathbf{B}$ are the only two independent Lorentz invariant quantities [duplicate]
How to prove that $\mathbf{E}^2-\mathbf{B}^2$ and $\mathbf{E}\cdot\mathbf{B}$ are the only two independent Lorentz invariant quantities that are constructed by $\mathbf{E}$ and $\mathbf{B}$? It's ...