# 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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### What Lorentz covariance has to do with Lorentz invariance? [duplicate]

Does saying that the Dirac equation is invariant under Lorentz transformations is the same as saying that it is Lorentz covariant?
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### Distance formula in Euclidean space vs. Spacetime Interval - why is one Pythagorean and one not?

I appreciate if this question has been posited before and easily findable by Google searching, but as of yet I haven't found anything to answer this. I'm sure I'm making an incorrect assumption in the ...
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### Why is the Ricci scalar the only independent scalar constructed from products of the metric and its first and second derivatives? [duplicate]

In Sean Carroll's book, last paragraph of page 160, this statement is found: "The Riemann tensor is of course made from the second derivatives of the metric, and we argued earlier that the only ...
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### Why are the metric and the Levi-Civita tensor the only invariant tensors?

The only numerical tensors that are invariant under some relevant symmetry group (the Euclidean group in Newtonian mechanics, the Poincare group in special relativity, and the diffeomorphism group in ...
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### importance of invariant tensors

while studying representations of SL(2,C), for raising and lowering indices of spinors invariant tensor $\epsilon$ was constructed analogous to $\eta$ in SO(1,3).What is the importance of invariant ...
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### The implications of Einstein's first law

I'm struggling with the physical meaning/consequence of Einstein's first postulate of Special Relativity, which states that all physical laws are the same (invariant) in all inertial frames. Any ...
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### energy threshold of proton-proton collision

Could you please help me understand what's wrong with the following calculation? When a proton moves toward a fixed proton with very high speed and collides with it, then the following interaction ...
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### What is the definition of invariance under Lorentz transformation?

I want to learn how to check if any scalar is a Lorentz scalar, so what is the definition of being invariant under Lorentz transformation? Is it correct to say that $\phi$ is invarant under Lorentz ...
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### Providing an intuitive description of scalar and vector quantities in physics [closed]

Often the standard introduction to the concept of scalars and vectors in physics is something along the lines of: A scalar is a quantity that is completely described by a single number (it has no ...
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### Finding Casimir operators for the Poincare group $ISO(1,2)$

I was asked to write the generators for translations and Lorentz-transforms in 1+2 dimensions and then to find the Casimir operators. For the generators I can take the same ones as in 1+3 case P_\...
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### Quadratic Casimir operator of higher dimensional $\mathfrak{su}(3)$ representations

In higher dimensional representations of $\mathfrak{su(3)}$, what will be the quadratic Casimir operator? Is it same as in lower dimensions or different?
In Field Quantization by Greiner and Reinhardt as well as The Qunatum Theory of Fields by Weinberg, concerning the spectral function, the authors say a scalar function of the four-vector $p^\mu$ can ...