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Questions tagged [invariants]

The tag has no usage guidance.

2
votes
1answer
227 views

Does a constant of motion always imply a Hamiltonian formulation?

If a continuous dynamical system has a constant of motion that is a function of all its variables, and is not already evidently Hamiltonian, is it always possible to use a change of variables and ...
1
vote
1answer
661 views

Calculating electromagnetic invariant in matrix form

I'm kind of confused. I want to calculate the electromagnetic invariant $I := F^{\mu\nu}F_{\mu\nu} $, but I'm not sure what is the easiest way to do so. So, I was trying to do it in matrix form, i.e. ...
22
votes
4answers
4k views

To which extent is general relativity a gauge theory?

In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the ...
4
votes
2answers
703 views

Invariance and forms of the Lagrangian

I have been reading the 1st chapter of Landau & Lifshitz Mechanics, and due to its concise style been facing a few problems. I hope you can help me out here somehow. Does the "homogeneity of ...
12
votes
4answers
4k views

Definitions and usage of Covariant, Form-invariant & Invariant?

Just wondering about the definitions and usage of these three terms. To my understanding so far, "covariant" and "form-invariant" are used when referring to physical laws, and these words are ...
-1
votes
3answers
3k views

Is kinetic energy a scalar? [closed]

Is it correct to say that kinetic energy is a scalar?