Carroll contractions of Lorentz-invariant theories

Understand

We consider Carroll-invariant limits of Lorentz-invariant field theories.

• We show that just as in the case of electromagnetism, there are two inequivalent limits, one "electric" and the other "magnetic".
• Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same "contraction" procedure of taking the ultrarelativistic limit $c \rightarrow 0$ where $c$ is the speed of light, but with two different consistent rescalings of the canonical variables.
• This procedure can be applied to general Lorentz-invariant theories ($p$-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion).