Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

This is something I've been unsure of for a while but still don't quite get.

How does one tell whether an expression (e.g. the Dirac equation) is covariant or not? I get it for a single tensor, but how is it defined when there is no overall up/down index to base it on? Any advice?

share|improve this question

1 Answer 1

up vote 3 down vote accepted

The covariance of Dirac equation in the ordinary Hamiltonian form

$$i\hbar \frac{\partial \Psi}{\partial t} = H \Psi$$

is far from evident. The 'trick' consists on rewriting it in terms of invariant/covariant quantities such as the Dirac matrices $\gamma_\mu$ and kinetic four-momenta $\pi^\mu$

$$\gamma_\mu \pi^\mu \Psi = m \Psi$$

This rewritten form can be found in any standard textbook (check e.g. Feynman's Quantum electrodynamics) and its covariance is rather evident.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.