Griffiths Introduction to Elementary Particles · Problem 7.1

Electrodynamics of Quarks and Hadrons — David J. Griffiths

Physics — QFT · covariant-four-vectors

Problem

Show that

\partial\phi/\partial x^\mu

is a covariant four-vector (

\phi

is a scalar function of

x

y

z

, and

t

). [Hint: First determine [from (3.7)] how covariant four-vectors transform; then use

\partial\phi/\partial x^{\mu'} = (\partial\phi/\partial x^\nu)(\partial x^\nu/\partial x^{\mu'})

to find out how

\partial\phi/\partial x^\mu

transforms.]