Griffiths Introduction to Elementary Particles · Problem 7.5

Electrodynamics of Quarks and Hadrons — David J. Griffiths

Physics — QFT · dirac-spinors-nonrelativistic-limit

Problem

Show that for

u^{(1)}

and

u^{(2)}

[eq. (7.46)] the lower components (

u_B

) are smaller than the upper ones (

u_A

), in the nonrelativistic limit, by a factor

v/c

. [This observation simplifies matters, when we are doing nonrelativistic approximations; we think of

u_A

as the ``big'' components and

u_B

as the ``little'' components. (For

u^{(3)}

and

u^{(4)}

the roles are reversed.) In the relativistic limit, by contrast,

u_A

and

u_B

are comparable in size.]