A. Zee, Quantum Field Theory in a Nutshell · Problem N.2.8

Field Theory Redux

Physics — QFT

Problem

Show that

SL(4, R)

is locally isomorphic to the conformal group. [Hint: Identify the

15 = 4^2 - 1

generators of the conformal group (3 rotations

J^i

, 3 boosts

K^i

, 1 dilation

D

, 4 translations

P^\mu

, and 4 conformal transformations

K^\mu

) with the 15 traceless real

4 \times 4

matrices.]