Srednicki — Quantum Field Theory · Problem 38.1

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · spinor-technology

Problem

Use eq. (38.12) to compute

u_s(\mathbf{p})

and

v_s(\mathbf{p})

explicitly. Hint: show that the matrix

2i\hat{\mathbf{p}}\cdot\mathbf{K}

has eigenvalues

\pm 1

, and that, for any matrix

A

with eigenvalues

\pm 1

e^{cA} = (\cosh c) + (\sinh c)A

, where

c

is an arbitrary complex number.