.4.3 dynamical
susceptibility

4.4 dispersion relations

4.5 spectral representation

4.6 fluctuation-dissipation theorem

4.7 examples of applications

4.8 symmetry properties

4.9 sum rules

problems

bibliography for part i

part ii. relativistic wave equations

5. relativistic wave equations and their derivation

5.1 introduction

5.2 the klein-gordon equation

5.3 dirac equation

problems

6. lorentz transformations and covariance of the dirac
equation

6.1 lorentz transformations

6.2 lorentz covariance of the dirac equation

6.3 solutions of the dirac equation for free particles

problems

7. orbital angular momentum and spin

7.1 passive and active transformations

7.2 rotations and angular momentum

problems

8. the coulomb potential

8.1 klein-gordon equation with electromagnetic field

8.2 dirac equation for the coulomb potential

problems

9. the foldy-wouthuysen transformation and relativistic
corrections

9.1 the foldy-wouthuysen transformation

9.2 relativistic corrections and the lamb shift

problems

10. physical interpretation of the solutions to the dirac
equation

10.1 wave packets and "zitterbewegung"

10.2 the hole theory

problems

11. symmetries and further properties of the dirac equation

11.1 active and passive transformations, transformations of
vectors

11.2 invariance and conservation laws

11.3 charge conjugation

11.4 time reversal (motion reversal)

11.5 helicity

11.6 zero-mass fermions (neutrinos)

problems

bibliography for part ii

part iii. relativistic fields

12. quantization of relativistic fields

12.1 coupled oscillators, the linear chain, lattice
vibrations

12.2 classical field theory

12.3 canonical quantization

12.4 symmetries and conservation laws, noether's theorem

problems

13. free fields

13.1 the real klein-gordon field

13.2 the complex klein-gordon field

13.3 quantization of the dirac field

13.4 the spin statistics theorem

problems

14. quantization of the radiation field

14.1 classical electrodynamics

14.2 the coulomb gauge

14.3 the lagrangian density for the electromagnetic field

14.4 the free electromagnatic field and its quantization

14.5 calculation of the photon propagator

problems

15. interacting fields, quantum electrodynamics

15.1 lagrangians, interacting fields

15.2 the interaction representation, perturbation theory

15.3 the s matrix

15.4 wick's theorem

15.5 simple scattering processes, feynman diagrams

15.6 radiative corrections

problems

bibliography for part iii

appendix

a alternative derivation of the dirac. equation

b dirac matrices

c projection operators for the spin

d the path-integral representation of quantum mechanics

e covariant quantization of the electromagnetic field, the
gupta-bleuler method

f coupling of charged scalar mesons to the electromagnetic
field

index