Self-energy

In quantum field theory and statistical mechanics one encounters the
concept of the self-energy of a particle.

But self-energy is not a fraction of the energy associated with a
single particle but a function of momentum describing the off-shell
dispersion of the associated wave functions in interactions.

The self-energy governs the form of the kinetic energy term in a single-particle equation, and describes kinetic corrections to the Schroedinger or Pauli equation for nonrelativistic particles, and to the Klein-Gordon equation, the Dirac equation, or the Maxwell equations. for relativistic scalar, spinor, and vector particles. (The correction to the interaction term is goverend by form factors; see the FAQ entry ''Are electrons pointlike/structureless?''.)

The ''self'' is a misnomer, due only to historical reasons. Instead, the self-energy is created by the cooperative effects of the environment of a particle.

In statistical mechanics, another term for the self-energy is ''memory function''. These terms are used synonymously, and describe (together with form factor corrections, if they exist) the memory a particle has of its multiparticle origin, when a multiparticle system is (approximately) separated into a single particle and an effective field representing the remainder of the universe.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ