selfenergies

Self-energies are corrections to the propagator of a particle that arise from interactions with fields or with other particles. They are a central concept in quantum field theory and in many-body physics, where a particle is considered to be dressed by its environment rather than free.

In perturbation theory, the self-energy Σ represents the sum of all one-particle-irreducible two-point diagrams. The full propagator G is related to the bare propagator G0 by the Dyson equation G = G0 + G0 Σ G, or equivalently G = 1/(G0^{-1} - Σ). The self-energy thus encodes how interactions modify the propagation of a particle through space and time.

The self-energy is generally a complex function of energy and momentum. Its real part shifts the particle’s mass or dispersion relation, while its imaginary part yields a finite lifetime or damping, reflecting decay processes or scattering into other states. This distinction underlies the notion of quasiparticles in many systems, where well-defined peaks in spectral functions persist when the real part dominates near certain energies.

Examples and methods. In quantum electrodynamics, the electron self-energy and the photon self-energy (vacuum polarization) are standard, with ultraviolet divergences addressed by renormalization. In condensed matter and many-body theory, the electron self-energy Σ(k, ω) accounts for interactions with other electrons, phonons, or plasmons. Practical calculations include approximate schemes such as the GW method, where Σ ≈ iGW, and the extraction of spectral functions A(k, ω) = −(1/π) Im G(k, ω), which are probed by experiments like photoemission.