a single particle with well-defined momentum and energy. The self-energy operator (often denoted by , and less frequently by ) is related to the bare and dressed propagators (often denoted by and respectively) via the Dyson equation (named after Freeman Dyson): Multiplying on the left by the inverse of the operator and on the right by yields The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass. This is a consequence of the Ward identity. The W-boson and the Z-boson get their masses through the Higgs mechanism; they do undergo mass renormalization through the renormalization of the electroweak theory. Neutral particles with internal quantum numbers can mix with each other through virtual pair production. The primary example of this phenomenon is the mixing of neutral kaons. Under appropriate simplifying assumptions this can be described without quantum field theory. Other uses In chemistry, the self-energy or Born energy of an ion is the energy associated with the field of the ion itself. In solid state and condensed-matter physics self-energies and a myriad of related quasiparticle properties are calculated by Green's function methods and Green's function (many-body theory) of interacting low-energy excitations on the basis of electronic band structure calculations. Self-energies also find extensive application in the calculation of particle transport through open quantum systems and the embedding of sub-regions into larger systems (for example the surface of a semi-infinite crystal). See also Quantum field theory QED vacuum Renormalization Self-force GW approximation Wheeler–Feynman absorber theory References A. L. Fetter, and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971); (Dover, New York, 2003) J. W. Negele, and H. Orland, Quantum Many-Particle Systems (Westview Press, Boulder, 1998) A. A. Abrikosov, L. P. Gorkov and I. E. Dzyaloshinski (1963): Methods of Quantum Field Theory in Statistical Physics Englewood Cliffs: Prentice-Hall. A. N. Vasil'ev The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (Routledge Chapman & Hall 2004); ; Quantum electrodynamics Quantum field theory Renormalization group