# Self-energy > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Self-energy > Markdown URL: https://mediated.wiki/source/Self-energy.md > Source: https://en.wikipedia.org/wiki/Self-energy > Source revision: 1336768628 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Use American English|date = February 2019}} {{Short description|Energy quantum particles contribute to themselves}} In [quantum field theory](/source/quantum_field_theory), the [energy](/source/energy) that a [particle](/source/particle) has as a result of changes that it causes in its environment defines its '''self-energy''' \Sigma. The self-energy represents the contribution to the particle's energy, or [effective mass](/source/Effective_mass_(solid-state_physics)), due to interactions between the particle and its environment. In [electrostatics](/source/electrostatics), the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero. In a [condensed matter](/source/condensed_matter) context, self-energy is used to describe interaction induced [renormalization](/source/renormalization) of [quasiparticle](/source/quasiparticle) mass ([dispersions](/source/Dispersion_relation)) and lifetime. Self-energy is especially used to describe [electron](/source/electron)-electron interactions in [Fermi liquids](/source/Fermi_liquid_theory). Another example of self-energy is found in the context of [phonon](/source/phonon) softening due to electron-phonon coupling. ==Characteristics== Mathematically, this energy is equal to the so-called [on mass shell](/source/On_shell_and_off_shell) value of the proper self-energy ''operator'' (or proper mass ''operator'') in the momentum-energy representation (more precisely, to [\hbar](/source/Planck_constant) times this value). In this, or other representations (such as the space-time representation), the self-energy is pictorially (and economically) represented by means of [Feynman diagram](/source/Feynman_diagram)s, such as the one shown below. In this particular diagram, the three arrowed straight lines represent particles, or particle [propagator](/source/propagator)s, and the wavy line a particle-particle interaction; removing (or ''amputating'') the left-most and the right-most straight lines in the diagram shown below (these so-called ''external'' lines correspond to prescribed values for, for instance, momentum and energy, or [four-momentum](/source/four-momentum)), one retains a contribution to the self-energy operator (in, for instance, the momentum-energy representation). Using a small number of simple rules, each Feynman diagram can be readily expressed in its corresponding algebraic form. In general, the on-the-mass-shell value of the self-energy operator in the momentum-energy representation is [complex](/source/complex_number). In such cases, it is the real part of this self-energy that is identified with the physical self-energy (referred to above as particle's "self-energy"); the inverse of the imaginary part is a measure for the lifetime of the particle under investigation. For clarity, elementary excitations, or [dressed particle](/source/dressed_particle)s (see [quasi-particle](/source/quasi-particle)), in interacting systems are distinct from stable particles in vacuum; their state functions consist of complicated superpositions of the [eigenstates](/source/Eigenvalues_and_eigenvectors) of the underlying many-particle system, which only momentarily, if at all, behave like those specific to isolated particles; the above-mentioned lifetime is the time over which a dressed particle behaves as if it were a single particle with well-defined momentum and energy. The self-energy operator (often denoted by \Sigma_{}^{}, and less frequently by M_{}^{}) is related to the bare and dressed propagators (often denoted by G_0^{} and G_{}^{} respectively) via the '''Dyson equation''' (named after [Freeman Dyson](/source/Freeman_Dyson)): :G = G_0^{} + G_0 \Sigma G. Multiplying on the left by the inverse G_0^{-1} of the operator G_0 and on the right by G^{-1} yields :\Sigma = G_0^{-1} - G^{-1}. :File:electron self energy.svg :File:Dyson.svg The [photon](/source/photon) and [gluon](/source/gluon) do not get a mass through [renormalization](/source/renormalization) because [gauge symmetry](/source/gauge_symmetry) protects them from getting a mass. This is a consequence of the [Ward identity](/source/Ward%E2%80%93Takahashi_identity). The [W-boson](/source/W-boson) and the [Z-boson](/source/Z-boson) get their masses through the [Higgs mechanism](/source/Higgs_mechanism); they do undergo mass renormalization through the renormalization of the [electroweak](/source/electroweak) theory. Neutral particles with internal quantum numbers can mix with each other through [virtual pair](/source/virtual_pair) production. The primary example of this phenomenon is the mixing of neutral [kaon](/source/kaon)s. Under appropriate simplifying assumptions this can be described [without quantum field theory](/source/Neutral_particle_oscillations). == Other uses == In [chemistry](/source/chemistry), the self-energy or '''Born energy''' of an ion is the energy associated with the field of the ion itself.{{Citation needed|date=March 2021}} In [solid state](/source/Solid-state_physics) and [condensed-matter](/source/Condensed-matter_physics) physics self-energies and a myriad of related [quasiparticle](/source/quasiparticle) properties are calculated by [Green's function](/source/Green's_function) methods and [Green's function (many-body theory)](/source/Green's_function_(many-body_theory)) of '''interacting low-energy excitations''' on the basis of [electronic band structure](/source/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).{{Citation needed|date=March 2021}} == See also == * [Quantum field theory](/source/Quantum_field_theory) * [QED vacuum](/source/QED_vacuum) * [Renormalization](/source/Renormalization) * [Self-force](/source/Self-force) * [GW approximation](/source/GW_approximation) * [Wheeler–Feynman absorber theory](/source/Wheeler%E2%80%93Feynman_absorber_theory) == References == {{Reflist}} * 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. * {{cite book |last = Alexei M. Tsvelik |title = Quantum Field Theory in Condensed Matter Physics |edition = 2nd |publisher = Cambridge University Press |year = 2007 |isbn = 978-0-521-52980-8 }} * A. N. Vasil'ev ''The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics'' (Routledge Chapman & Hall 2004); {{ISBN|0-415-31002-4}}; {{ISBN|978-0-415-31002-4}} * {{cite book |last = John E. Inglesfield |title = The Embedding Method for Electronic Structure |publisher = IOP Publishing |year = 2015 |isbn = 978-0-7503-1042-0 }} {{QED}} Category:Quantum electrodynamics Category:Quantum field theory Category:Renormalization group --- Adapted from the Wikipedia article [Self-energy](https://en.wikipedia.org/wiki/Self-energy) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Self-energy?action=history)). 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