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Fermionic field information


In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics. Fermionic fields obey canonical anticommutation relations rather than the canonical commutation relations of bosonic fields.

The most prominent example of a fermionic field is the Dirac field, which describes fermions with spin-1/2: electrons, protons, quarks, etc. The Dirac field can be described as either a 4-component spinor or as a pair of 2-component Weyl spinors. Spin-1/2 Majorana fermions, such as the hypothetical neutralino, can be described as either a dependent 4-component Majorana spinor or a single 2-component Weyl spinor. It is not known whether the neutrino is a Majorana fermion or a Dirac fermion; observing neutrinoless double-beta decay experimentally would settle this question.

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Fermionic field

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quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics. Fermionic fields obey canonical...

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Fermionic condensate

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A fermionic condensate (or Fermi–Dirac condensate) is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the...

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Fermion

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Chirality (physics), left-handed and right-handed Fermionic condensate Weyl semimetal Fermionic field Identical particles Kogut–Susskind fermion, a type...

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Fermion doubling

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In lattice field theory, fermion doubling occurs when naively putting fermionic fields on a lattice, resulting in more fermionic states than expected...

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Hamiltonian constraint of LQG

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variables on the three-dimensional spatial slices in terms of a SU(2) gauge field and its complementary variable. The Hamiltonian was much simplified in this...

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Bosonic field

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relations obeyed by fermionic fields. Examples include scalar fields, describing spin-0 particles such as the Higgs boson, and gauge fields, describing spin-1...

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Composite field

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formalism, composite fields, which are usually nonlocal, are used to model asymptotic bound states. Fermionic field Bosonic field Auxiliary field v t e...

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Relationship between string theory and quantum field theory

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in spacetime. These arrows are described by a field "living" on the string. This is a fermionic field, because at each point of the string there is only...

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Proton

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found to be equal and opposite to that of a proton. Physics portal Fermionic field Hydrogen Hydron (chemistry) List of particles Proton–proton chain Quark...

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Feynman diagram

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point xi; A fermionic field ψ(xi) is represented by a solid line attached to the point xi with an arrow toward the point; An anti-fermionic field ψ(xi) is...

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Auxiliary field

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{1}{2}}A^{2}+Af}={\sqrt {2\pi }}e^{\frac {f^{2}}{2}}.} Bosonic field Fermionic field Composite Field Fujimori, Toshiaki; Nitta, Muneto; Yamada, Yusuke (2016-09-19)...

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Grassmann number

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early use in physics to express a path integral representation for fermionic fields, although they are now widely used as a foundation for superspace,...

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Mathematical formulation of the Standard Model

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following fields. These describe one generation of leptons and quarks, and there are three generations, so there are three copies of each fermionic field. By...

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Thermal quantum field theory

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the above trace (Tr) leads to the requirement that all bosonic and fermionic fields be periodic and antiperiodic, respectively, with respect to the Euclidean...

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Dirac sea

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annihilate a positive energy particle, and lower the energy. For a fermionic field, the creation operator a † ( k ) {\displaystyle a^{\dagger }(k)} gives...

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Dirac equation

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physics". In the context of quantum field theory, the Dirac equation is reinterpreted to describe quantum fields corresponding to spin-1⁄2 particles....

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Higgsino

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higgsino, symbol H͂ , is the superpartner of the Higgs field. A higgsino is a Dirac fermionic field with spin 1⁄2 and it refers to a weak isodoublet with...

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Primary field

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containing fermionic generators. Quantum field theories invariant with respect to such extended algebras are called superconformal. In superconformal field theories...

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Effective action

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effective action for a single scalar field, however, similar results exist for multiple scalar or fermionic fields. These generating functionals also have...

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Super Virasoro algebra

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boundary conditions), described by the Neveu–Schwarz algebra. For a fermionic field, the periodicity depends on the choice of coordinates on the worldsheet...

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Supersymmetry algebra

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symmetries. Bosonic fields commute while fermionic fields anticommute. In order to have a transformation that relates the two kinds of fields, the introduction...

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Quantum field theory

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Shing-Tung (2017). "Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions". Annals of Physics...

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Superspace

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correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom. The word "superspace" was first used by John Wheeler...

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List of scientific laws named after people

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people (eponymous laws). For other lists of eponyms, see eponym. Eponym Fields of science List of eponymous laws (overlaps with this list but includes...

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Schwinger function

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real-analytic, symmetric under the permutation of arguments (antisymmetric for fermionic fields), Euclidean covariant and satisfy a property known as reflection positivity...

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