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Four-fermion Interaction
In quantum field theory, fermions are described by anticommuting spinor fields. A four-fermion interaction describes a local interaction between four fermionic fields at a point. Local here means that it all happens at the same spacetime point. This might be an effective field theory or it might be fundamental. Relativistic models Some examples are the following: * Fermi's theory of the weak interaction. The interaction term has a (vector minus axial) form. *The Gross–Neveu model. This is a four-fermi theory of Dirac fermions without chiral symmetry and as such, it may or may not be massive. *The Thirring model. This is a four-fermi theory of fermions with a vector coupling. *The Nambu–Jona-Lasinio model. This is a four-fermi theory of Dirac fermions with chiral symmetry and as such, it has no bare mass. Nonrelativistic models A nonrelativistic example is the BCS theory BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gross–Neveu Model
The Gross–Neveu (GN) model is a quantum field theory model of Dirac fermions interacting via four-fermion interactions in 1 spatial and 1 time dimension. It was introduced in 1974 by David Gross and André Neveu as a toy model for quantum chromodynamics (QCD), the theory of strong interactions. It shares several features of the QCD: GN theory is asymptotically free thus at strong coupling the strength of the interaction gets weaker and the corresponding \beta function of the interaction coupling is negative, the theory has a dynamical mass generation mechanism with \mathbb_2 chiral symmetry breaking, and in the large number of flavor (N \to \infty) limit, GN theory behaves as t'Hooft's large N_c limit in QCD. It consists of N Dirac fermions \psi_1, \psi_2, \cdots, \psi_N. The Lagrangian density is :\mathcal=\bar \psi_a \left(i\partial\!\!\!/-m \right) \psi^a + \frac\left bar \psi_a \psi^a\right2. Einstein summation notation is used, \psi^a is a two component spinor objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Term
Contact may refer to: Interaction Physical interaction * Contact (geology), a common geological feature * Contact lens or contact, a lens placed on the eye * Contact sport, a sport in which players make contact with other players or objects * Contact juggling * Contact mechanics, the study of solid objects that deform when touching each other * Contact process (mathematics), a model of an interacting particle system * Electrical contacts * ''Sparśa'', a concept in Buddhism that in Sanskrit/Indian language is translated as "contact", "touching", "sensation", "sense impression", etc. Social interaction * Contact (amateur radio) * Contact (law), a concept related to visitation rights * Contact (social), a person who can offer help in achieving goals * Contact Conference, an annual scientific conference * Extraterrestrial contact, see Search for extraterrestrial intelligence * First contact (anthropology), an initial meeting of two cultures * Language contact, the interaction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dressed Particle
In theoretical physics, the term dressed particle refers to a bare particle together with some excitations of other quantum fields that are physically inseparable from the bare particle. For example, a dressed electron includes the cloud of virtual electron–positron pairs and photons surrounding the original electron. A further noteworthy example is represented by polaritons in solid-state physics, dressed quasiparticles of dipolar excitations in a medium with photons. In radiobiology, a dressed particle is a bare particle together with its Debye sphere that neutralizes its electric charge. Dressed particles are also often called clothed particles. See also * Constituent quark A constituent quark is a current quark with a notional "covering" induced by the renormalization group. In the low-energy limit of QCD, a description by means of perturbation theory is not possible: Here, no asymptotic freedom exists, but collectiv ... References Theoretical physics Quantum field t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BCS Theory
BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes superconductivity as a microscopic effect caused by a condensation of Cooper pairs. The theory is also used in nuclear physics to describe the pairing interaction between nucleons in an atomic nucleus. It was proposed by Bardeen, Cooper, and Schrieffer in 1957; they received the Nobel Prize in Physics for this theory in 1972. History Rapid progress in the understanding of superconductivity gained momentum in the mid-1950s. It began with the 1948 paper, "On the Problem of the Molecular Theory of Superconductivity", where Fritz London proposed that the phenomenological London equations may be consequences of the coherence of a quantum state. In 1953, Brian Pippard, motivated by penetration experiments, proposed that this would modify the Lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonrelativistic
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bare Mass
In quantum field theory, specifically the theory of renormalization, the bare mass of an elementary particle is the limit of its mass as the scale of distance approaches zero or, equivalently, as the energy of a particle collision approaches infinity. It differs from the invariant mass as usually understood because the latter includes the 'clothing' of the particle by pairs of virtual particles that are temporarily created by the fields around the particle. In some versions of QFT, the bare mass of some particles may be plus or minus infinity. In the theory of the electroweak interaction using the Higgs boson, all particles have a bare mass of zero. This allows us to write m = m_0 + \delta_m, where m denotes the experimentally observable mass of the particle, m_0 its bare mass, and \delta_m the increase in mass owing to the interaction of the particle with the medium or field. See also * Pole mass In quantum field theory, the pole mass of an elementary particle is the limiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nambu–Jona-Lasinio Model
In quantum field theory, the Nambu–Jona-Lasinio model (or more precisely: ''the Nambu and Jona-Lasinio model'') is a complicated effective theory of nucleons and mesons constructed from interacting Dirac fermions with chiral symmetry, paralleling the construction of Cooper pairs from electrons in the BCS theory of superconductivity. The "complicatedness" of the theory has become more natural as it is now seen as a low-energy approximation of the still more basic theory of quantum chromodynamics, which does not work perturbatively at low energies. Overview The model is much inspired by the different field of solid state theory, particularly from the BCS breakthrough of 1957. The first inventor of the Nambu–Jona-Lasinio model, Yoichiro Nambu, also contributed essentially to the theory of superconductivity, i.e., by the "Nambu formalism". The second inventor was Giovanni Jona-Lasinio. The common paper of the authors that introduced the model appeared in 1961. A subsequent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thirring Model
The Thirring model is an exactly solvable quantum field theory which describes the self-interactions of a Dirac field in (1+1) dimensions. Definition The Thirring model is given by the Lagrangian density : \mathcal= \overline(i\partial\!\!\!/-m)\psi -\frac\left(\overline\gamma^\mu\psi\right) \left(\overline\gamma_\mu \psi\right)\ where \psi=(\psi_+,\psi_-) is the field, ''g'' is the coupling constant, ''m'' is the mass, and \gamma^\mu, for \mu = 0,1, are the two-dimensional gamma matrices. This is the unique model of (1+1)-dimensional, Dirac fermions with a local (self-)interaction. Indeed, since there are only 4 independent fields, because of the Pauli principle, all the quartic, local interactions are equivalent; and all higher power, local interactions vanish. (Interactions containing derivatives, such as (\bar \psi\partial\!\!\!/\psi)^2, are not considered because they are non-renormalizable.) The correlation functions of the Thirring model (massive or massless) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Symmetry
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Chirality and helicity The helicity of a particle is positive (“right-handed”) if the direction of its spin is the same as the direction of its motion. It is negative (“left-handed”) if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: “left” is negative, “right” is positive. The chirality ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Fermion
In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. The vast majority of fermions – perhaps all – fall under this category. Description In particle physics, all fermions in the standard model have distinct antiparticles (''perhaps'' excepting neutrinos) and hence are Dirac fermions. They are named after Paul Dirac, and can be modeled with the Dirac equation. A Dirac fermion is equivalent to two Weyl fermions. The counterpart to a Dirac fermion is a Majorana fermion, a particle that must be its own antiparticle. Dirac quasi-particles In condensed matter physics, low-energy excitations in graphene and topological insulators, among others, are fermionic quasiparticles described by a pseudo-relativistic Dirac equation. See also * Dirac spinor, a wavefunction-like description of a Dirac fermion * Dirac–Kähler fermion, a geometric formulation of Dirac fermions * Majorana fermion, an alternate category of fermion, possibly de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axial Vector
In physics and mathematics, a pseudovector (or axial vector) is a quantity that is defined as a function of some vectors or other geometric shapes, that resembles a vector, and behaves like a vector in many situations, but is changed into its opposite if the orientation of the space is changed, or an improper rigid transformation such as a reflection is applied to the whole figure. Geometrically, the direction of a reflected pseudovector is opposite to its mirror image, but with equal magnitude. In contrast, the reflection of a ''true'' (or polar) vector is exactly the same as its mirror image. In three dimensions, the curl of a polar vector field at a point and the cross product of two polar vectors are pseudovectors. One example of a pseudovector is the normal to an oriented plane. An oriented plane can be defined by two non-parallel vectors, a and b, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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