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Thirring–Wess Model
The Thirring–Wess model or Vector Meson model is an exactly solvable quantum field theory, describing the interaction of a Dirac field with a vector field in dimension two. Definition The Lagrangian density is made of three terms: the free vector field A^\mu is described by : + (A^\mu)^2 for F^= \partial^\mu A^\nu - \partial^\nu A^\mu and the boson mass \mu must be strictly positive; the free fermion field \psi is described by : \overline(i\partial\!\!\!/-m)\psi where the fermion mass m can be positive or zero. And the interaction term is : qA^\mu(\bar\psi\gamma^\mu\psi) Although not required to define the massive vector field, there can be also a gauge-fixing term : (\partial^\mu A^\mu)^2 for \alpha \ge 0 There is a remarkable difference between the case \alpha > 0 and the case \alpha = 0 : the latter requires a field renormalization to absorb divergences of the two point correlation. History This model was introduced by Thirring and Wess a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermion Field
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. Basic properties Free (non-interacting) fermionic fields obey canonical anticommutation relations; i.e., involve the anticommutators = ''ab'' + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Density
Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with an easier problem having an enlarged feasible set ** Lagrangian dual problem, the problem of maximizing the value of the Lagrangian function, in terms of the Lagrange-multiplier variable; See Dual problem * Lagrangian, a functional whose extrema are to be determined in the calculus of variations * Lagrangian submanifold, a class of submanifolds in symplectic geometry * Lagrangian system, a pair consisting of a smooth fiber bundle and a Lagrangian density Physics * Lagrangian mechanics, a reformulation of classical mechanics * Lagrangian (field theory), a formalism in classical field theory * Lagrangian point, a position in an orbital configuration of two large bodies * Lagrangian coordinates, a way of describing the motions of particles of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renormalization
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian. For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwinger Model
In physics, the Schwinger model, named after Julian Schwinger, is the model describing 1+1D (1 spatial dimension + time) '' Lorentzian'' quantum electrodynamics which includes electrons, coupled to photons. The model defines the usual QED Lagrangian : \mathcal = - \fracF_F^ + \bar (i \gamma^\mu D_\mu -m) \psi over a spacetime with one spatial dimension and one temporal dimension. Where F_ = \partial_\mu A_\nu - \partial_\nu A_\mu is the U(1) photon field strength, D_\mu = \partial_\mu - iA_\mu is the gauge covariant derivative, \psi is the fermion spinor, m is the fermion mass and \gamma^0, \gamma^1 form the two-dimensional representation of the Clifford algebra. This model exhibits confinement of the fermions and as such, is a toy model for QCD. A handwaving argument why this is so is because in two dimensions, classically, the potential between two charged particles goes linearly as r, instead of 1/r in 4 dimensions, 3 spatial, 1 time. This model also exhibits a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Physics
''Annals of Physics'' is a monthly peer-reviewed scientific journal covering all aspects of physics. It was established in 1957 and is published by Elsevier. The editor-in-chief is Neil Turok (University of Edinburgh School of Physics and Astronomy). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 2.73. References External links * Physics journals Monthly journals Publications established in 1957 English-language journals Elsevier academic journals {{physics-journal-stub ... [...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] |
Il Nuovo Cimento
''Nuovo Cimento'' is a series of peer-reviewed scientific journals of physics. The series was first established in 1855, when Carlo Matteucci and Raffaele Piria started publishing ''Il Nuovo Cimento'' as the continuation of ''Il Cimento'', which they established in 1844. In 1897, it became the official journal of the Italian Physical Society. Over time, the journal split into several sub-journals: * ''Nuovo Cimento A'' (1965–1999): Focused on particle physics. The journal ended when it was merged into the ''European Physical Journal'', in 1999. * ''Nuovo Cimento B'' (1965–2010): Focused on relativity, astronomy, and mathematical physics. As of 1 January 2011 it continues publication as the ''European Physical Journal Plus''. * ''Nuovo Cimento C'' (1978–present): Focuses on geophysics, astrophysics, and biophysics. * ''Nuovo Cimento D'' (1982–1998): Focuses on solid state physics, atomic physics, and molecular biology. The journal ended when it was merged into the '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Il Nuovo Cimento A
''Nuovo Cimento'' is a series of peer-reviewed scientific journals of physics. The series was first established in 1855, when Carlo Matteucci and Raffaele Piria started publishing ''Il Nuovo Cimento'' as the continuation of ''Il Cimento'', which they established in 1844. In 1897, it became the official journal of the Italian Physical Society. Over time, the journal split into several sub-journals: * ''Nuovo Cimento A'' (1965–1999): Focused on particle physics. The journal ended when it was merged into the ''European Physical Journal'', in 1999. * ''Nuovo Cimento B'' (1965–2010): Focused on relativity, astronomy, and mathematical physics. As of 1 January 2011 it continues publication as the ''European Physical Journal Plus''. * ''Nuovo Cimento C'' (1978–present): Focuses on geophysics, astrophysics, and biophysics. * ''Nuovo Cimento D'' (1982–1998): Focuses on solid state physics, atomic physics, and molecular biology. The journal ended when it was merged into the ''Europ ... [...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] |
