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On-shell Scheme
In quantum field theory, and especially in quantum electrodynamics, the interacting theory leads to infinite quantities that have to be absorbed in a renormalization procedure, in order to be able to predict measurable quantities. The renormalization scheme can depend on the type of particles that are being considered. For particles that can travel asymptotically large distances, or for low energy processes, the on-shell scheme, also known as the physical scheme, is appropriate. If these conditions are not fulfilled, one can turn to other schemes, like the minimal subtraction scheme (MS scheme). Fermion propagator in the interacting theory Knowing the different propagators is the basis for being able to calculate Feynman diagrams which are useful tools to predict, for example, the result of scattering experiments. In a theory where the only field is the Dirac field, the Feynman propagator reads : \langle 0 , T(\psi(x)\bar(0)), 0 \rangle =iS_F(x) = \int \frac\frac where T is t ... [...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] |
Minkowski Space
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be implied by the postulates of special relativity. Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events.This makes spacetime distance an invariant. Becaus ... [...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] |
Electromagnetic Four-potential
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector.Gravitation, J.A. Wheeler, C. Misner, K.S. Thorne, W.H. Freeman & Co, 1973, As measured in a given frame of reference, and for a given gauge, the first component of the electromagnetic four-potential is conventionally taken to be the electric scalar potential, and the other three components make up the magnetic vector potential. While both the scalar and vector potential depend upon the frame, the electromagnetic four-potential is Lorentz covariant. Like other potentials, many different electromagnetic four-potentials correspond to the same electromagnetic field, depending upon the choice of gauge. This article uses tensor index notation and the Minkowski metric sign convention . See also covariance and contravariance of vectors and raising and lowering in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavefunction
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi, respectively). The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Tensor
In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely, and allows for the quantization of the electromagnetic field by Lagrangian formulation described below. Definition The electromagnetic tensor, conventionally labelled ''F'', is defined as the exterior derivative of the electromagnetic four-potential, ''A'', a differential 1-form: :F \ \stackrel\ \mathrmA. Therefore, ''F'' is a differential 2-form—that is, an antisymmetric rank-2 tensor field—on Minkowski space. In component form, :F_ = \partial_\mu A_\nu - \partial_\nu A_\mu. where \partial is the four-gradient and A is the four ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomalous Magnetic Dipole Moment
In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. (The ''magnetic moment'', also called ''magnetic dipole moment'', is a measure of the strength of a magnetic source.) The "Dirac" magnetic moment, corresponding to tree-level Feynman diagrams (which can be thought of as the classical result), can be calculated from the Dirac equation. It is usually expressed in terms of the ''g''-factor; the Dirac equation predicts g = 2. For particles such as the electron, this classical result differs from the observed value by a small fraction of a percent. The difference is the anomalous magnetic moment, denoted a and defined as a = \frac Electron The one-loop contribution to the anomalous magnetic moment—corresponding to the first and largest quantum mechanical correction—of the electron is found by calculating the vertex functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ward–Takahashi Identity
In quantum field theory, a Ward–Takahashi identity is an identity between correlation functions that follows from the global or gauge symmetries of the theory, and which remains valid after renormalization. The Ward–Takahashi identity of quantum electrodynamics (QED) was originally used by John Clive Ward and Yasushi Takahashi to relate the wave function renormalization of the electron to its vertex renormalization factor, guaranteeing the cancellation of the ultraviolet divergence to all orders of perturbation theory. Later uses include the extension of the proof of Goldstone's theorem to all orders of perturbation theory. More generally, a Ward–Takahashi identity is the quantum version of classical current conservation associated to a continuous symmetry by Noether's theorem. Such symmetries in quantum field theory (almost) always give rise to these generalized Ward–Takahashi identities which impose the symmetry on the level of the quantum mechanical amplitudes. This g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex Function
In quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory. In particular, it is the one particle irreducible correlation function involving the fermion \psi, the antifermion \bar, and the vector potential A. Definition The vertex function \Gamma^\mu can be defined in terms of a functional derivative of the effective action Seff as :\Gamma^\mu = - The dominant (and classical) contribution to \Gamma^\mu is the gamma matrix \gamma^\mu, which explains the choice of the letter. The vertex function is constrained by the symmetries of quantum electrodynamics — Lorentz invariance; gauge invariance or the transversality of the photon, as expressed by the Ward identity; and invariance under parity — to take the following form: : \Gamma^\mu = \gamma^\mu F_1(q^2) + \frac F_2(q^2) where \sigma^ = (i/2) gamma^, \gamma^, q_ is the incoming four-momentum of the external photon (on the rig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Electrodynamics
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics, which is a quantum field theory. Fundamental physical aspects of classical electrodynamics are presented in many texts, such as those by Feynman, Leighton and Sands, Griffiths, Panofsky and Phillips, and Jackson. History The physical phenomena that electromagnetism describes have been studied as separate fields since antiquity. For example, there were many advances in the field of optics centuries before light was understood to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. History The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, who ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
