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Pauli–Villars Regularization
__NOTOC__ In theoretical physics, Pauli–Villars regularization (P–V) is a procedure that isolates divergent terms from finite parts in loop calculations in field theory in order to renormalize the theory. Wolfgang Pauli and Felix Villars published the method in 1949, based on earlier work by Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfl ..., Ernst Stueckelberg and Dominique Rivier. In this treatment, a divergence arising from a loop integral (such as vacuum polarization or electron self-energy) is modulated by a spectrum of auxiliary particles added to the Lagrangian (field theory), Lagrangian or propagator. When the masses of the fictitious particles are taken as an infinite limit (i.e., once the regulator is removed) one expects to recover the original theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert Einstein was concerned wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ghosts (physics)
In the terminology of quantum field theory, a ghost, ghost field, ghost particle, or gauge ghost is an unphysical state in a gauge theory. Ghosts are necessary to keep gauge invariance in theories where the local fields exceed a number of physical degrees of freedom. If a given theory is self-consistent by the introduction of ghosts, these states are labeled "good". Good ghosts are virtual particles that are introduced for regularization, like Faddeev–Popov ghosts. Otherwise, "bad" ghosts admit undesired non-virtual states in a theory, like Pauli–Villars ghosts that introduce particles with negative kinetic energy. An example of the need of ghost fields is the photon, which is usually described by a four component vector potential , even if light has only two allowed polarizations in the vacuum. To remove the unphysical degrees of freedom, it is necessary to enforce some restrictions, one way to do this reduction is to introduce some ghost field in the theory. While it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Regularization
__NOTOC__ In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter ''d'', the analytic continuation of the number of spacetime dimensions. Dimensional regularization writes a Feynman integral as an integral depending on the spacetime dimension ''d'' and the squared distances (''x''''i''−''x''''j'')2 of the spacetime points ''x''''i'', ... appearing in it. In Euclidean space, the integral often converges for −Re(''d'') sufficiently large, and can be analytically continued from this region to a meromorphic function defined for all complex ''d''. In general, there will be a pole at the physical value (usually 4) of ''d'', which needs to be canceled by renormalization to obtain physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martinus J
Martinus may refer to: * Martin (magister militum per Armeniam), 6th-century Byzantine/East Roman general * Martinus (son of Heraclius), 7th-century Byzantine/East Roman co-emperor * Martinus of Arles, doctor of theology, priest, and author on demonology and witches * Saint Martinus or Saint Martin of Tours * Martinus College, a secondary school in the Netherlands * VV Martinus, a Dutch volleyball club People with the name * Derek Martinus (1931–2014), British television and theatre director * Flavius Martinus, ''vicarius'' (governor) of the Roman provinces of Britain * Martinus Beijerinck, Dutch microbiologist * Martinus von Biberach (died 1498), theologian from Heilbronn, Germany * Martinus Bosselaar, Dutch football (soccer) player * Martinus Brandal, Norwegian engineer and businessman * Martinus Dom, first abbot of the Trappist Abbey of Westmalle * Martinus Fabri, Dutch composer of the late 14th century * Martinus Gosia, scholar and Italian jurist, one of the Four Docto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerard 't Hooft
Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions". His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization and the holographic principle. Personal life He is married to Albertha Schik (Betteke) and has two daughters, Saskia and Ellen. Biography Early life Gerard 't Hooft was born in Den Helder on July 5, 1946, but grew up in The Hague. He was the middle child of a family of three. He comes from a family of scholars. His great uncle was Nobel prize laureate Frits Zernike, and his grandmother was married to Pieter Nicolaas van Kampen, a professor of zoology at Leiden Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Matrices
In mathematical physics, the gamma matrices, \left\ , also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cl1,3(\mathbb). It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations in general, and in particular are fundamental to the Dirac equation for relativistic spin- particles. In Dirac representation, the four contravariant gamma matrices are :\begin \gamma^0 &= \begin 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Regularization
__NOTOC__ In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter ''d'', the analytic continuation of the number of spacetime dimensions. Dimensional regularization writes a Feynman integral as an integral depending on the spacetime dimension ''d'' and the squared distances (''x''''i''−''x''''j'')2 of the spacetime points ''x''''i'', ... appearing in it. In Euclidean space, the integral often converges for −Re(''d'') sufficiently large, and can be analytically continued from this region to a meromorphic function defined for all complex ''d''. In general, there will be a pole at the physical value (usually 4) of ''d'', which needs to be canceled by renormalization to obtain physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Covariant Derivative
The gauge covariant derivative is a variation of the covariant derivative used in general relativity, quantum field theory and fluid dynamics. If a theory has gauge transformations, it means that some physical properties of certain equations are preserved under those transformations. Likewise, the gauge covariant derivative is the ordinary derivative modified in such a way as to make it behave like a true vector operator, so that equations written using the covariant derivative preserve their physical properties under gauge transformations. Overview There are many ways to understand the gauge covariant derivative. The approach taken in this article is based on the historically traditional notation used in many physics textbooks. Another approach is to understand the gauge covariant derivative as a kind of connection, and more specifically, an affine connection.Alexandre Guay, Geometrical aspects of local gauge symmetry' (2004) The affine connection is interesting because it does ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Invariance
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations ( Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the '' symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called '' gauge bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regularization (physics)
In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use. It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self-interaction feedback. Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. However, it is now well understood and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propagator
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the respective diagram. These may also be viewed as the inverse of the wave operator appropriate to the particle, and are, therefore, often called ''(causal) Green's functions'' (called "''causal''" to distinguish it from the elliptic Laplacian Green's function). Non-relativistic propagators In non-relativistic quantum mechanics, the propagator gives the probability amplitude for a particle to travel from one spatial point (x') at one time (t') to another spatial point (x) at a later time (t). Consider a system with Hamiltonian . The Green's function (fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
