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Beta-function
In theoretical physics, specifically quantum field theory, a beta function, ''β(g)'', encodes the dependence of a coupling parameter, ''g'', on the energy scale, ''μ'', of a given physical process described by quantum field theory. It is defined as :: \beta(g) = \frac ~, and, because of the underlying renormalization group, it has no explicit dependence on ''μ'', so it only depends on ''μ'' implicitly through ''g''. This dependence on the energy scale thus specified is known as the running of the coupling parameter, a fundamental feature of scale-dependence in quantum field theory, and its explicit computation is achievable through a variety of mathematical techniques. Scale invariance If the beta functions of a quantum field theory vanish, usually at particular values of the coupling parameters, then the theory is said to be scale-invariant. Almost all scale-invariant QFTs are also conformally invariant. The study of such theories is conformal field theory. The coup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Invariance
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry. *In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity. *In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale. *In quantum field theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Freedom
In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases. Asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory of the strong interaction between quarks and gluons, the fundamental constituents of nuclear matter. Quarks interact weakly at high energies, allowing perturbative calculations. At low energies, the interaction becomes strong, leading to the confinement of quarks and gluons within composite hadrons. The asymptotic freedom of QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the same year. For this work all three shared the 2004 Nobel Prize in Physics. Discovery Asymptotic freedom in QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the same year. T ... [...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] |
Higgs Boson
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positive) parity, no electric charge, and no colour charge, that couples to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately. The Higgs field is a scalar field, with two neutral and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry. Its " Mexican hat-shaped" potential leads it to take a nonzero value ''everywhere'' (including otherwise empty space), which breaks the weak isospin symmetry of the electroweak interaction, and via the Higgs mechanism gives mass to many particles. Both the field and the boson are named after physicist Peter Higgs, who in 1964, along ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yukawa Interaction
In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is a scalar field (or pseudoscalar field) and a Dirac field of the type :~ V \approx g \, \bar\psi \, \phi \, \psi \quad (scalar) \qquad or \qquad g \, \bar\psi \, i \,\gamma^5 \, \phi \, \psi \quad (pseudoscalar). The Yukawa interaction was developed to model the strong force between hadrons. A Yukawa interaction is thus used to describe the nuclear force between nucleons mediated by pions (which are pseudoscalar mesons). A Yukawa interaction is also used in the Standard Model to describe the coupling between the Higgs field and massless quark and lepton fields (i.e., the fundamental fermion particles). Through spontaneous symmetry breaking, these fermions acquire a mass proportional to the vacuum expectation value of the Higgs field. This Higgs-fermion coupling was first described by Steven Weinberg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy. Although the Standard Model is believed to be theoretically self-consistent and has demonstrated huge successes in providing experimental predictions, it leaves some physics beyond the standard m ... [...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] |
List Of Nobel Laureates In Physics
The Nobel Prize in Physics ( sv, Nobelpriset i fysik) is awarded annually by the Royal Swedish Academy of Sciences to scientists in the various fields of physics. It is one of the five Nobel Prizes established by the 1895 will of Alfred Nobel (who died in 1896), awarded for outstanding contributions in physics. As dictated by Nobel's will, the award is administered by the Nobel Foundation and awarded by the Royal Swedish Academy of Sciences. The award is presented in Stockholm at an annual ceremony on 10 December, the anniversary of Nobel's death. Each recipient receives a medal, a diploma and a monetary award prize that has varied throughout the years. Statistics The Nobel Prize in Physics has been awarded to 221 individuals until 2022. The first prize in physics was awarded in 1901 to Wilhelm Conrad Röntgen, of Germany, who received 150,782 SEK. John Bardeen is the only laureate to win the prize twice—in 1956 and 1972. Marie Skłodowska-Curie also won two Nobel Prizes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Wilczek
Frank Anthony Wilczek (; born May 15, 1951) is an American theoretical physicist, mathematician and Nobel laureate. He is currently the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT), Founding Director of T. D. Lee Institute and Chief Scientist at the Wilczek Quantum Center, Shanghai Jiao Tong University (SJTU), distinguished professor at Arizona State University (ASU) and full professor at Stockholm University. Wilczek, along with David Gross and H. David Politzer, was awarded the Nobel Prize in Physics in 2004 "for the discovery of asymptotic freedom in the theory of the strong interaction". In May 2022, he was awarded the Templeton Prize for Progress Toward Research or Discoveries about Spiritual Realities. Early life and education Born in Mineola, New York, Wilczek is of Polish and Italian origin. His grandparents were immigrants, who "really did work with their hands", according to Wilczek, but Frank's father took night ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Gross
David Jonathan Gross (; born February 19, 1941) is an American theoretical physicist and string theorist. Along with Frank Wilczek and David Politzer, he was awarded the 2004 Nobel Prize in Physics for their discovery of asymptotic freedom. Gross is the Chancellor's Chair Professor of Theoretical Physics at the Kavli Institute for Theoretical Physics (KITP) of the University of California, Santa Barbara (UCSB), and was formerly the KITP director and holder of their Frederick W. Gluck Chair in Theoretical Physics. He is also a faculty member in the UCSB Physics Department and is currently affiliated with the Institute for Quantum Studies at Chapman University in California. He is a foreign member of the Chinese Academy of Sciences. Early life and education Gross was born to a Jewish family in Washington, D.C., in February 1941. His parents were Nora (Faine) and Bertram Myron Gross (1912–1997). Gross received his bachelor's degree from the Hebrew University of Jerusalem, Isr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamental Representation
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra whose highest weight is a fundamental weight. For example, the defining module of a classical Lie group is a fundamental representation. Any finite-dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to Élie Cartan. Thus in a certain sense, the fundamental representations are the elementary building blocks for arbitrary finite-dimensional representations. Examples * In the case of the general linear group, all fundamental representations are exterior products of the defining module. * In the case of the special unitary group SU(''n''), the ''n'' − 1 fundamental representations are the wedge products \operatorname^k\ ^n consisting of the alternating tensors, for ''k'' = 1,&nbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjoint Representation Of A Lie Group
In mathematics, the adjoint representation (or adjoint action) of a Lie group ''G'' is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if ''G'' is GL(n, \mathbb), the Lie group of real ''n''-by-''n'' invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible ''n''-by-''n'' matrix g to an endomorphism of the vector space of all linear transformations of \mathbb^n defined by: x \mapsto g x g^ . For any Lie group, this natural representation is obtained by linearizing (i.e. taking the differential of) the action of ''G'' on itself by conjugation. The adjoint representation can be defined for linear algebraic groups over arbitrary fields. Definition Let ''G'' be a Lie group, and let :\Psi: G \to \operatorname(G) be the mapping , with Aut(''G'') the automorphism group of ''G'' and given by the inner automorphism (conjugation) :\Psi_g(h)= ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
