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Custodial Symmetry
In particle physics, a symmetry that remains after spontaneous symmetry breaking that can prevent higher-order radiative corrections from spoiling some property of a theory is called a custodial symmetry. Motivation In the Standard Model of particle physics, the custodial symmetry is a residual global SU(2) symmetry of the Higgs potential V_ = -\mu (H^\dagger H) - \lambda(H^\dagger H)^2 beyond the basic SU(2)×U(1) gauge symmetry of the Weak Interaction that prevents higher-order radiative-corrections from driving the Standard Model parameter \rho away from ≈ 1 after spontaneous symmetry breaking. (Note: \rho is a ratio involving the masses of the weak bosons and the Weinberg angle). With one or more electroweak Higgs doublets in the Higgs sector, the effective action term \left, H^\dagger D_\mu H\^2/\Lambda^2 which generically arises with physics beyond the Standard Model at the scale Λ contributes to the Peskin–Takeuchi parameter T. Current precision electroweak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, but ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons, and electrons and electron neutrinos. The three fundamental interactions known to be mediated by bosons are electromagnetism, the weak interaction, and the strong interaction. Quarks cannot exist on their own but form hadrons. Hadrons that contain an odd number of quarks are called baryons and those that contain an even number are called mesons. Two baryons, the proton and the neutron, make up most of the mass of ordinary matter. Mesons are unstable and the longest-lived last for only a few hundredths of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Left-right Model
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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagonal Subgroup
In the mathematical discipline of group theory, for a given group the diagonal subgroup of the ''n''-fold direct product is the subgroup :\. This subgroup is isomorphic to Properties and applications * If acts on a set the ''n''-fold diagonal subgroup has a natural action on the Cartesian product induced by the action of on defined by :(x_1, \dots, x_n) \cdot (g, \dots, g) = (x_1 \!\cdot g, \dots, x_n \!\cdot g). * If acts - transitively on then the -fold diagonal subgroup acts transitively on More generally, for an integer if acts -transitively on acts -transitively on * Burnside's lemma Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, the orbit-counting theorem, or the Lemma that is not Burnside's, is a result in group theory that is often useful in taking account of symmetry when ... can be proved using the action of the twofold diagonal subgroup. See also * Diagonalizable group References *. Group theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum Expectation Value
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. One of the most widely used examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect. This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking. Examples are: *The Higgs field has a vacuum expectation value of 246 GeV. This nonzero value underlies the Higgs mechanism of the Standard Model. This value is given by v = 1/\sqrt = 2M_W/g \approx 246.22\, \rm, where ''MW'' is the mass of the W Boson, G_F^0 the reduced Fermi constant, and the weak isospin coupling, in natural units. It is also near the limit of the most massive nuclei, at v = 264.3 Da. *The chiral condensate in quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypercharge
In particle physics, the hypercharge (a portmanteau of hyperonic and charge) ''Y'' of a particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a single charge operator that accounts for properties of isospin, electric charge, and flavour. The hypercharge is useful to classify hadrons; the similarly named weak hypercharge has an analogous role in the electroweak interaction. Definition Hypercharge is one of two quantum numbers of the SU(3) model of hadrons, alongside isospin . The isospin alone was sufficient for two quark flavours — namely and — whereas presently 6 flavours of quarks are known. SU(3) weight diagrams (see below) are 2 dimensional, with the coordinates referring to two quantum numbers: (also known as ), which is the component of isospin, and , which is the hypercharge (the sum of strangeness , charm , bottomness , topness , and baryon number ). Mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Interaction
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms: The weak interaction participates in nuclear fission and nuclear fusion. The theory describing its behaviour and effects is sometimes called quantum flavourdynamics (QFD); however, the term QFD is rarely used, because the weak force is better understood by Electroweak interaction, electroweak theory (EWT). The effective range of the weak force is limited to subatomic distances and is less than the diameter of a proton. Background The Standard Model of particle physics provides a uniform framework for understanding electromagnetic, weak, and strong interactions. An interaction occurs when two particles ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Representation
In the mathematical field of representation theory a real representation is usually a representation on a real vector space ''U'', but it can also mean a representation on a complex vector space ''V'' with an invariant real structure, i.e., an antilinear equivariant map :j\colon V\to V which satisfies :j^2=+1. The two viewpoints are equivalent because if ''U'' is a real vector space acted on by a group ''G'' (say), then ''V'' = ''U''⊗C is a representation on a complex vector space with an antilinear equivariant map given by complex conjugation. Conversely, if ''V'' is such a complex representation, then ''U'' can be recovered as the fixed point set of ''j'' (the eigenspace with eigenvalue 1). In physics, where representations are often viewed concretely in terms of matrices, a real representation is one in which the entries of the matrices representing the group elements are real numbers. These matrices can act either on real or complex column vectors. A real representati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Physics And Representation Theory
There is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincaré group. Moreover, the properties of the various particles, including their energy spectrum, spectra, can be related to representations of Lie algebras, corresponding to "approximate symmetries" of the universe. General picture Symmetries of a quantum system In quantum mechanics, any particular one-particle state is represented as a vector space, vector in a Hilbert space \mathcal H. To help understand what types of particles can exist, it is important to classify the possibilities for \mathcal H allowed by Wigner's theorem#Symmetry transformations, symmetries, and their properties. Let \mathcal H be a Hilbert space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Hierarchy Problem
In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger than gravity. Technical definition A hierarchy problem occurs when the fundamental value of some physical parameter, such as a coupling constant or a mass, in some Lagrangian is vastly different from its effective value, which is the value that gets measured in an experiment. This happens because the effective value is related to the fundamental value by a prescription known as renormalization, which applies corrections to it. Typically the renormalized value of parameters are close to their fundamental values, but in some cases, it appears that there has been a delicate cancellation between the fundamental quantity and the quantum corrections. Hierarchy problems are related to fine-tuning problems and problems of naturalness. Over the past deca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peskin–Takeuchi Parameter
In particle physics, the Peskin–Takeuchi parameters are a set of three measurable quantities, called ''S'', ''T'', and ''U'', that parameterize potential new physics contributions to electroweak radiative corrections. They are named after physicists Michael Peskin and Tatsu Takeuchi, who proposed the parameterization in 1990; proposals from two other groups (see References below) came almost simultaneously. The Peskin–Takeuchi parameters are defined so that they are all equal to zero at a ''reference point'' in the Standard Model, with a particular value chosen for the (then unmeasured) Higgs boson mass. The parameters are then extracted from a global fit to the high-precision electroweak data from particle collider experiments (mostly the Z pole data from the CERN LEP collider) and atomic parity violation. The measured values of the Peskin–Takeuchi parameters agree with the Standard Model. They can then be used to constrain models of new physics beyond the Standard Mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Action
In quantum field theory, the quantum effective action is a modified expression for the classical action taking into account quantum corrections while ensuring that the principle of least action applies, meaning that extremizing the effective action yields the equations of motion for the vacuum expectation values of the quantum fields. The effective action also acts as a generating functional for one-particle irreducible correlation functions. The potential component of the effective action is called the effective potential, with the expectation value of the true vacuum being the minimum of this potential rather than the classical potential, making it important for studying spontaneous symmetry breaking. It was first defined perturbatively by Jeffrey Goldstone and Steven Weinberg in 1962, while the non-perturbative definition was introduced by Bryce DeWitt in 1963 and independently by Giovanni Jona-Lasinio in 1964. The article describes the effective action for a single scalar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
