In mathematics and mathematical physics, the Lie group SU(3) × SU(2) × U(1) is the formulation of the Standard Model as a gauge theory with the gauge group SU(3) × SU(2) × U(1) or SU(3) × SU(2) × U(1)/Z₆ with a couple of fermion fields and a Higgs field, which is a and/or a . SU(3) describes quantum chromodynamics, SU(2) describes the weak interaction* and U(1) describes hypercharge. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Mathematical physics is an interdisciplinary field of academic study in between mathematics and physics, aimed at studying and solving problems inspired by physics within a mathematically rigorous framework. ... In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Higgs bosons are hypothetical elementary particles predicted to exist by the Standard Model of particle physics. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... Quantum chromodynamics (QCD) is the physical theory describing one of the fundamental forces, the strong interaction. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In mathematics, the unitary group of degree n over the field F (which is either the field R of real numbers or the field C of complex numbers) is the group of n by n unitary matrices with entries from F, with the group operation that of matrix multiplication. ... In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before...

*Technically speaking, the Z and W bosons are described by a field which is really a linear combination of SU(2) and U(1). See electroweak. In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ...

There are three families of fermions, each consisting of the representations, (q for left-handed quark), (d^c for the left-handed anti d-quark), (u^c for the left handed up antiquark), (l for the left handed leptons), (1,1)₁(e^c for the left-handed positron) and (1,1)₀(ν^c for the left-handed antineutrino, which is now known to exist. See Neutrino oscillation.). In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. ... 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... A lepton is also a unit of currency. ... A positron is the antiparticle of the electron. ... An antineutrino is the antimatter equivalent particle of the neutrino. ... The solar neutrino problem was a major discrepancy between measurements of the neutrinos flowing through the Earth and theoretical models of the solar interior, lasting from the mid-1960s to about 2002. ...

The Higgs field acquires a VEV, resulting in a spontaneous symmetry breaking from or to U(1)_em. Wikipedia does not yet have an article with this exact name. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some Lie group goes into a vacuum state that is not symmetric. ...

Of course, calling the representations things like is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, but still, it is standard among high energy physicists. In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. ... In mathematics, a Young tableau is a combinatorial object useful in representation theory. ... See also Simple Lie group. ...

Since the homotopy group In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. ...

this model predicts no monopoles associated with the electroweak breaking scale. See Hooft-Polyakov monopole. In physics, magnetic monopole is a term describing a hypothetical particle that could be quickly clarified to a person familiar with magnets but not electromagnetic theory as a magnet with only one pole. In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle... In theoretical physics, the t Hooft-Polyakov monopole is a generalization of the Dirac monopole (i. ...

The Yukawa couplings of the scalar Higgs fields with the fermions produces the fermion masses after the Higgs field acquires a VEV. In particle physics, Yukawa interaction, named after Hideki Yukawa, is an interaction between a scalar field and a Dirac field of the type In the Standard Model, this interaction is responsible for the fermion masses after the Higgs field acquires a VEV. Its also possible to have a Yukawa... Higgs bosons are hypothetical elementary particles predicted to exist by the Standard Model of particle physics. ... Wikipedia does not yet have an article with this exact name. ...

See also grand unified theory. Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ...