Concept
Mathematical formulation of the Standard Model
Related concepts (16)
Gauge theory
In physics, a gauge theory is a field theory in which the Lagrangian 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.
Sterile neutrino
Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that are believed to interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term sterile neutrino is used to distinguish them from the known, ordinary active neutrinos in the Standard Model, which carry an isospin charge of ± 1/ 2 and engage in the weak interaction. The term typically refers to neutrinos with right-handed chirality (see right-handed neutrino), which may be inserted into the Standard Model.
Symmetry (physics)
In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries.
Seesaw mechanism
In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of the order of eV, compared to those of quarks and charged leptons, which are millions of times heavier. The name of the seesaw mechanism was given by Tsutomu Yanagida in a Tokyo conference in 1981. There are several types of models, each extending the Standard Model.
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 spectra, can be related to representations of Lie algebras, corresponding to "approximate symmetries" of the universe.
X (charge)
In particle physics, the X charge (or simply X) is a conserved quantum number associated with the SO(10) grand unification theory. It is thought to be conserved in strong, weak, electromagnetic, gravitational, and Higgs interactions. Because the X charge is related to the weak hypercharge, it varies depending on the helicity of a particle. For example, a left-handed quark has an X charge of +1, whereas a right-handed quark can have either an X charge of −1 (for up, charm and top quarks), or −3 (for down, strange and bottom quarks).
Unitarity gauge
In theoretical physics, the unitarity gauge or unitary gauge is a particular choice of a gauge fixing in a gauge theory with a spontaneous symmetry breaking. In this gauge, the scalar fields responsible for the Higgs mechanism are transformed into a basis in which their Goldstone boson components are set to zero. In other words, the unitarity gauge makes the manifest number of scalar degrees of freedom minimal. The gauge was introduced to particle physics by Steven Weinberg in the context of the electroweak theory.
Weak hypercharge
In the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted and corresponds to the gauge symmetry U(1). It is conserved (only terms that are overall weak-hypercharge neutral are allowed in the Lagrangian). However, one of the interactions is with the Higgs field. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum.
Physics beyond the Standard Model
Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the standard model, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itself: the Standard Model is inconsistent with that of general relativity, and one or both theories break down under certain conditions, such as spacetime singularities like the Big Bang and black hole event horizons.
Charge (physics)
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by the letter Q, and so the invariance of the charge corresponds to the vanishing commutator , where H is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues q of the generator Q.