In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α, is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.
Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle.
Technicolor theories are models of physics beyond the Standard Model that address electroweak gauge symmetry breaking, the mechanism through which W and Z bosons acquire masses. Early technicolor theories were modelled on quantum chromodynamics (QCD), the "color" theory of the strong nuclear force, which inspired their name.
In theoretical physics, supergravity is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the Poincaré algebra a superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way.
In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.
In particle physics, the hypothetical dilaton particle is a particle of a scalar field that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears as a radion in Kaluza–Klein theory's compactifications of extra dimensions. In Brans–Dicke theory of gravity, Newton's constant is not presumed to be constant but instead 1/G is replaced by a scalar field and the associated particle is the dilaton.
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.
In physics, an infrared fixed point is a set of coupling constants, or other parameters, that evolve from arbitrary initial values at very high energies to fixed, stable values, usually predictable, at low energies. This usually involves the use of the renormalization group, which specifically details the way parameters in a physical system depend on the energy scale being probed.
In physics, a coupling constant or gauge coupling parameter, is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies divided by the distance squared, , between the bodies; thus: in for Newtonian gravity and in for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers.
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.
In physics, the Landau pole is the momentum scale at which the coupling constant of a quantum field theory becomes infinite. Such a possibility was pointed out by the physicist Lev Landau and his colleagues. The fact that couplings depend on the momentum scale is the central idea behind the renormalization group.
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
A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory.
In a quantum field theory, one may calculate an effective or running coupling constant that defines the coupling of the theory measured at a given momentum scale. One example of such a coupling constant is the electric charge.
In theoretical particle physics, the non-commutative Standard Model, is a model based on noncommutative geometry that unifies a modified form of general relativity with the Standard Model.
In a quantum field theory, charge screening can restrict the value of the observable "renormalized" charge of a classical theory. If the only resulting value of the renormalized charge is zero, the theory is said to be "trivial" or noninteracting. Thus, surprisingly, a classical theory that appears to describe interacting particles can, when realized as a quantum field theory, become a "trivial" theory of noninteracting free particles. This phenomenon is referred to as quantum triviality. Strong evidence supports the idea that a field theory involving only a scalar Higgs boson is trivial in four spacetime dimensions, but the situation for realistic models including other particles in addition to the Higgs boson is not known in general. Nevertheless, because the Higgs boson plays a central role in the Standard Model of particle physics, the question of triviality in Higgs models is of great importance.
In theoretical physics, functional renormalization group (FRG) is an implementation of the renormalization group (RG) concept which is used in quantum and statistical field theory, especially when dealing with strongly interacting systems. The method combines functional methods of quantum field theory with the intuitive renormalization group idea of Kenneth G. Wilson. This technique allows to interpolate smoothly between the known microscopic laws and the complicated macroscopic phenomena in physical systems. In this sense, it bridges the transition from simplicity of microphysics to complexity of macrophysics. Figuratively speaking, FRG acts as a microscope with a variable resolution. One starts with a high-resolution picture of the known microphysical laws and subsequently decreases the resolution to obtain a coarse-grained picture of macroscopic collective phenomena. The method is nonperturbative, meaning that it does not rely on an expansion in a small coupling constant. Mathematically, FRG is based on an exact functional differential equation for a scale-dependent effective action.
Asymptotic safety is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. In this respect, it is similar to quantum triviality.
In particle physics, composite Higgs models (CHM) are speculative extensions of the Standard Model (SM) where the Higgs boson is a bound state of new strong interactions. These scenarios are models for physics beyond the SM presently tested at the Large Hadron Collider (LHC) in Geneva.
