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 approximate calculations in several quantum field theories, notably quantum electrodynamics and theories of the Higgs particle, the running coupling appears to become infinite at a finite momentum scale. This is sometimes called the Landau pole problem.
It is not known whether the appearance of these inconsistencies is an artifact of the approximation, or a real fundamental problem in the theory. However, the problem can be avoided if an ultraviolet or UV fixed point appears in the theory. A quantum field theory has a UV fixed point if its renormalization group flow approaches a fixed point in the ultraviolet (i.e. short length scale/large energy) limit. [1] This is related to zeroes of the beta-function appearing in the Callan–Symanzik equation. [2] The large length scale/small energy limit counterpart is the infrared fixed point.
Among other things, it means that a theory possessing a UV fixed point may not be an effective field theory, because it is well-defined at arbitrarily small distance scales. At the UV fixed point itself, the theory can behave as a conformal field theory.
The converse statement, that any QFT which is valid at all distance scales (i.e. isn't an effective field theory) has a UV fixed point is false. See, for example, cascading gauge theory.
Noncommutative quantum field theories have a UV cutoff even though they are not effective field theories.
Physicists distinguish between trivial and nontrivial fixed points. If a UV fixed point is trivial (generally known as Gaussian fixed point), the theory is said to be asymptotically free. On the other hand, a scenario, where a non-Gaussian (i.e. nontrivial) fixed point is approached in the UV limit, is referred to as asymptotic safety. [3] Asymptotically safe theories may be well defined at all scales despite being nonrenormalizable in perturbative sense (according to the classical scaling dimensions).
Steven Weinberg has proposed that the problematic UV divergences appearing in quantum theories of gravity may be cured by means of a nontrivial UV fixed point. [4] Such an asymptotically safe theory is renormalizable in a nonperturbative sense, and due to the fixed point physical quantities are free from divergences. As yet, a general proof for the existence of the fixed point is still lacking, but there is mounting evidence for this scenario. [3]
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 terakelvin. Quarks and gluons must clump together to form hadrons. The two main types of hadron are the mesons and the baryons. In addition, colorless glueballs formed only of gluons are also consistent with confinement, though difficult to identify experimentally. Quarks and gluons cannot be separated from their parent hadron without producing new hadrons.
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.
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, 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 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 in 1954. The fact that couplings depend on the momentum scale is the central idea behind the renormalization group.
In physics, an ultraviolet divergence or UV divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with unbounded energy, or, equivalently, because of physical phenomena at infinitesimal distances.
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 physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales. It compensates for the possibility of separation of scales that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use.
The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution.
In theoretical physics, ultraviolet completion, or UV completion, of a quantum field theory is the passing from a lower energy quantum field theory to a more general quantum field theory above a threshold value known as the cutoff. In particular, the more general high energy theory must be well-defined at arbitrarily high energies.
In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation.
In theoretical physics, super QCD is a supersymmetric gauge theory which resembles quantum chromodynamics (QCD) but contains additional particles and interactions which render it supersymmetric.
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.
Superfluid vacuum theory (SVT), sometimes known as the BEC vacuum theory, is an approach in theoretical physics and quantum mechanics where the fundamental physical vacuum is considered as a superfluid or as a Bose–Einstein condensate (BEC).
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.
The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interaction and spacetime geometry. It is based upon a nontrivial fixed point of the corresponding renormalization group (RG) flow such that the running coupling constants approach this fixed point in the ultraviolet (UV) limit. This suffices to avoid divergences in physical observables. Moreover, it has predictive power: Generically an arbitrary starting configuration of coupling constants given at some RG scale does not run into the fixed point for increasing scale, but a subset of configurations might have the desired UV properties. For this reason it is possible that — assuming a particular set of couplings has been measured in an experiment — the requirement of asymptotic safety fixes all remaining couplings in such a way that the UV fixed point is approached.
Dynamical dimensional reduction or spontaneous dimensional reduction is the apparent reduction in the number of spacetime dimensions as a function of the distance scale, or conversely the energy scale, with which spacetime is probed. At least within the current level of experimental precision, our universe has three dimensions of space and one of time. However, the idea that the number of dimensions may increase at extremely small length scales was first proposed more than a century ago, and is now fairly commonplace in theoretical physics. Contrary to this, a number of recent results in quantum gravity suggest the opposite behavior, a dynamical reduction of the number of spacetime dimensions at small length scales.