Unitarity gauge

Last updated

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 [1] [2] in the context of the electroweak theory. In electroweak theory, the degrees of freedom in a unitarity gauge are the massive spin-1 W+, W and Z bosons with three polarizations each, the photon with two polarizations, and the scalar Higgs boson.

The unitarity gauge is usually used in tree-level calculations. For loop calculations, other gauge choices such as the 't Hooft–Feynman gauge often reduce the mathematical complexity of the calculation.

Related Research Articles

Electroweak interaction Unified description of electromagnetism and the weak interaction

In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single force. Thus, if the universe is hot enough (approximately 1015 K, a temperature not believed to have been exceeded since shortly after the Big Bang), then the electromagnetic force and weak force merge into a combined electroweak force. During the quark epoch, the electroweak force split into the electromagnetic and weak force.

Standard Model Theory of particle physics

The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.

Scalar field Assignment of numbers to points in space

In mathematics and physics, a scalar field or scalar-valued function associates a scalar value to every point in a space – possibly physical space. The scalar may either be a (dimensionless) mathematical number or a physical quantity. In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory.

Technicolor (physics) Hypothetical model through which W and Z bosons acquire mass

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.

Spontaneous symmetry breaking Symmetry breaking through the vacuum state

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.

In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu in particle physics within the context of the BCS superconductivity mechanism, and subsequently elucidated by Jeffrey Goldstone, and systematically generalized in the context of quantum field theory. In condensed matter physics such bosons are quasiparticles and are known as Anderson–Bogoliubov modes.

Higgs mechanism Mechanism that explains the generation of mass for gauge bosons

In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W+, W, and Z0 bosons actually have relatively large masses of around 80 GeV/c2. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field (the Higgs field) that permeates all Hilbert spaces of the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W±, and Z weak gauge bosons through electroweak symmetry breaking. The Large Hadron Collider at CERN announced results consistent with the Higgs particle on 14 March 2013, making it extremely likely that the field, or one like it, exists, and explaining how the Higgs mechanism takes place in nature.

The Alternative models to the Standard Higgs Model are models which are considered by many particle physicists to solve some of the Higgs boson's existing problems. Two of the most currently researched models are quantum triviality, and Higgs hierarchy problem.

Benjamin W. Lee Korean-born American theoretical physicist

Benjamin Whisoh Lee, or Ben Lee, was a Korean-born American theoretical physicist. His work in theoretical particle physics exerted great influence on the development of the standard model in the late 20th century, especially on the renormalization of the electro-weak model and gauge theory.

Erick J. Weinberg is a theoretical physicist and professor of physics at Columbia University.

The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is

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 came almost simultaneously.

François Englert Belgian theoretical physicist

François, Baron Englert is a Belgian theoretical physicist and 2013 Nobel prize laureate.

Christopher T. Hill American theoretical physicist

Christopher T. Hill is an American theoretical physicist at the Fermi National Accelerator Laboratory who did undergraduate work in physics at M.I.T., and graduate work at Caltech. Hill's Ph.D. thesis, "Higgs Scalars and the Nonleptonic Weak Interactions" (1977) contains one of the first discussions of the two-Higgs-doublet model.

Topcolor is a model in theoretical physics, of dynamical electroweak symmetry breaking in which the top quark and anti-top quark form a composite Higgs boson by a new force arising from massive "top gluons". The solution to composite Higgs models was actually anticipated in 1981, and found to be the Infrared fixed point for the top quark mass.

Higgs boson Elementary particle

The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positive) parity, no electric charge, and no colour charge, that couples to mass. It is also very unstable, decaying into other particles almost immediately.

The 1964 PRL symmetry breaking papers were written by three teams who proposed related but different approaches to explain how mass could arise in local gauge theories. These three papers were written by: Robert Brout and François Englert; Peter Higgs; and Gerald Guralnik, C. Richard Hagen, and Tom Kibble (GHK). They are credited with the theory of the Higgs mechanism and the prediction of the Higgs field and Higgs boson. Together, these provide a theoretical means by which Goldstone's theorem can be avoided. They show how gauge bosons can acquire non-zero masses as a result of spontaneous symmetry breaking within gauge invariant models of the universe.

In particle physics, W′ and Z′ bosons refer to hypothetical gauge bosons that arise from extensions of the electroweak symmetry of the Standard Model. They are named in analogy with the Standard Model W and Z bosons.

In theoretical physics, a mass generation mechanism is a theory that describes the origin of mass from the most fundamental laws of physics. Physicists have proposed a number of models that advocate different views of the origin of mass. The problem is complicated because the primary role of mass is to mediate gravitational interaction between bodies, and no theory of gravitational interaction reconciles with the currently popular Standard Model of particle physics.

Ghost (physics) Conceptual field without physical meaning

In the terminology of quantum field theory, a ghost, ghost field, ghost particle, or gauge ghost is an unphysical state in a gauge theory. Ghosts are necessary to keep gauge invariance in theories where the local fields exceed a number of physical degrees of freedom.

References

  1. Weinberg, Steven (1971). "Physical Processes in a Convergent Theory of the Weak and Electromagnetic Interactions". Physical Review Letters. 27 (24): 1688–1691. Bibcode:1971PhRvL..27.1688W. doi:10.1103/PhysRevLett.27.1688.
  2. Weinberg, Steven (1973). "General Theory of Broken Local Symmetries". Physical Review D. 7 (4): 1068–1082. Bibcode:1973PhRvD...7.1068W. doi:10.1103/PhysRevD.7.1068.

Further reading