# Field Theories

## The Standard Model And Beyond

In 1967 and 1968, the American nuclear physicist Steven Weinberg and the Pakistani nuclear physicist Abdus Salam independently proposed a gauge theory of the weak interactions
that unified the electromagnetic and the weak interactions using the Higgs mechanism. Their model incorporated suggestions advanced by the American theoretical physicist Sheldon Glashow in 1961 on how to formulate a gauge theory in which the weak forces were mediated by gauge bosons. Glashow's theory had been set aside because physicists doubted the consistency of gauge theories with *massive* gauge bosons, and such theories were not renormalizable. SBS offered the possibility of giving masses to the gauge bosons. The renormalizability of such theories was proved by the Dutch physicist Gerardus 't Hooft in 1972 under the guidance of Martinus Veltman. The Glashow-Weinberg-Salam theory (GWS) rose to prominence. Experiments in 1973 corroborated the existence of weak neutral currents embodied in this "electroweak" theory. The detection of the *W* ^{±} and of the *Z* _{0} in 1983 gave further confirmation. Gauge theory, the mathematical framework for generating dynamics-incorporating symmetries, now plays a central role in the extension of QFT. Symmetry, gauge theories, and spontaneous symmetry breaking are the three pegs upon which modern particle physics rests.

Particles such as protons and neutrons are now understood as composed of "quarks." Quantum chromodynamics (QCD) describes the strong interactions between six quarks. Evidence for the sixth was confirmed in 1995. Quarks carry electrical charge and also a strong "color" charge, in any of three color states. QCD does not involve leptons because they have no strong interactions. It is a gauge theory involving eight massless gluons and the tricolor gauge bosons. The GWS of the weak interactions is a gauge theory involving two colors. Each quark thus carries an additional weak color (or weak charge). Four gauge bosons mediate the weak interactions between quarks. Since the 1980s, successful accounts of high energy phenomena using QCD have proliferated.

This elegant "standard model" does not accord with the known characteristics of weak interactions nor with the phenomenological properties of quarks. Local gauge invariance requires that the gauge bosons be massless, and therefore that the forces they generate be of long range. But actually, the weak force is of minute range and the masses of the *W* and *Z* bosons are large. Nor does the model accommodate quark masses. A Higgs SBS mechanism is commonly invoked to overcome such difficulties. Establishing its reality is an outstanding problem.

The work of the American physicist Kenneth Wilson and Weinberg gave support to a more restrictive view: All extant field theoretic representations of phenomena are only partial descriptions, valid in the energy domain specified by the masses of the particles that are included, and delimited by the masses of the particles that are excluded. QFTs can be viewed as low energy approximations to a more fundamental theory that is not necessarily a field theory. Such reconceptualizations have led to a hierarchical structuring of the submicroscopic realm with the dynamics in each domain described by an effective field theory. Some see it as rectifying the reductionist ideology that gripped physics. Others pursue the possibility of a more global and symmetric unification than provided by the standard model. String theory is the only extant candidate for a consistent quantum theory to incorporate general relativity and yield a finite theory. The finiteness of the theory is the result of the fact that its fundamental entities are not point-like, but string-like, and space-time is not limited to four dimensions. Particles are then conceived as the quantum states corresponding to excitations of the basic stringlike entities.

Some theorists herald the possibility of a "final theory" that will consistently fuse quantum mechanics and general relativity and unify the four known interactions. This hope was given some credence in 1984 when superstring theory emerged as a candidate to unify all the particles and forces, including gravitation. A newer version in 1994 imagined that there is a single "big theory" with many different phases, consisting of the previously known string theories, among other things. Yet very many questions remain, including how to make contact with the experimental data explained by the standard model. Nor is it clear that such a theory—if formulated—would constitute a final theory and that no lower level might exist.

*See also* **Physics**; **Relativity**; **Quantum**.

## BIBLIOGRAPHY

Buchwald, Jed Z. *From Maxwell to Microphysics: Aspects of Electromagnetic Theory in the Last Quarter of the Nineteenth Century.* Chicago: University of Chicago Press, 1985.

Cao, T. Yu. *Conceptual Developments of Twentieth Century Field Theories.* Cambridge, U.K.: Cambridge University Press, 1997.

Davies, Paul. ed. *The New Physics.* Cambridge, U.K.: Cambridge University Press, 1989.

Dirac, P. A. M. "Quantised Singularities in the Electromagnetic Field." *Proceedings of the Royal Society of London* Series A 133 (1931): 60–72.

Fitch, V. and Rosner, J. "Elementary Particle Physics in the Second Half of the Twentieth Century." In *Twentieth Century Physics,* edited by Laurie M. Brown, Abraham Pais, and Sir Brian Pippard. Philadelphia: American Institute of Physics, 1995.

Hoddeson, Lillian, et al., eds. *The Rise of the Standard Model: Particle Physics in the 1960s and 1970s.* Cambridge, U.K.: Cambridge University Press, 1997.

Marshak, Robert E. *Conceptual Foundations of Modern Particle Physics.* Singapore: World Scientific, 1993.

Pais, Abraham. *Inward Bound: Of Matter and Forces in the Physical World.* Oxford: Oxford University Press, 1986.

Pickering, Andrew. *Constructing Quarks: A Sociological History of Particle Physics.* Chicago: University of Chicago Press, 1984.

Purrington, Robert D. *Physics in the Nineteenth Century.* New Brunswick, N.J.: Rutgers University Press, 1997.

Schweber, Silvan S. *QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga.* Princeton, N.J.: Princeton University Press, 1994.

Weinberg, Steven. *The Quantum Theory of Fields.* 3 vols. Cambridge, U.K.: Cambridge University Press, 1995–2000.

Whittaker, E. T. *A History of the Theories of Aether and Electricity.* London: Longmans, Green, 1910. Reprint, Los Angeles: Tomash, 1989.

*Alberto* *A.* *Martínez*

*Silvan* *S.* *Schweber*

## Additional topics

- Field Theories - Bibliography
- Field Theories - Fields And Subatomic Particles
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