., .,.,,,, ,, ,”. .,, ,:, L, weak force was invoked to understand the trans- mutation of a neutron in the nucleus into a proton during the particularly slow form of radioactive decay known as beta decay. Since neither the weak force nor the strong force is directly observed in the macroscopic world, both must be very short-range relative to the more familiar gravitational and electromagnetic forces. Furthermore, the relative strengths of the forces associated with all four interactions are quite dif- ferent, as can be seen in Table 1. It is therefore not too surprising that for a very long period these interactions were thought to be quite separate. In spite of this, there has always been a lingering suspicion (and hope) that in some miraculous fashion all four were simply manifestations of one source or principle and could therefore be de- scribed by a single unified field theory. Table 1 The four basic fcmes. Differences in stretr@m smwng the 1o-” square centimeter.) The stronger the force, the larger basic interactions are observed by comparhqg &tractdatic is the effective scattering area, or cross section, and the cross sections and particle lifetimes. (Cress sections are shorter tie lifetime of the particle state, At 1 GeV strong often expressed in barns beeause the cross-secthd mms ~MS tike Place 102 times faster than electromagnetic of nuclei are of this order of magnitude one barn equals ~rocesses and 10Stimes faster than weak processes. - 24 Summer/Fall 1984 LOS .4L.4MOS SCIENCE Particle Physics and the Standard Model THE STANDARD MODEL Interaction Strong Electroweak Local Symmetry SU(3) SU(2)X U(1) Coupling 9 T ‘d Matter Fields Quarks Quarks, Leptons, and Electrically Higgs Particles Charged Particles Gauge Fields Gluons W+, w-, zc’ Photon Conserved Quantities Coior CIsarga Etee@wrr f%msber Electric Bar~cn Number MswMsN4wnber Charge Tau Wsmber Fig. 1. The main features of the standard model. The strong metry of the Lagrangian of the theory but not of the solu- force and the electroweak force are each induced by a local tions to the theory. The standard model ascribes this sym- symmetry group, SU(3) and SU(2) X U(I), respectively. metry breaking to the Higgs particles, particles that create a These two symmetries are entirely independent of each other. nonzero weak charge in the vacuum (the lowest energy state SU(3) symmetry (called the color symmetry) is exact and of the system). The only conserved quantity that remains therefore predicts conservation of color charge. The SU(2) X after the symmetry breaking is electric charge. U(1) symmetry of the electro weak theory is an exact sym- The spectacular progress in particle phys- model’” and serves as the point ofdcparture clcctromagnctic interactions as different ics over the pasl tcn years or so has renewed for discussing a grand unification of all manifestations of a single symmetry prln - Ibis dream: many physicists today believe forces. including thal of gravitation. ciplc. the principic of local symnlet~. AS wc Ihal we are on the verge of uncovering the The elements of the standard model are shall see. [hc standard model has man> s[ructurc of[his unified theory. The theoreti- summarized in Fig. 1. In this description the arbitrary parameters and leaves unanswered cal description of the s[rong. weak. and elec- basic constituents of matter are quarks and a number of important questions, [t can tromagnetic interactions is now considered Icptons. and {hese constituents interact with hardly be regarded as a thing of great well established. and. amazingly enough. the each other through the exchange of gauge beauty—unless one keeps in mind that it iheory shows these forces to be quite similar particles (vec[or bosons). the modern embodies a single unifying prtnciple and despite their experimental differences. The analogue of force fields. These so-called local therefore seems to point [he way toward a weak and strong forces have sources gauge interactions are inscribed in the lan- grander unification. analogous to. but more complicated than. guage of Lagrangian quantum field theory. For those readers who arc more electric charge. and. like the electromagnetic whose rich formalism contains mysteries mathematically incllned. the arguments here force. both can be described by a special type that escape even its most faithful practi- are complemented b} a series of lecture notes of field theo~ called a local gauge theory. tioners. Here we will introduce the central lmmcdiatcly followlng the main text and This formulation has been so successful at themes and concepts that have led to [he entitled “From Simple Field Theories to the explaining all known phenomenology up to standard model. emphasizing how its for- Standard Model.’” The IccIurc notes in- energies of 100 GeV ( I GcV = 109 electron malism enables us to dcscrlbc all [roducc Lagranglan formalism and stress the volts) that it has been coined “the standard phenomenology of the strong. weak. and symmetry principles underlying construc- LOS AI.AMOS SCIENCE Summer/Fall 1984 ~~ — tion of the standard model. The main electric currents. Thus it was known that Maxwell obtained a consistent solution by emphasis is on the classical limit of the static charges give rise to an electric field amending Amp&e’s law to read model, but indications of its quantum gen- E and that moving charges give rise to a eralizations are also included. magnetic field B. Then in 1831 Faraday dis- vxB=47cwoJ+&opo#. covered that the field itself has a life of its Unification and Extension own, independent of the sources. A time- With this new equation, Maxwell showed dependent magnetic field induces an electric that both E and B satisfy the wave equation. Two central themes of physics that have field. This was the first clear hint that electric For example, led to the present synthesis are “unification” and magnetic phenomena were manifesta- and “extension.” By “unification” we mean tions of the same force field. V*–&o&o: E=O. the coherent description of phenomena that Until the time of Maxwell, the basic laws ( ) are at first sight totally unrelated. This takes of electricity and magnetism were expressed the form of a mathematical description with in a variety of different mathematical forms, This fact led him to propose the elec- specific rules of application. A theory must all of which left the central role of the fields tromagnetic theory of light. Thus, from Max- not only describe the known phenomena but obscure. One of Maxwell’s great achieve- well’s unification of electric and magnetic also make predictions of new ones. Almost ments was to rewrite these laws in a single phenomena emerged the concept of elec- all theories are incomplete in that they formalism using the fields E and B as the tromagnetic waves. Moreover, the speed c of provide a description of phenomena only fundamental physical entities, whose sources the electromagnetic waves, or light, is given within a specific range of parameters. Typi- are the charge density p and the current by (Eowo)-1/2 and is thus determined uniquely cally, a theory changes as it is extended to density J, respectively. In this formalism the in terms of purely static electric and magne- explain phenomena over a larger range of laws of electricity and magnetism are ex- tic measurements alone! parameters, and sometimes it even pressed as differential equations that mani- It is worth emphasizing that apart from simplifies. Hence, the second theme is called fest a clear interrelationship between the two the crucial change in Amp&e’s law, Max- extension—and refers in particular to the fields. Nowadays they are usually written in well’s equations were well known to natural extension of theories to new length or energy standard vector notation as follows. philosophers before the advent of Maxwell! scales. It is usually extension and the result- The unification, however, became manifest ing simplification that enable unification. Coulomb’s law v . E = 4zp/EQ; only through his masterstroke of expressing Perhaps the best-known example of ex- them in terms of the “right” set of variables, Amp&-e’s law V X B = 4rcp&J; tension and unification is Newton’s theory of namely, the fields E and B. gravity (1666), which unifies the description Faraday’s law VXE+dB/N=O; of ordinary-sized objects falling to earth with Extension to Small Distance and the absence of that of the planets revolving around the sun. Scales magnetic monopole5 V. B=O. It describes phenomena over distance scales ranging from a few centimeters up to Maxwell’s unification provides an ac- The parameters so and V. are determined by 1025 centimeters (galactic scales). Newton’s curate description of large-scale elec- measuring Coulomb’s force between two theory is superseded by Einstein’s theory of tromagnetic phenomena such as radio static charges and Amp&e’s force between relativity only when one tries to describe waves, current flow, and electromagnets. two current-carrying wires, respectively. phenomena at extremely high densities This theory can also account for the effects of Although these equations clearly “unite” and/or velocities or relate events over cos- a medium, provided macroscopic concepts E with B, they are incomplete. In 1865 Max- mological distance and time scales. such as conductivity and permeability are well realized that the above equations were The other outstanding example of unifica- introduced. However, if we try to extend it to not consistent with the conservation of elec- tion in classical physics is Maxwell’s theory very short distance scales, we run into tric charge, which requires that of electrodynamics, which unifies electricity trouble; the granularity, or quantum nature, with magnetism. Coulomb (1785) had estab- v.