than the speed of light. Instead, in a relativistic theory, the interaction must bemediatedby
another particle. That particle is the graviton for the gravitational force and the photon for the
electromagnetic force. The true interaction then occurs atan instant in time and at a point in
space, thus expressing the forces in terms oflocal interactionsonly. Thus, the Coulomb force is
really a limit of relativistic “retarded” and “advanced” interactions, mediated by the exchange of
photons. The exchange is pictorially represented in Figure??.
One may realize this picture concretely in terms of local fields, which have local couplings to
one another. The most basic prototype for such a field is the electro-magnetic field. Once a field
has been associated to the photon, then it will become natural to associate a field to every particle
that is viewed aselementaryin the theory. Thus, electrons and positrons will have their(Dirac)
field. There was a time that a field was associated also to the proton, but we now know that the
proton is composite and thus, instead, there are now fields for quarks and gluons, which are the
elementary particles that make up a proton. The gluons are the analogs for the strong force of the
photon for the electro-magnetic force, namely the gluons mediate the strong force. Analogously,
theW±andZ^0 mediate the weak interactions.
18.4 Some History and present significance of QFT
The quantization of the elctro-magnetic field was initiatedby Born, Heisenberg and Jordan in
1926, right after quantum mechanics had been given its definitive formulation by Heisenberg and
Schr ̈odinger in 1925. The complete formulation of the dynamics was given by Dirac Heiseberg and
Pauli in 1927. Infinities in perturbative corrections due tohigh energy (or UV – ultraviolet) effects
were first studied by Oppenheimer and Bethe in the 1930’s. It took until 1945-49 until Tomonaga,
Schwinger and Feynman gave a completely relativistic formulation of Quantum Electrodynamics
(or QED) and evaluated the radiative corrections to the magnetic moment of the electron. In 1950,
Dyson showed that the UV divergences of QED can be systematically dealt with by the process of
renormalization.
In the 1960’s Glashow, Weinberg and Salam formulated a renormalizable quantum field theory
of the weak interactions in terms of a Yang-Mills theory. Yang-Mills theory was shown to be
renormalizable by ‘t Hooft in 1971, a problem that was posed to him by his advisor Veltman. In
1973, Gross, Wilczek and Politzer discovered asymptotic freedom of certain Yang-Mills theories (the
fact that the strong force between quarks becomes weak at high energies) and using this unique clue,
they formulated (independently also Weinberg) the quantumfield theory of the strong interactions.
Thus, the elctro-magnetic, weak and strong forces are presently described – and very accurately
so – by quantum field theory, specifically Yang-Mills theory,and this combined theory is usually
referred to asthe STANDARD MODEL. To give just one example of the power of the quantum
field theory approach, one may quote the experimentally measured and theoretically calculated
values of the muon magnetic dipole moment,
1
2
gμ(exp) = 1.001159652410(200)
1
2
gμ(thy) = 1.001159652359(282) (18.2)