A Concise Introduction to Quantum Field Theory 191magnetic dipole moment of the muon
(gμ−2)theor. = 233 169 436× 10 −^11 , (3.1)fits impressively well with the experimentally measured value
(gμ−2)exp. = 233 184 182× 10 −^11. (3.2)If we include all corrections due to the Standard Model of Particle Physics
(gμ−2)theor. = 233 183 606× 10 −^11 , (3.3)the theoretical agreement is even more impressive.
However, in the late 1950s it was remarked that the renormalization of the
theory generates another UV catastrophe due to the appearance of a singular pole
in the effective electric charge of the electron. The phenomenon know as Landau
pole motivated that the majority of particle physicists considered that quantum
field theory was not a suitable theory for weak and strong interactions of the newly
discoveredelementaryparticles.
However, with the discovery of the theory of gauge fields and the formulation
of the Standard Model of Particle Physics the perspective radically changed and
today, quantum field theory is the basic framework of Fundamental Physics.
(1)What are the essential features of quantum field theory which
make it so special?
A first answer is that QFT provides a unified framework where the quantum
theory and the theory of relativity are consistently integrated.
Sometimes field theory is identified as the theory of particle physics. This is
not completely correct. Field theory isa framework which goes beyond particle
physics. In fact there are field theories where there is no particle interpretation of
the states of the theory.
But it is also true that most of the successful field theories admit a particle
interpretation. That means that there are states which can be correctly interpreted
as particle states and in those cases, field theory provides a causal framework for
particle interactions where action at a distance is replaced by local field interac-
tions. Although this picture also holds for classical field theories, the difference
between the classical and quantum theories lies on the fact that in the quantum
theory, the interaction between the particles can be interpreted as a process of
creation and destruction of messenger particles. The association of forces and
interactions with particle exchange is one of the most interesting features of QFT.
The particles that appear in field theory are very special: they are all identical.
This means that the electrons in the earth are the same as the electrons in Alpha
Centauri because all of them are excitations of the same electron field in QED.