21 March 2006
Review on quantum field theory
There is a nice review on quantum field theory published today hep-th/0603155. It discusses in a fair way all approaches to QFT (perturbative, axiomatic and constructive) showing the advantages and limitations of each one. The perturbative approach is by far the most known and developed. It is the one usually teached in QFT courses. It can be applied in many situations and in particular to the standard model. It incorporates gauge symmetry, spontaneous symmetry breaking and anomalies, but infrared effects are tricky. Of course, the summation of the perturbative series is the great problem. The axiomatic approach tries to derive general properties of QFT using just its fundamental principles (like locality and Lorentz symmetry). Strong results are limited to two and three dimensional models without gauge symmetry. The constructive approach on the other side tries to build nontrivial QFT's satisfying some set of axioms. It is more versatile than the axiomatic approach but its success in treating gauge theories in four dimensions is still very limited. There is also a good discussion on renormalizability and the several meanings for effective quantum field theories. There are also some remarks on loop quantum gravity and string theory. At the end the authors are fair in saying that the gaps of QFT could be of a technical nature or could indicate some fundamental shortcoming. And I would not be surprised if gravity would be responsible for this.