Causal perturbation theory

The finite quantum field theory ( FQFT ) is an attempt to cope with the classic difficulties of quantum field theory ( QFT ).

One of these difficulties is the classical UV catastrophe that is treated in the classical theory by renormalization. Problems here are conceptual and mathematical nature: On the one hand, one obtains a theory in which many elements have to be used on an ad hoc or experimental experience, go to the other many of the theory lost intrinsic symmetries, the reconstructed after renormalization "by hand" must be. The difficulties are due mainly to mathematical facts. This includes, for example, the fact that in general, distributions functions, as opposed to no algebra form (for example, a delta distribution should not be raised ).

The FQFT circumvents this problem by the so-called causal perturbation theory, which was developed by Ernst Carl Gerlach Stueckelberg, Nikolai Nikolaevich Bogolyubov, the physicist Henri Epstein and Vladimir Glaser. The S- matrix of order order is constructed:

With a tempered test function, and the operator valued distributions. The first order here specifies the model. All higher orders will now be inductively constructed in which causality plays an essential role. The method by H. Epstein and W. Glaser now is to split distributions with support on a generalized forward and backward light cone causally correct (which can be carried out in momentum space in theories with massive fields by a dispersion integral). This causal splitting occurring in the inductive construction essentially corresponds to the operator- distributions time order of operator products, and at the correct treatment of the problem will not occur UV divergences. However, the construction is generally not clear: local operator- distributions, the carrier lie on the so-called diagonal, can be optionally added to the. The shape of these distributions is local but limited by their scaling behavior and general symmetry conditions (for example, the Poincaré symmetry). The FQFT been successfully applied to various model theories, but also on (massive ) gauge theories such as the standard model of elementary particle physics applied.

During the calculation of the perturbative S- matrix are generally left, and at the end of the adiabatic limit can be carried out, which is calculated using controls the infrared divergences and cross sections can finally be calculated.

Development opportunities

The FQFT is a very general theory that can be developed in different directions now. Worth mentioning is the approach in the non assumes classical fields and the corresponding Lagrangians, but general scalar, vector and tensor fields are quantized. Together with suitable geometric calibration conditions can be, for example, the theory of the electroweak interaction construct. The existence of the Higgs boson or a Higgs sector automatically follow from the theory, and not have to "manually" are introduced into the theory.

Next can be generalized to curvilinear coordinates the FQFT, which eventually may allow the connection to the quantum gravity.

Assessment

The main advantage of FQFT is that the theory is well defined from a mathematical point as perturbative theory. An interesting application of this theory may lie in the assessment of higher dimensional theories such as string theory, since this should lead back in a suitable reducing the dimensions to a ( mathematically correct ) QFT.

The methods used here are the experts so far less common. In the professional world many calculations with the help of path integrals ( Feynman diagrams ) can be performed, which are used in FQFT not apply.