Current algebra
Current algebra (English: Current algebra) is a mathematical construct quantum field theory in which the fields obey the commutation relations of a Lie algebra. From today's perspective, their development is an important step on the way to quantum chromodynamics dar.
History
When, after the Second World War many new hadrons were discovered, there was great uncertainty about their nature ( whether it was elementary or composite particles). The attempt to apply the concepts of quantum electrodynamics on the interactions between hadrons, proved to be extremely difficult, since - as we now know - hadron composite systems, their interaction with each other only in the context of the interaction of its constituents ( quarks ) can be understood.
In the 1960s, among other things, the S-matrix theory has been discussed as a possible alternative to the (already developed in the 1940s ) conventional quantum field theory. It was hoped to develop a theoretical framework that provides a consistent description of the observed interactions. Based on the large number of hadrons, this was problematic, however, because each theory had to choose which to be elementary and which should be assumed to be composed of many discovered hadrons.
Starting from this situation developed Murray Gell-Mann approaches, instead of the usual in quantum field theory fields directly with streams of electromagnetic and weak charge (or weak isospin ) and Flavour (then still strong isospin ) as algebraic structures expected ( current -current approach). In this way he avoided the dilemma of having to commit to specific particles as elementary, and then derive the currents that arise from the associated fields.
Since the underlying commutation relations were not relativistically covariant formulated, the choice of a reference system was mandatory for stromalgebraische bills. However, the rest system first used resulted in the appearance of infinities in calculations - just like in the then still heavily criticized for quantum field theory. Sergio Fubini was finally able to eliminate these infinities by selecting the Infinite Momentum Frame the reference system.
Another problem of the early theory was that the ratio of vector and Axialvektorkopplung could not be calculated from theory. The breakthrough came here only the discovery of the Eagle Weissenberger- sum rule, which made it possible to express the axial- vector coupling constant depending on the cross section of the pion -proton scattering.
On the basis of Gell- Mann's Eightfold Way, this 1964 also postulated the existence of quarks. This current quarks served initially as a vivid justification of the current algebra. However, in the following years, this ratio was reversed, and the current algebra became the probaten means to investigate the properties of the current quarks. This development culminated in the early 1970s with the discovery and introduction of modern quantum chromodynamics.
Swell
- Quantum field theory