Current algebra
Current algebra (English: Current algebra ) is a mathematical construct of quantum field theory in which the fields to the commutation of a Lie algebra obey. From today's perspective, their development represents an important step on the way to quantum chromodynamics .
history
When numerous new hadrons were discovered after the Second World War , there was great uncertainty about their nature (whether they were elementary or composite particles). The attempt to transfer the concepts of quantum electrodynamics to interactions between hadrons turned out to be extremely difficult, since - as we know today - hadrons are composite systems whose interaction with one another can only be understood within the framework of the interaction of their constituents (the quarks ).
In the 1960s, among other things, the S-matrix theory was discussed as a possible alternative to conventional quantum field theory (developed in the 1940s) . It was hoped to develop a body of theory that would provide a consistent description of the observed interactions . Given the large number of hadrons, this was problematic because every theory had to specify which of the many discovered hadrons should be assumed to be elementary and which should be assumed to be composite.
Based on this situation, Murray Gell-Mann developed approaches to calculate directly with currents of electromagnetic and weak charge (or weak isospin ) and flavor (at that time still strong isospin ) as algebraic structures instead of the fields usual in quantum field theory (current-current- Approach). In this way, he avoided the dilemma of having to fixate on certain particles as elementary and then derive the currents from the associated fields.
Since the underlying commutation relations were not formulated in a relativistically covariant manner, the choice of a reference system was imperative for current algebraic calculations . The rest system initially used , however, led to the occurrence of infinities in calculations - just like in the quantum field theory, which was still strongly criticized for it at the time. Sergio Fubini finally succeeded in eliminating these infinities by choosing the Infinite Momentum Frame as a reference system.
Another problem with the early theory was that the quotient of vector and axial vector coupling could not be calculated from the theory. The breakthrough came with the finding of the Adler-Weissberger sum rule , which made it possible to express the axial-vector coupling constant as a function of the cross-section of the pion - proton scattering.
Based on Gell-Mann's Eightfold Way , he postulated the existence of quarks in 1964. These current quarks initially only served as a clear justification for the current algebra. In the following years, however, this relationship was reversed, and current algebra became an effective means of investigating the properties of current quarks. This development culminated in the early 1970s with the discovery and introduction of modern quantum chromodynamics .
swell
- ↑ a b Stephen L. Adler : Remarks on the History of Quantum Chromodynamics
- ^ Tian Yu Cao: From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism . Cambridge University Press, November 22, 2010, ISBN 978-0-521-88933-9 , pp. 1-41 (accessed February 10, 2012).
- ^ A b c Herbert Pietschmann : On the Early History of Current Algebra