Abstract
Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial gauge theories in their own right and as effective theories of QCD at high temperatures. I shall review the basics of our Hamiltonian approach to this theory, emphasizing symmetries with a short update on its status. We will show that the calculation of the vacuum wave function for Yang-Mills theory in 2+1 dimensions is in the lowest order of a systematic expansion. Expectation values of observables can be calculated using an effective interacting chiral boson theory, which also leads to a natural expansion as a double series in the coupling constant (to be interpreted within a resummed perturbation series) and a particular kinematical factor. The calculation of the first set of corrections in this expansion shows that the string tension is modified by about −0.3% to −2.8% compared to the lowest order value. This is in good agreement with lattice estimates.
Highlights
As many of you know, Yang-Mills theory in 2 + 1 dimensions has been the focus of research as well as an object of fascination for my collaborators and myself for many years
I shall zero in on our recent calculations of corrections to the string tension. This latter part is more than just a calculation of specific results; it formulates a systematic calculational framework which may prove to be a gateway to newer results such as glueball masses
Step 1 We rewrite the derivation of the vacuum wave function as a recursive procedure for the solution of the Schrödinger equation from which it will be clear that (2.10) is the lowest order result in a systematic expansion
Summary
As many of you know, Yang-Mills theory in 2 + 1 dimensions has been the focus of research as well as an object of fascination for my collaborators and myself for many years. I shall zero in on our recent calculations of corrections to the string tension. This latter part is more than just a calculation of specific results; it formulates a systematic calculational framework which may prove to be a gateway to newer results such as glueball masses. In 2 + 1 dimensions, there are propagating degrees of freedom, the theory has nontrivial dynamics, yet seems to be within reach of some level of analytical investigation. This is aided by the fact that the theory has a dimensional coupling constant and, as a related fact, because it is super-renormalizable. One can use Yang-Mills theory in 3 Euclidean dimensions as the high temperature approximation to real QCD; calculations in the Minkowskian 2 + 1 dimensional theory can be continued to the Euclidean signature to make predictions about the magnetic screening mass and other related phenomena
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
