Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-07-28
Physics
High Energy Physics
High Energy Physics - Theory
7 pages. Contribution to Proceedings of the $8^{\rm th}$ International Wigner Symposium, May 27-30, 2003, New York, NY
Scientific paper
The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss's law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. To circumvent the problem that this Hamiltonian, which is expressed entirely in terms of gauge-invariant variables, must be used with nonnormalizable complicated states that implement the non-Abelian Gauss's law, we demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of $S$-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of `standard' perturbative states. The fact that the gauge-invariant chromoelectric field is not hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this nonhermiticity is taken into account, the `extra' perturbative terms in Christ and Lee's Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this nonhermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results.
No associations
LandOfFree
Using gauge-invariant variables in QCD does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Using gauge-invariant variables in QCD, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Using gauge-invariant variables in QCD will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-108063