Abstract
Hamiltonian SU(2) lattice gauge theory is formulated in an orthonormal and complete set of gauge-invariant eigenstates of the color-electric energy (electric-field basis). For a three-dimensional cubic lattice of linear extension L, these states are labeled by 6L3 quantum numbers: one gauge angular momentum for every link and three additional angular momenta specifying the intermediate couplings to a gauge singlet at every site. The Hamiltonian matrix elements in this basis are evaluated, and it is shown that the matrix elements of the color-magnetic energy carry an “irreducible” phase. We establish a representation of the independent-plaquette wave function in the electric-field basis as a sum over products of recoupling coefficients. Two applications to two space dimensions are given, demonstrating the feasibility of the present approach, and its extension to SU(3) is discussed.
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.
