Spectral Degeneracy of the Lattice Dirac Equation as a Function of Lattice Shape
Apr, 197721 pages
Published in:
- Nucl.Phys.B 127 (1977) 426-446
- Published: 1977
Report number:
- COO-3075-168
Citations per year
Abstract: (Elsevier)
We investigate the free Dirac equation in 2 + 1 dimensions on square, triangular, and hexagonal lattices. For each lattice the spectrum exhibits a degeneracy not present in the continuum limit. In the square and hexagonal cases there is a 4-fold degeneracy corresponding to 2 independent symmetries of the Hamiltonian; the degeneracy is eliminated by diagonalizing these symmetries and projecting onto the subspace characterized by a particular pair of eigenvalues. For the triangular case the degeneracy is 6-fold, but the naive Hamiltonian does not possess enough symmetry to eliminate the degeneracy. Certain ambiguities in the lattice Hamiltonian are pointed out and by the addition of terms which vanish in the continuum limit, it is cast in a form with sufficient symmetry to remove the degeneracy entirely, just as was done for the hexagonal and square lattices. It is found that after elimination of the spectral degeneracy the Hamiltonians for the hexagonal and triangular lattices are identical. The solutions to these theories are shown to have the correct continuum limit.- Dirac equation
- APPROXIMATION: LATTICE
- MODEL: LATTICE
- FERMION: DEGENERACY
- QUARK
- SYMMETRY: INTERNAL
- MODEL: PARTON
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