Some Novel Features of the {Gross-Neveu} Model

Dec, 1979
4 pages
Published in:
  • Phys.Lett.B 92 (1980) 333-336
  • Published: 1980
Report number:
  • Print-79-0983 (YALE)

Citations per year

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Abstract: (Elsevier)
The dynamics of the O(2 N ) Gross-Neveu model seems to be liked to the O(2 N ) group by more than just O(2 N ) invariance. It is shown that the P 3 symmetry of the O(8) Dynkin diagram leads to a triality symmetry in the dynamics that allows us to transform the ψ particles and the two kinds of kinks into each other. It is also pointed out that (i) particles appear in the spectrum only in the N basic representations that enter the Dynkin diagram, (ii) their masses squared (in units of kink mass) are just the eigenvalues of the Cartan matrix for the SU( N −1) subgroup, (iii) in bosonized form, the potential energy is of the form Σα exp( i √4 πφ · α ), where is the boson field and α are the roots of the O(2 N ) Lie algebra. Thus this model seems to be a field theory variant of a class of completely integrable systems (like the Toda chain) investigated by Kostant, and Perelomov and Olshanetsky.
  • FIELD THEORY: TWO-DIMENSIONAL
  • FIELD THEORY: SPINOR
  • SPINOR: FIELD THEORY
  • FIELD THEORY: O(2N)
  • FIELD EQUATIONS: NONLINEAR
  • FIELD EQUATIONS: KINK
  • FIELD THEORY: VACUUM STATE
  • ALGEBRA: LIE