Bethe-Ansatz construction of the Chiral-Invariant Gross-Neveu model

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:6760082

Destri, C

The Chiral-Invariant Gross-Neveu model with SU(n) color symmetry is studied from the canonical point of view. The hamiltonian is diagonalized, in the presence of volume and ultraviolet cut-offs, by means of repeated Bethe Ansaetze. With the first Ansatz the infinite-dimensional differential problem is reduced to a finite-dimensional matrix eigenvalue problem in color space; this problem is then shown to be equivalent, thorugh n-1 nested Bethe Ansaetze formulated with the Quantum Inverse Scattering Method, to a set of coupled algebraic equations (the Bethe Ansatz equations). These are solved in detail for all states of interest from the field-theoretic point of view, i.e. for all the states describing, in the infinite-volume limit, the interaction of a finite number of physical, particle-like excitations of the physical ground state. The solution is obtained without invoking the time-honored string hypothesis, and it is found that the correct description in general does not involve strings of length greater than two. An interesting result is that the solution is expressed in terms of new algebraic equations which are very similar to the original ones, but are finite in number and involve only the rapidities of physical colored particles and a minimal set of complex numbers needed to distinguish the various internal color states of these particles. The general solution of the Bethe Ansatz equations also allows one to determine a self-consistent description of the full scattering of colored particles. The S-matrix is found to be factorizable and is identical to the S-matrix derived by previous authors on the basis of factorizability. The complete picture of the interaction between colored particles can be neatly interpreted in terms of an asymptotic higher level Bethe Ansatz structure.

• Research Organization: New York Univ., NY (USA)
• OSTI ID: 6760082
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
CHIRAL SYMMETRY
COLOR MODEL
COMPOSITE MODELS
EIGENVALUES
EXTENDED PARTICLE MODEL
FIELD THEORIES
INVERSE SCATTERING PROBLEM
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL MODELS
MATRICES
PARTICLE MODELS
PARTICLE PROPERTIES
PARTICLE RAPIDITY
QUARK MODEL
S MATRIX
SCATTERING
STRING MODELS
SYMMETRY
UNIFIED-FIELD THEORIES