Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Journal Article · Wed Aug 01 00:00:00 EDT 1979 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(79)90391-9· OSTI ID:5752517

Zamolodchikov, A B; Zamolodchikov, A B

The general properties of the factorized S-matrix in two-dimensional space-time are considered. The relation between the factorization property of the scattering theory and the infinite number of conservation laws of the underlying field theory is discussed. The factorization of the total S-matrix is shown to impose hard restrictions on two-particle matrix elements: they should satisfy special identities, the so-called factorization equations. The general solution of the unitarity, crossing and factorization equations is found for the S-matrices having isotopic O (N) -symmetry. The solution turns out to have different properties for the cases N=2 and N> or =3. For N=2 the general solution depends on one parameter (of coupling constant type), whereas the solution for N> or =3 has no parameters but depends analytically on N. The solution for N=2 is shown to be an exact soliton S-matrix of the sine-Gordon model (equivalently the massive Thirring model). The total S-matrix of the model is constructed. In the case of N> or =3 there are two ''minimum'' solutions, i.e., those having a minimum set of singularities. One of them is shown to be an exact S matrix of the quantum O (N) -symmetric nonlinear sigma-model, the other is argued to describe the scattering of elementary particles of the Gross-Neveu model.

• Research Organization: Institute of Theoretical and Experimental Physics, Moscow, USSR
• OSTI ID: 5752517
• Journal Information: Ann. Phys. (N.Y.); (United States), Vol. 120:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
S MATRIX
TWO-DIMENSIONAL CALCULATIONS
SINE-GORDON EQUATION
CONSERVATION LAWS
CROSSING SYMMETRY
MATRIX ELEMENTS
O GROUPS
SCATTERING
SIGMA MODEL
SOLITONS
SPACE-TIME
UNITARITY
DYNAMICAL GROUPS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
LIE GROUPS
MATHEMATICAL MODELS
MATRICES
PARTICLE MODELS
QUASI PARTICLES
SYMMETRY
SYMMETRY GROUPS
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