Quantum spin model for Reggeon field theory

Journal Article · Tue Mar 15 00:00:00 EST 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.1756· OSTI ID:7120179

Brower, R C; Furman, M A; Subbarao, K

We study the Hamiltonian form of Reggeon field theory on a lattice in the two-dimensional (D = 2) transverse or impact-parameter space. The Hamiltonian formalism allows naturally for the privileged character of the longitudinal variable or rapidity, which is kept continuous. Based on recent results for the one-dimensional theory, we argue that we may truncate the single-site basis of the Hamiltonian by retaining the lowest two states only, and we arrive at a lattice spin model. In terms of Pauli spin matrices sigma/sub k//sup n/ at each site n = (n/sub 1/,n/sub 2/), our Reggeon quantum spin model has the Hamiltonian H = summation/sub n/(delta/2)(1 - sigma/sub x//sup n/) + summation/sub n , i/A((1 - 2sigma/sub +//sup n/sup +//sup i/)(1 - 2sigma/sub +//sup n/) - sigma/sub z//sup n/sup +//sup i/sigma/sub z//sup n/), where i represents the lattice unit vectors (1,0) and (0,1). The parameters delta and A are related to those of the original field theory. All the approximations are valid for small Regge slope ..cap alpha../sup prime//sub 0/ in the region of the phase transition at output Regge intercept ..cap alpha.. (0) = 1. The critical exponents of the original system can be determined by the properties of the low-energy states of H in strict analogy with the established relation between the phi/sup 4/ theory in d = 2 and the ground state of the quantum Ising model with a transverse magnetic field in D = d - 1 =1 dimension. The general properties of the Reggeon quantum spin model are exhibited, and several new approximation schemes for Reggeon field-theoretic calculations are suggested. While the above Hamiltonian is adequate, by universality, to describe the critical Pomeron, systematic improvements can be made to study the theory away from criticality by retaining more states in the single-site basis of the Hamiltonian.

• Research Organization: Division of Natural Sciences, Physics, University of California, Santa Cruz, California 95064
• OSTI ID: 7120179
• Journal Information: Phys. Rev., D; (United States), Vol. 15:6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
REGGE CUTS
CROSS SECTIONS
EIGENSTATES
GREEN FUNCTION
HAMILTONIANS
POMERANCHUK PARTICLES
SPIN
TRANSVERSE MOMENTUM
ANGULAR MOMENTUM
BOSONS
ELEMENTARY PARTICLES
FIELD THEORIES
FUNCTIONS
HADRONS
LINEAR MOMENTUM
MATHEMATICAL OPERATORS
MESONS
PARTICLE PROPERTIES
POSTULATED PARTICLES
QUANTUM OPERATORS
645400* - High Energy Physics- Field Theory