Exact nonperturbative unitary amplitudes for 1 r arrow N transitions

Journal Article · Mon Nov 23 04:00:00 EST 1992 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.69.3017· OSTI ID:6950179

Goldberg, H ^[1]

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1. Department of Physics, Northeastern University, Boston, Massachusetts 02115 (United States)

I present an extension to arbitrary {ital N} of a previously proposed field theoretic model, in which unitary amplitudes for 1{r arrow}8 processes were obtained. The Born amplitude in this extension has the behavior {ital A}{sub 1{r arrow}{ital N}}{sup tree}={ital g}{sup {ital N}{minus}1}{ital N} expected in a bosonic field theory. Unitarity is violated when {vert bar}{ital A}{sub 1{r arrow}{ital N}}{vert bar}{gt}1, or when {ital N}{gt}{ital N}{sub crit}{congruent}{ital e}/{ital g}. Numerical solutions of the coupled Schroedinger equations show that for weak coupling and a large range of {ital N}{gt}{ital N}{sub crit}, the exact unitary amplitude is reasonably fitted by a factorized expression {vert bar}{ital A}{sub 1{minus}{gt}{ital N}}{vert bar}{sub max}{congruent}(0.73/{ital N})exp({minus}0.025/{ital g}{sup 2}). The very small size of the coefficient 1/{ital g}{sup 2}, indicative of a very weak exponential suppression, is not in accord with standard discussions based on saddle-point analysis, which give a coefficient of {similar to}1. The weak dependence on {ital N} could have experimental implications in theories where the exponential suppression is weak (as in this model). Nonperturbative contributions to few-point correlation functions in this theory would arise at order {ital K}{congruent}((0.05/{ital g}{sup 2})+2 ln{ital N})/ln(1/{ital g}{sup 2}) in an expansion in powers of {ital g}{sup 2}.

• OSTI ID: 6950179
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 69:21; ISSN PRLTA; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
BORN APPROXIMATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
LIMITING VALUES
MANY-BODY PROBLEM
MATHEMATICS
NUMERICAL ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTUM FIELD THEORY
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
UNITARITY
WAVE EQUATIONS