Dressing the nucleon propagator

Journal Article · Fri Oct 15 00:00:00 EDT 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.14.2162· OSTI ID:7333590

Fishman, S; Gersten, A

The nucleon propagator in the ''nested bubbles'' approximation is analyzed. The approximation is built from the minimal set of diagrams which is needed to maintain the unitarity condition under two-pion production threshold in the two-nucleon Bethe--Salpeter equation. Recursive formulas for subsets of ''nested bubbles'' diagrams calculated in the framework of the pseudoscalar interaction are obtained by the use of dispersion relations. We prove that the sum of all the ''nested bubbles'' diverges. Moreover, the successive iterations are plagued with ghost poles. We prove that the first approximation--which is the so-called chain approximation--has ghost poles for any nonvanishing coupling constant. In an earlier paper we have shown that ghost poles lead to ghost cuts. These cuts are present in the ''nested bubbles.'' Ghost elimination procedures are discussed. Modifications of the ''nested bubbles'' approximation are introduced in order to obtain convergence and in order to eliminate the ghost poles and ghost cuts. In a similar way as in the Lee model, cutoff functions are introduced in order to eliminate the ghost poles. The necessary and sufficient conditions for the absence of ghost poles are formulated and analyzed. The spectral functions of the modified ''nested bubbles'' are analyzed and computed. Finally, we present a theorem, similar in its form to Levinson's theorem in scattering theory, which enables one to compute in a simple way the number of ghost poles. (AIP)

• Research Organization: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
• OSTI ID: 7333590
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 14:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYON-BARYON INTERACTIONS
BARYONS
BETHE-SALPETER EQUATION
DISPERSION RELATIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FUNCTIONS
HADRON-HADRON INTERACTIONS
HADRONS
INTERACTIONS
NUCLEON-NUCLEON INTERACTIONS
NUCLEONS
PARTICLE INTERACTIONS
PARTICLE PRODUCTION
PROPAGATOR
PSEUDOSCALARS
RECURSION RELATIONS
REGGE CUTS
REGGE POLES
SPECTRAL FUNCTIONS
UNITARITY