Covariant three-body equations in field theory

Journal Article · Wed May 10 04:00:00 EDT 1995 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.48085· OSTI ID:165684

Kvinikhidze, A N ^[1]; Blankleider, B ^[2]

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1. Mathematical Institute of Georgian Academy of Sciences, Z. Rukhadze 1, 380093 Tbilisi (Georgia)
2. School of Physical Sciences, Flinders University of South Australia, Bedford Park, S.A. 5042 (Australia)

We have derived four-dimensional relativistic three-body equations for the case of a field theory with a three-point interaction vertex. These equations describe the coupled 2{r_arrow}2, 2{r_arrow}3, and 3{r_arrow}3 processes, and provide the means of calculating the kernel of the 2{r_arrow}2 Bethe-Salpeter equation. Our equations differ from all previous formulations in two essential ways. First, we have overcome the overcounting problems inherent in earlier works. Second, we have retained all possible two-body forces when one particle is a spectator. In this respect, we show how it is necessary to also retain certain three-body forces as these can give rise to (previously overlooked) two-body forces when used in a 2{r_arrow}3 process. The revealing of such hidden two-body forces is necessary for unitarity, and gives rise to a rich description where, for example, all the crossing contributions of the ladder graphs are retained. A further novel feature of our equations is the appearance of a number of subtraction terms. In the case of the {pi}{ital NN} system, for example, the {ital NN} potential involves a subtraction term where two pions, exchanged between the nucleons, interact with each other through the {pi}-{pi} t-matrix. The necessity of an input {pi}-{pi} interaction is surprising and contrasts markedly with the corresponding three-dimensional description of the {pi}{ital NN} system where no such interaction explicitly appears. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

• Sponsoring Organization: USDOE
• OSTI ID: 165684
• Report Number(s): CONF-9405132--
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 334; ISSN 0094-243X; ISSN APCPCS
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BETHE-SALPETER EQUATION
BOSON-EXCHANGE MODELS
EQUATIONS
FEYNMAN DIAGRAM
LORENTZ INVARIANCE
QUANTUM FIELD THEORY
THREE-BODY PROBLEM