Stability of the scalar {chi}{sup 2}{phi} interaction

Journal Article · Mon Oct 01 00:00:00 EDT 2001 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.64.076008· OSTI ID:40277418

Gross, Franz; Tjon, John

A scalar field theory with a {chi}{sup {dagger}}{chi}{phi} interaction is known to be unstable. Yet it has been used frequently without any sign of instability in standard textbook examples and research articles. In order to reconcile these seemingly conflicting results, we show that the theory is stable if the Fock space of all intermediate states is limited to a finite number of closed {chi}{bar {chi}} loops associated with a field {chi} that appears quadradically in the interaction, and that instability arises only when intermediate states include these loops to all orders. In particular, the quenched approximation is stable.

• Research Organization: Thomas Jefferson National Accelerator Facility
• Sponsoring Organization: (US)
• DOE Contract Number: AC05-84ER40150; FG02-97ER41032
• OSTI ID: 40277418
• Journal Information: Physical Review D, Vol. 64, Issue 7; Other Information: DOI: 10.1103/PhysRevD.64.076008; Othernumber: PRVDAQ000064000007076008000001; 048119PRD; PBD: 1 Oct 2001; ISSN 0556-2821
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
INSTABILITY
SCALAR FIELDS
SCALARS
STABILITY