The stability of the scalar {chi}{sup 2}{phi} interaction
Abstract
A scalar field theory with a {chi}{dagger}{chi}{phi} interaction is known to be unstable. Yet it has been used frequently without any sign of instability in standard text book 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 {chi}{bar {chi}} loops associated with field {chi} that appears quadradically in the interaction, and that instability arises only when intermediate states include these loops to all orders.
- Authors:
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE Office of Energy Research (ER) (US)
- OSTI Identifier:
- 775029
- Report Number(s):
- JLAB-THY-01-07; DOE/ER/40150-1811; nucl-th/0102041; WM-01-103
TRN: US0200922
- DOE Contract Number:
- AC05-84ER40150
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review
- Additional Journal Information:
- Journal Volume: D; Journal Issue: 64; Other Information: No journal information given for this preprint; PBD: 16 Feb 2001; PBD: 16 Feb 2001
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; INSTABILITY; SCALAR FIELDS; SCALARS; STABILITY
Citation Formats
Gross, Franz, Savkli, Cetin, and Tjon, John. The stability of the scalar {chi}{sup 2}{phi} interaction. United States: N. p., 2001.
Web.
Gross, Franz, Savkli, Cetin, & Tjon, John. The stability of the scalar {chi}{sup 2}{phi} interaction. United States.
Gross, Franz, Savkli, Cetin, and Tjon, John. 2001.
"The stability of the scalar {chi}{sup 2}{phi} interaction". United States. https://www.osti.gov/servlets/purl/775029.
@article{osti_775029,
title = {The stability of the scalar {chi}{sup 2}{phi} interaction},
author = {Gross, Franz and Savkli, Cetin and Tjon, John},
abstractNote = {A scalar field theory with a {chi}{dagger}{chi}{phi} interaction is known to be unstable. Yet it has been used frequently without any sign of instability in standard text book 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 {chi}{bar {chi}} loops associated with field {chi} that appears quadradically in the interaction, and that instability arises only when intermediate states include these loops to all orders.},
doi = {},
url = {https://www.osti.gov/biblio/775029},
journal = {Physical Review},
number = 64,
volume = D,
place = {United States},
year = {Fri Feb 16 00:00:00 EST 2001},
month = {Fri Feb 16 00:00:00 EST 2001}
}
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