Polaron variational methods in the particle representation of field theory. I. General formalism

Journal Article · Fri Mar 01 04:00:00 EST 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.3337· OSTI ID:279219

Rosenfelder, R ^[1]; Schreiber, A W ^[1]

---

1. Paul Scherrer Institute, CH-5232 Villigen PSI (Switzerland)

We apply nonperturbative variational techniques to a relativistic scalar field theory in which heavy bosons ({open_quote}{open_quote}nucleons{close_quote}{close_quote}) interact with light scalar mesons via a Yukawa coupling. Integrating out the meson field and neglecting the nucleon vacuum polarization, one obtains an effective action in terms of the heavy particle coordinates which is nonlocal in the proper time. As in Feynman{close_quote}s polaron approach, we approximate this action by a retarded quadratic action whose parameters are to be determined variationally on the pole of the two-point function. Several {ital Ans{umlt a}tze} for the retardation function are studied and for the most general case we derive a system of coupled variational equations. An approximate analytic solution displays the instability of the system for coupling constants beyond a critical value. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 279219
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 6 Vol. 53; ISSN 0556-2821; ISSN PRVDAQ
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOSONS
COUPLING CONSTANTS
FIELD THEORIES
MESONS
SCALAR FIELDS
VACUUM POLARIZATION
VARIATIONAL METHODS
YUKAWA POTENTIAL