Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model

Journal Article · · Physical Review. D.
 [1]
  1. Argonne National Laboratory (ANL), Argonne, IL (United States); Argonne National Laboratory
+ Show Author Affiliations

Here in order to solve the Bethe-Salpeter equation (BSE) in the Minkowski space, we first introduce the Nakanishi integral representations of the Bethe-Salpeter amplitude and the Bethe-Salpeter wave function. We then derive the explicit integral equations for the corresponding spectral functions from the BSE for states of two scalar particles bound by a scalar-particle exchange interaction, where the propagators of constituents are allowed to be fully dressed. These integral equations are subsequently solved numerically in the variation of the Wick-Cutkosky model with massive exchange particles, where an algorithm of adaptive mash grid is proposed. The equations and algorithm we develop here serve as the foundation of Minkowski-space formulation of BSE for bound states of fermions.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
2309765
Alternate ID(s):
OSTI ID: 2474231
OSTI ID: 2529447
Journal Information:
Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 3 Vol. 109; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (19)

Bethe–Salpeter bound-state structure in Minkowski space journal August 2016
Gauge covariance of the fermion Schwinger–Dyson equation in QED journal June 2017
NIST’s Digital Library of Mathematical Functions journal February 2018
A gauge covariant approximation to quantum electrodynamics journal June 1977
Renormalizable Electrodynamics of Vector Mesons journal May 1963
Renormalizable Electrodynamics of Scalar and Vector Mesons. II journal September 1964
Modified Perturbation Method for Spinor Electrodynamics journal September 1964
Bethe-Salpeter study of vector meson masses and decay constants journal October 1999
New form of kernel in equation for Nakanishi function journal September 2021
Going to the light front with contour deformations journal February 2022
Solving the Bethe-Salpeter equation for scalar theories in Minkowski space journal June 1995
Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space journal October 1997
Quantitative studies of the homogeneous Bethe-Salpeter equation in Minkowski space journal January 2014
Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space journal October 2016
Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions journal April 2017
Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED journal August 2017
Solving Bethe-Salpeter equation in Minkowski space journal January 2006
Cross-ladder effects in Bethe-Salpeter and light-front equations journal January 2006
Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach journal August 2014

Similar Records

Solving the Bethe-Salpeter equation for scalar theories in Minkowski space
Journal Article · Thu Jun 15 00:00:00 EDT 1995 · Physical Review, D · OSTI ID:55221
Wick-Cutkosky model in the large-temperature limit
Journal Article · Wed Jun 15 00:00:00 EDT 1988 · Phys. Rev. D; (United States) · OSTI ID:7186660

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Bethe-Salpeter equation
Schwinger-Dyson equation
integral equations