34 research outputs found
Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space
We apply the perturbation theory integral representation (PTIR) to solve for
the bound state Bethe-Salpeter (BS) vertex for an arbitrary scattering kernel,
without the need for any Wick rotation. The results derived are applicable to
any scalar field theory (without derivative coupling). It is shown that solving
directly for the BS vertex, rather than the BS amplitude, has several major
advantages, notably its relative simplicity and superior numerical accuracy. In
order to illustrate the generality of the approach we obtain numerical
solutions using this formalism for a number of scattering kernels, including
cases where the Wick rotation is not possible.Comment: 28 pages of LaTeX, uses psfig.sty with 5 figures. Also available via
WWW at
http://www.physics.adelaide.edu.au/theory/papers/ADP-97-10.T248-abs.html or
via anonymous ftp at
ftp://bragg.physics.adelaide.edu.au/pub/theory/ADP-97-10.T248.ps A number of
(crucial) typographical errors in Appendix C corrected. To be published in
Phys. Rev. D, October 199
Solving the Bethe-Salpeter Equation for Scalar Theories in Minkowski Space
The Bethe-Salpeter (BS) equation for scalar-scalar bound states in scalar
theories without derivative coupling is formulated and solved in Minkowski
space. This is achieved using the perturbation theory integral representation
(PTIR), which allows these amplitudes to be expressed as integrals over weight
functions and known singularity structures and hence allows us to convert the
BS equation into an integral equation involving weight functions. We obtain
numerical solutions using this formalism for a number of scattering kernels to
illustrate the generality of the approach. It applies even when the na\"{\i}ve
Wick rotation is invalid. As a check we verify, for example, that this method
applied to the special case of the massive ladder exchange kernel reproduces
the same results as are obtained by Wick rotation.Comment: 23 pages with 3 uuencoded, compressed Postscript figures. Entire
manuscript available as a ps file at
http://www.physics.adelaide.edu.au/theory/home.html . Also available at
ftp://adelphi.adelaide.edu.au/pub/theory/ADP-94-24.T164.p
Deep Inelastic Structure Functions in a Covariant Spectator Model
Deep-inelastic structure functions are studied within a covariant scalar
diquark spectator model of the nucleon. Treating the target as a two-body bound
state of a quark and a scalar diquark, the Bethe-Salpeter equation (BSE) for
the bound state vertex function is solved in the ladder approximation. The
valence quark distribution is discussed in terms of the solutions of the BSE.Comment: 22 pages, LaTeX, 7 Postscript figures included using epsfig.st