Schoonschip '91
The symbolic manipulation program Schoonschip is being made freely available for a number of computers with Motorola 680x0 cpu’s. It can run on machines with relatively modest memory and disk resources, and is designed to run as fast as possible given the host constraints. Memory and disk utilization can be adapted to tune performance. Recently added capabilities include a system for efficient generation of diagrams, gamma algebra for continuous dimensions, algorithmic improvements for handling large problems, and an increase in the allowed number of X expressions. 1. History The first working version of Schoonschip ran on an IBM 7094 in December, 1963. A basic problem in particle physics, namely, radiative corrections to photons interacting with a charged vector boson, was successfully completed. In 1966 Schoonschip was ported to the CDC 6600 series computers; and gradually, as hard disks and file storage became available, the distribution extended to encompass virtually all existing CDC machines. Even quite recently this version was used for a very complicated calculation of higher order effects in quantum chromodynamics in the USSR. Notable applications in quantum electrodynamics include works by Kinoshita and coauthors,  and Remiddi and coauthors,  among which we cite only a few. The early version of the Schoonschip manual by H. Strubbe  has been the standard reference for citations of Schoonschip itself. In 1983, when microprocessors of sufficient capability became available, Schoonschip was ported to a computer built around the Motorola 68000 microprocessor, the Charles River Data Systems machine. The operating system was UNIX-like, and the port to any other machine containing a 68000 series processor and featuring a UNIX-type operating system became trivial. 2. Features It is not likely that Schoonschip will ever have the popular constituency of programs like Maple and Mathematica. It does not have a graphics interface, and has much less built-in. ⋆ It can output formulas in Fortran format, but not in TeX or PostScript format. Although there is no reason why it cannot be used for general purposes, with a few exceptions its primary role so far has been that of a scientific instrument (especially in particle physics); and it demands a certain level of mathematical expertise for its effective use. In this section, we review some of the features that are special to Schoonschip, or relatively new to it. ⋆ There does exist the beginning of a mathematics and particle physics knowledge base of Schoonschip procedures, some of which is provided in the current distribution.

title: Instability of the existence of non-abelian vector potentials
abstract: We show the instability of the existence of vector potentials against variations of the field tensor in regions where it is “strongly non-abelian”.

title: On the lattice approach to the maximum Higgs boson mass
abstract: If the triviality upper bound on the Higgs boson mass mH occurs for strong self-coupling, inferring properties of the Higgs from the euclidean propagator is in principle theoretically difficult whether in coordinate or momentum space. In that case, common methods of identifying mH in lattice field theory simulations may produce a value for which is at best distantly related to the true upper limit. We discuss some shortcomings and ambiguities of recent results suggesting that the maximum occurs for weak coupling and emphasize potential complications due to finite-size and non-Lorentz-invariant effects of the lattice. The situation is illustrated by reference to the behavior in an analytically soluble approximation based on a 1/N expansion.

title: Large width in the Lee model for the Higgs-Goldstone sector
abstract: We discuss a variant of the unstable particle Lee model motivated by the problem of large width in Higgs meson decay. The essential result is that, in the point-interaction model, the width for decay into Goldstone bosons (W's and Z's), defined from the second-sheet unstable particle pole, obeys Γ0 ⩽ Γ <32Γ0, where Γ0 is the naive perturbative width, and the ordering is from weak coupling at the lower end to strong coupling at the upper end. If the point interaction of the Lee model is modified to make the tree scattering amplitude for Goldstone particles relativistically invariant, a large-coupling upper bound for the width results. Γ < 10.7 mH, where by comparison, the naive perturbative width grows like mH3. 
 
We find that defining the renormalized coupling at the complex Higgs pole is reasonable in the Lee model, even when the pole moves far from the real axis. Furthermore, scattering effects remain strong, in the sense that the unitarity bound is roughly approached over a large range of energies, although the scattering amplitude never reaches more than about 80% of saturation in the point-interaction model, contrary to naive perturbation theory. We also point out, without discussing it in this paper, what appears to be a new fact about the Lee model, that the Higgs propagator has a bound-state pole in addition to the resonance pole.

title: Euclidean nonlinear classical field equations with unique vacuum
abstract: AbstractWe study the real, Euclidean, classical field equation
$$( )\varphi + \lambda F(\varphi ) = f,\mu ^2 > 0$$
 where φ: ℝd→ℝ is suitably small at infinity. We study existence and regularity assuming that λ≧0,F∈C∞(ℝ), andaF(a)≧0∀a∈∝. These hypotheses allow strongly nonlinearF and nonunique solutions forf≠0. WhenF′≧0, we prove uniqueness, various contractivity properties, analytic dependence on the coupling constant λ, and differentiability in the external sourcef. For applications in the loop expansion in quantum field theory, it is useful to know that φ is in the Schwartz classL wheneverf is, and we provide a proof of this fact. The technical innovations of the problem lie in treating the noncompactness of Rd, the strong nonlinearity ofF, and the polynomial weights in the seminorms definingL.

title: Euclidean Fermi fields with a hermitean Feynman-Kac-Nelson formula. I
abstract: We construct free, Euclidean, spin one-half, quantum fields with the following properties: (i) CAR; (ii) Symanzik positivity; (iii) Osterwalder-Schrader positivity; (iv) no doubling of particle or spin states. They admit the recovery of the relativistic Dirac field by the Osterwalder-Schrader technique. We then formally parametrize interacting theories by a natural class of Hermitean, Euclidean actions, and obtain a simple, Hermitean, Feynman-Kac-Nelson formula. The interacting theory formally obeys all the properties (i)–(iv), and admits the reconstruction of a physical Hilbert space, including a Hermitean, contraction semigroup for the Wick rotated time evolution. We propose a system of axioms for the interacting theory.

title: Search for pair production of the scalar top quark in the electron+muon final state
abstract: We report the result of a search for the pair production of the lightest supersymmetric partner of the top quark ($\tilde{t}_1$) in $p\bar{p}$ collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider corresponding to an integrated luminosity of 5.4 fb$^{-1}$. The scalar top quarks are assumed to decay into a $b$ quark, a charged lepton, and a scalar neutrino ($\tilde{\nu}$), and the search is performed in the electron plus muon final state. No significant excess of events above the standard model prediction is detected, and improved exclusion limits at the 95% C.L. are set in the the ($M_{\tilde{t}_1}$,$M_{\tilde{\nu}}$) mass plane.