Poincar\'e Supersymmetry Representations Over Trace Class Noncommutative Graded Operator Algebras

We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges, constructed from fields that form a trace class noncommutative graded operator algebra. In particular, supersymmetry theories can be turned into supersymmetric matrix models this way. We demonstrate our results by detailed component field calculations for the Wess-Zumino and the supersymmetric Yang-Mills models (the latter with axial gauge fixing), and then show that they are also implied by a simple and general superspace argument.Comment: plaintex, 23 Page

A Strategy for a Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking

Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace action becomes the statement $0=Re Tr T_{\mu}^{\mu}$, with $T_{\mu \nu}$ the operator stress energy tensor, and with $Tr$ the trace over the underlying Hilbert space. We show that this condition implies the vanishing of the cosmological constant and vacuum energy in the emergent quantum field theory. However, since the scale invariance condition does not require the operator $T_{\mu}^{\mu}$ to vanish, the spontaneous breakdown of scale invariance is still permitted.Comment: Second award in the Gravity Research Foundation Essay Competition for 1997; to appear in General Relativity and Gravitation. Plain Tex, no figure

Structure of Fluctuation Terms in the Trace Dynamics Ward Identity

We give a detailed analysis of the anti-self-adjoint operator contribution to the fluctuation terms in the trace dynamics Ward identity. This clarifies the origin of the apparent inconsistency between two forms of this identity discussed in Chapter 6 of our recent book on emergent quantum theory.Comment: TeX; 14 pages. Dedicated to Rafael Sorkin on the occasion of his 60th birthda

Efficient Simulation of Quantum State Reduction

The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the phenomenon of quantum state reduction. Here we construct a general closed form solution to this equation, for any given initial condition, in terms of a random variable representing the terminal value of the energy and an independent Brownian motion. The solution is essentially algebraic in character, involving no integration, and is thus suitable as a basis for efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur

Composite leptons and quarks constructed as triply occupied quasiparticles in quaternionic quanutm mechanics

\noindent We propose a set of rules for constructing composite leptons and quarks as triply occupied quasiparticles, in the quaternionic quantum mechanics of a pair of Harari-Shupe preons $T$ and $V$. The composites fall into two classes, those with totally antisymmetric internal wave functions, and those with internal wave functions of mixed symmetry. The mixed symmetry states consist of precisely the three spin 1/2 quark lepton families used in the standard model (48 particle states, {\it not} counting the doubling arising from antiparticles), plus one doublet of spin 3/2 quarks (24 particle states). The antisymmetric states consist of a set of spin 3/2 leptonic states with charges as in a standard model family (16 particle states), and a spin 1/2 leptonic fractionally charged doublet (4 particle states). We sketch ideas for deriving our rules from a fundamental quaternionic preonic field theory.Comment: 10pages,plain tex, IASSNS-HEP-94/2

Anomalies to All Orders

I give an account of my involvement with the chiral anomaly, and with the nonrenormalization theorem for the chiral anomaly and the all orders calculation of the trace anomaly, as well as related work by others. I then briefly discuss implications of these results for more recent developments in anomalies in supersymmetric theories.Comment: 35 pages, latex; To appear in Fifty Years of Yang-Mills Theory, G. 't Hooft editor, to be published by World Scientific. Final version; references adde