Discrete Physics and the Dirac Equation

We rewrite the 1+1 Dirac equation in light cone coordinates in two significant forms, and solve them exactly using the classical calculus of finite differences. The complex form yields ``Feynman's Checkerboard''---a weighted sum over lattice paths. The rational, real form can also be interpreted in terms of bit-strings.Comment: LaTex 16 pages, 10 figures. To obtain a copy, send e-mail to [email protected]

A New Model for Oversight of Commercial Activities by Nonprofits?

This Note discusses a New Jersey tax case, Fields v. Trustees of Princeton University, that settled in 2016 after motion practice. The plaintiffs were twenty-eight municipal taxpayers in Princeton who challenged Princeton University’s entire property-tax exemption on the ground that the way the University distributed royalty payments from patents to faculty inventors and licensed these patents in joint ventures and other partnerships ran afoul of the “profit test” that applies to educational property-tax exemptions in New Jersey. This Note uses this litigation to discuss a potential conflict between the Bayh-Dole Act, which encourages academic patent development, and such profit tests on charitable and educational property exemptions in several states. It concludes that while the model of litigation in Fields could offer a new procedural oversight means over nonprofits, a better solution involves substantive legislative reform that regularizes current ad hoc payments between municipalities and large nonprofits and better aligns local property taxes with federal policy