Generalized quantum mechanics of non-Abelian gauge theories

Abstract

Hartle's generalized quantum mechanics in the sum-over-histories formalism is used to describe a nonabelian gauge theory. Predictions are made for certain alternatives, with particular attention given to coarse grainings involving the constraint. In this way, the theory is compared to other quantum-mechanical descriptions of gauge theories in which the constraints are imposed by hand. The vanishing of the momentum space constraint is seen to hold, both through a simple formal argument and via a more careful description of the Lorentzian path integral as defined on a spacetime lattice. The configuration space realization of the constraint is shown to behave in a more complicated fashion. For some coarse grainings, we recover the known result from an abelian theory, that coarse grainings by values of the constraint either predict its vanishing or fail to decohere. However, sets of alternatives defined in terms of a more complicated quantity in the abelian case are exhibited where definite predictions can be made which disagree with the assumption that the constraints vanish. Finally, the configuration space sum-over-histories theory is exhibited in a manifestly Lorentz-invariant formulation.04.60. Gw, 03.65.Bz, 98.80.Hw

Critical Readings: African American Girls and Urban Fiction

“…Although research is needed to specifically examine claims about the significance of teachers and students engaging in urban fiction as a means of bridging dominant and nondominant reading interests and skills, there are some instructive examples of teachers who have used nondominant and controversial forms of text to engage student populations with more traditional forms of text that are promoted within curricula. For example, Alan Sitomer, a high school English teacher from Los Angeles, established connections between themes pervasive within controversial rapper Tupac Shakur's lyrics from "Me Against the World" and works of Shakespeare; parallel themes referenced in both works emerged including greed, isolation, power, and love (Whelan, 2007).…”