Showing papers on "Quantum geometry published in 1972"

Quantum mechanics and field theory on multiply connected and on homogeneous spaces

Abstract: The basic framework for discussing quantum mechanics on multiply connected spaces is presented using the covering space concept. The theorem of Laidlaw and DeWitt is rederived and extended to the case of field theory. It is pointed out that chiral dynamics is similar to Skyrme's nonlinear theory and forms another example of Finkelstein's kink idea. The possible existence of ' pi geons' is raised, and the fact that the pion manifold may be any one of the Clifford-Klein constant curvature space-forms, rather than just the whole three-sphere, is suggested. The related formalism for quantum mechanics on homogeneous spaces is given in general terms.

Tachyons and Quantum Statistics

Abstract: A number of years ago, Bohm postulated the existence of a quantum potential in order to create a completely causal description of nonrelativistic quantum mechanics. It is shown that this quantum potential must be a tachyon field. An experimental test of the identification of tachyons with Bohm's quantum potential is described. It is shown that though in the above experiment spacelike intervals are investigated, the information arrives after timelike intervals. The experiment thus provides an example where tachyons can affect a measured quantity though they cannot be used to violate causality.

Quantum Space-Time

Abstract: Space-time is quantized so as to obtain a four-dimensional simple cubic lattice. The covariance under Poincare transformation is guaranteed. The particles interact non-locally. The interaction region is spread so as to form a closed (Euclidean) area in the lattice of space-time.

Variational trial functions in quantum theory. I. Bound states

Abstract: The authors give a method of calculating variational trial functions in quantum theory. Applications are made to the discrete spectra of some simple one and two particle systems.