Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space

The program of quantizing the gravitational field with the help of affine field variables is continued. For completeness, a review of the selection criteria that singles out the affine fields, the alternative treatment of constraints, and the choice of the initial (before imposition of the constraints) ultralocal representation of the field operators is initially presented. As analogous examples demonstrate, the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear. To achieve this introduction and enforcement of the constraints, a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical Hilbert space is developed and extensively analyzed.Comment: LaTeX, 42 pages, no figure

Comparison of the T-Matrix And Helmholtz Integral Equation Methods for Wave Scattering Calculations

The T-matrix method (TMM) and the Helmholtz integral equation method (HIEM) are wave scattering formalisms for irregularly shaped targets. They are both based on the Helmholtz integral formula (HIF) but they use different ways to achieve the discretization required for numerical evaluation.</p

A SHELL MODEL THEORY OF THE R-MATRIX

A method for dealing with the nuclear many-body problem is suggested. The approach is a refinement of the shell model in which the asymptotic boundary conditions are used as constraints in a variational calculation of the R-matrix. Since it is the R-matrix that is calculated, this method should provide a description of nuclear reactions and decays as well as of nuclear bound states. (auth

THEORY OF ALPHA DECAY

The relationship between nuclear reactions and nuclear decay derived by F. T. Smith is presented and illustrated by a simple example. (auth

Comparison of the T‐matrix and Helmholtz integral equation methods for wave scattering calculations

The T-matrix method (TMM) and the Helmholtz integral equation method (HIEM) are wave scattering formalisms for irregularly shaped targets. They are both based on the Helmholtz integral formula (HIF) but they use different ways to achieve the discretization required for numerical evaluation.</p

A SHELL MODEL THEORY OF THE R-MATRIX

A method for dealing with the nuclear many-body problem is suggested. The approach is a refinement of the shell model in which the asymptotic boundary conditions are used as constraints in a variational calculation of the R-matrix. Since it is the R-matrix that is calculated, this method should provide a description of nuclear reactions and decays as well as of nuclear bound states. (auth