The Kauffman bracket and the Jones polynomial in quantum gravity

An analysis of the action of the Hamiltonian constraint of quantum gravity on the Kauffman bracket and Jones knot polynomials is proposed. It is explicitely shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint with cosmological constant ($\Lambda$) to third order in $\Lambda$. The calculation is performed in the extended loop representation of quantum gravity. The analysis makes use of the analytical expressions of the knot invariants in terms of the two and three point propagators of the Chern-Simons theory. Some particularities of the extended loop calculus are considered and the implications of the results to the case of the conventional loop representation are discussed.Comment: 21 page

The Gauss Constraint in the Extended Loop Representation

The Gauss constraint in the extended loop representation for quantum gravity is studied. It is shown that there exists a sector of the state space that is rigorously gauge invariant without the generic convergence issues of the extended holonomies.Comment: 8 pages, latex, no figure

Human Capital Estimation through Structural Equation Models with some Categorical Observed Variables

The aim of this paper is to estimate, for US, Canada and Italy, the latent variable human capital and its causal relationship with labor income, through some Structural Equation Models. The analyzed models contain some observed categorical variables, which imply the use of the two-stage estimation technique.Human Capital ; Structural Equation Model (SEM) ; Polychoric Correlation ; Weighted Least Squares ; LISREL

Canonical quantization of constrained theories on discrete space-time lattices

We discuss the canonical quantization of systems formulated on discrete space-times. We start by analyzing the quantization of simple mechanical systems with discrete time. The quantization becomes challenging when the systems have anholonomic constraints. We propose a new canonical formulation and quantization for such systems in terms of discrete canonical transformations. This allows to construct, for the first time, a canonical formulation for general constrained mechanical systems with discrete time. We extend the analysis to gauge field theories on the lattice. We consider a complete canonical formulation, starting from a discrete action, for lattice Yang--Mills theory discretized in space and Maxwell theory discretized in space and time. After completing the treatment, the results can be shown to coincide with the results of the traditional transfer matrix method. We then apply the method to BF theory, yielding the first lattice treatment for such a theory ever. The framework presented deals directly with the Lorentzian signature without requiring an Euclidean rotation. The whole discussion is framed in such a way as to provide a formalism that would allow a consistent, well defined, canonical formulation and quantization of discrete general relativity, which we will discuss in a forthcoming paper.Comment: 18 pages, RevTex, one figur