1,897 research outputs found
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 () to third order in .
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
- …