Search Results (5 total)

The notion of semiclassical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is applied to kinematical coherent states to obtain physical semiclassical states. In the specific examples considered, the technique turns out to be surprisingly efficient, suggesting that it may well be possible to use kinematical structures to analyze the semiclassical behavior of physical states of an interesting class of constrained systems.

We consider a recently proposed theory of gravity, classically equivalent to Einstein's theory with the cosmological constant as an additional variable, in which spacetime volume plays the role of time. We develop a Hamiltonian formulation using Ashtekar's variables, set up the corresponding quantum theory, and show that the known loop state solutions of quantum general relativity are also solutions in the present theory. We conclude with some remarks on why we feel that this quantum theory deserves further study.

The Lorentz invariance of a discrete space-time (casual structure) is commented upon.

We propose that space-time at the smallest scales is in reality a causal set: a locally finite set of elements endowed with a partial order corresponding to the macroscopic relation that defines past and future. We explore how a Lorentzian manifold can approximate a causal set, noting in particular that the thereby defined effective dimensionality of a given causal set can vary with length scale. Finally, we speculate briefly on the quantum dynamics of causal sets, indicating why an appropriate choice of action can reproduce general relativity in the classical limit.

We associate to any quantum field propagating in the background metric of a black hole an effective density matrix whose statistical entropy can be interpreted as a contribution to the total entropy of the black hole. By evaluating this contribution in a simplified case, we show that in general it can be expected to be finite and proportional to the area of the black hole. As a by-product of our calculation we obtain a general expression for the entropy of any real Gaussian density matrix.