6 research outputs found
Quantization of Midisuperspace Models
We give a comprehensive review of the quantization of midisuperspace models.
Though the main focus of the paper is on quantum aspects, we also provide an
introduction to several classical points related to the definition of these
models. We cover some important issues, in particular, the use of the principle
of symmetric criticality as a very useful tool to obtain the required
Hamiltonian formulations. Two main types of reductions are discussed: those
involving metrics with two Killing vector fields and spherically symmetric
models. We also review the more general models obtained by coupling matter
fields to these systems. Throughout the paper we give separate discussions for
standard quantizations using geometrodynamical variables and those relying on
loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit
Minimal Length Scale Scenarios for Quantum Gravity
We review the question of whether the fundamental laws of nature limit our
ability to probe arbitrarily short distances. First, we examine what insights
can be gained from thought experiments for probes of shortest distances, and
summarize what can be learned from different approaches to a theory of quantum
gravity. Then we discuss some models that have been developed to implement a
minimal length scale in quantum mechanics and quantum field theory. These
models have entered the literature as the generalized uncertainty principle or
the modified dispersion relation, and have allowed the study of the effects of
a minimal length scale in quantum mechanics, quantum electrodynamics,
thermodynamics, black-hole physics and cosmology. Finally, we touch upon the
question of ways to circumvent the manifestation of a minimal length scale in
short-distance physics.Comment: Published version available at
http://www.livingreviews.org/lrr-2013-