zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Background independent quantum gravity: a status report. (English) Zbl 1077.83017
The consistent implementation of the gravitational interaction into the quantum framework is among the most important open problems in theoretical physics. A class of approaches to such a theory of quantum gravity is the application of quantization rules to Einstein’s theory of general relativity. Among these is the canonical approach which is characterized by the presence of constraints. The original choice of canonical variables were the three-metric and its momentum. More recently, a new set of variables was suggested consisting of a connection integrated around a loop in the three-manifold and its momentum (which is the flux of the triad through two-dimensional surfaces). The resulting approach is called Loop Quantum Gravity. From a mathematical point of view it leads much further than the old geometrodynamical approach, with one of the main results being the existence of a discrete spectrum for geometric operators such as the area operator. In their topical review, the authors give a comprehensive and up-to-date introduction into this approach on a level that is suitable for non-experts who possess some knowledge of general relativity and quantum field theory.
83C45Quantization of the gravitational field
83-02Research monographs (relativity)