zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
The case for background independence. (English) Zbl 1116.83013
Rickles, Dean (ed.) et al., The structural foundations of quantum gravity. Oxford: Clarendon Press (ISBN 0-19-926969-6/hbk). 196-239 (2006).

One of the problems both of quantum gravity and string theory is the fact that several useful theories start by a 3+1-decomposition of space-time into space and time. At the end, it is not clear in which sense the result depends on the fact, how this 3+1-decomposition has been done; this is the rough description of the problem of background independence. In a more detailed sense, one argues, that space-time is dynamical, i.e., the background for the motion of physical fields is itself a field in motion.

Lee Smolin gives a presentation about this problem and puts it into a historical context, starting from Newton’s absolute space via Leibniz’s relationalism to Mach and Einstein. He discusses several variants of the notion of background independence. Then he argues why a correct quantum theory of gravity must be background independent. Loop quantum gravity and dynamical triangulations are discussed, too.

MSC:
83C45Quantization of the gravitational field
83C30Asymptotic procedures (general relativity)
83C05Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83-03Historical (relativity)
01A50Mathematics in the 18th century
01A55Mathematics in the 19th century
01A60Mathematics in the 20th century