HTML Microdata document

This HTML5 document contains 66 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

Prefix	IRI
dcterms	http://purl.org/dc/terms/
dbo	http://dbpedia.org/ontology/
n14	http://dbpedia.org/resource/File:
foaf	http://xmlns.com/foaf/0.1/
n16	https://global.dbpedia.org/id/
dbt	http://dbpedia.org/resource/Template:
rdfs	http://www.w3.org/2000/01/rdf-schema#
freebase	http://rdf.freebase.com/ns/
n8	http://commons.wikimedia.org/wiki/Special:FilePath/
rdf	http://www.w3.org/1999/02/22-rdf-syntax-ns#
owl	http://www.w3.org/2002/07/owl#
wikipedia-en	http://en.wikipedia.org/wiki/
dbc	http://dbpedia.org/resource/Category:
dbp	http://dbpedia.org/property/
prov	http://www.w3.org/ns/prov#
xsdh	http://www.w3.org/2001/XMLSchema#
wikidata	http://www.wikidata.org/entity/
dbr	http://dbpedia.org/resource/

Statements

Subject Item: dbr:Loop_quantum_gravity
dbo:wikiPageWikiLink: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity

Subject Item: dbr:Wilson_loop
dbo:wikiPageWikiLink: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity

Subject Item: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity
rdfs:label: Loop representation in gauge theories and quantum gravity
rdfs:comment: Attempts have been made to describe gauge theories in terms of extended objects such as Wilson loops and holonomies. The loop representation is a quantum hamiltonian representation of gauge theories in terms of loops. The aim of the loop representation in the context of Yang–Mills theories is to avoid the redundancy introduced by Gauss gauge symmetries allowing to work directly in the space of physical states (Gauss gauge invariant states). The idea is well known in the context of lattice Yang–Mills theory (see lattice gauge theory). Attempts to explore the continuous loop representation was made by Gambini and Trias for canonical Yang–Mills theory, however there were difficulties as they represented singular objects. As we shall see the loop formalism goes far beyond a simple gauge invari
foaf:depiction: n8:The_Mandelstam_identity.jpg
dcterms:subject: dbc:Quantum_gravity dbc:Knot_theory dbc:Gauge_theories
dbo:wikiPageID: 43099469
dbo:wikiPageRevisionID: 1099967401
dbo:wikiPageWikiLink: dbc:Quantum_gravity dbr:Chern–Simons dbr:Wess–Zumino–Witten_model dbr:Edward_Witten dbr:Lattice_gauge_theory dbr:Parallel_transport dbr:Irreducible_representations dbr:Diffeomorphism dbr:Holonomies dbr:Topological_quantum_field_theories dbr:Conformal_field_theory dbr:Wilson_loop dbr:Mandelstam_variables n14:The_Mandelstam_identity.jpg dbr:Wheeler–DeWitt_equation dbr:Fields_Medal dbr:Lie_algebra dbr:Knot_invariant dbr:Knot_invariants dbr:Coplanar dbr:Pauli_matrices dbr:Canonical_quantum_gravity dbr:Loop_quantum_gravity dbr:General_relativity dbc:Knot_theory dbr:Ashtekar_variables dbc:Gauge_theories dbr:Vacuum_expectation_value dbr:Yang–Mills_theory dbr:Jones_polynomial dbr:Holonomy dbr:Position_and_momentum_spaces dbr:Link_(knot_theory) dbr:Ashtekar dbr:Quantum_gravity dbr:Unitary_group dbr:Spin_network dbr:Knot_theory dbr:Chern–Simons_theory
owl:sameAs: freebase:m.011c56nc wikidata:Q18350298 n16:n9jC
dbp:wikiPageUsesTemplate: dbt:Reflist dbt:Short_description dbt:Beyond_the_Standard_Model dbt:Main
dbo:thumbnail: n8:The_Mandelstam_identity.jpg?width=300
dbo:abstract: Attempts have been made to describe gauge theories in terms of extended objects such as Wilson loops and holonomies. The loop representation is a quantum hamiltonian representation of gauge theories in terms of loops. The aim of the loop representation in the context of Yang–Mills theories is to avoid the redundancy introduced by Gauss gauge symmetries allowing to work directly in the space of physical states (Gauss gauge invariant states). The idea is well known in the context of lattice Yang–Mills theory (see lattice gauge theory). Attempts to explore the continuous loop representation was made by Gambini and Trias for canonical Yang–Mills theory, however there were difficulties as they represented singular objects. As we shall see the loop formalism goes far beyond a simple gauge invariant description, in fact it is the natural geometrical framework to treat gauge theories and quantum gravity in terms of their fundamental physical excitations. The introduction by Ashtekar of a new set of variables (Ashtekar variables) cast general relativity in the same language as gauge theories and allowed one to apply loop techniques as a natural nonperturbative description of Einstein's theory. In canonical quantum gravity the difficulties in using the continuous loop representation are cured by the spatial diffeomorphism invariance of general relativity. The loop representation also provides a natural solution of the spatial diffeomorphism constraint, making a connection between canonical quantum gravity and knot theory. Surprisingly there were a class of loop states that provided exact (if only formal) solutions to Ashtekar's original (ill-defined) Wheeler–DeWitt equation. Hence an infinite set of exact (if only formal) solutions had been identified for all the equations of canonical quantum general gravity in this representation! This generated a lot of interest in the approach and eventually led to loop quantum gravity (LQG). The loop representation has found application in mathematics. If topological quantum field theories are formulated in terms of loops, the resulting quantities should be what are known as knot invariants. Topological field theories only involve a finite number of degrees of freedom and so are exactly solvable. As a result, they provide concrete computable expressions that are invariants of knots. This was precisely the insight of Edward Witten who noticed that computing loop dependent quantities in Chern–Simons and other three-dimensional topological quantum field theories one could come up with explicit, analytic expressions for knot invariants. For his work in this, in 1990 he was awarded the Fields Medal. He is the first and so far the only physicist to be awarded the Fields Medal, often viewed as the greatest honour in mathematics.
prov:wasDerivedFrom: wikipedia-en:Loop_representation_in_gauge_theories_and_quantum_gravity?oldid=1099967401&ns=0
dbo:wikiPageLength: 30256
foaf:isPrimaryTopicOf: wikipedia-en:Loop_representation_in_gauge_theories_and_quantum_gravity

Subject Item: dbr:Loop_representation
dbo:wikiPageWikiLink: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity
dbo:wikiPageRedirects: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity

Subject Item: dbr:The_loop_representation_in_gauge_theories_and_quantum_gravity
dbo:wikiPageWikiLink: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity
dbo:wikiPageRedirects: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity

Subject Item: wikipedia-en:Loop_representation_in_gauge_theories_and_quantum_gravity
foaf:primaryTopic: dbr:Loop_representation_in_gauge_theories_and_quantum_gravity