FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2565218974> ?p ?o ?g. }

• W2565218974 abstract "Noncommutative (NC) spaces commonly arise as solutions to matrix model equations of motion. They are natural generalizations of the ordinary commutative spacetime. Such spaces may provide insights into physics close to the Planck scale, where quantum gravity becomes relevant. Although there has been much research in the literature, aspects of these NC spaces need further investigation. In this dissertation, we focus on properties of NC spaces in several different contexts. In particular, we study exact NC spaces which result from solutions to matrix model equations of motion. These spaces are associated with finite-dimensional Lie-algebras. More specifically, they are two-dimensional fuzzy spaces that arise from a three-dimensional Yang-Mills type matrix model, four-dimensional tensorproduct fuzzy spaces from a tensorial matrix model, and Snyder algebra from a five-dimensional tensorial matrix model. In the first part of this dissertation, we study two-dimensional NC solutions to matrix equations of motion of extended IKKT-type matrix models in threespace-time dimensions. Perturbations around the NC solutions lead to NC field theories living on a two-dimensional space-time. The commutative limit of the solutions are smooth manifolds which can be associated with closed, open and static two-dimensional cosmologies. One particular solution is a Lorentzian fuzzy sphere, which leads to essentially a fuzzy sphere in the Minkowski space-time. In the commutative limit, this solution leads to an induced metric that does not have a fixed signature, and have a non-constant negative scalar curvature, along with singularities at two fixed latitudes. The singularities are absent in the ii matrix solution which provides a toy model for resolving the singularities of General relativity. We also discussed the two-dimensional fuzzy de Sitter space-time, which has irreducible representations of $su$(1, 1) Lie-algebra in terms of principal, complementary and discrete series. Field theories on such backgrounds result from perturbations about the solutions. The perturbative analysis requires nonstandard Seiberg-Witten maps which depend on the embeddings in the ambient space and the symplectic 2-form. We find interesting properties of the field theories in the commutative limit. For example, stability of the action may require adding symmetry breaking terms to the matrix action, along with a selected range for the matrix coefficients. In the second part of this dissertation, we study higher dimensional fuzzy spaces in a tensorial matrix model, which is a natural generalization to the threedimensional actions and is valid in any number of space-time dimensions. Fourdimensional tensor product NC spaces can be constructed from two-dimensional NC spaces and may provide a setting for doing four-dimensional NC cosmology. Another solution to the tensorial matrix model equations of motion is the Snyder algebra. A crucial step in exploring NC physics is to understand the structure of the quantized space-time in terms of the group representations of the NC algebra. We therefore study the representation theory of the Snyder algebra and implementation of symmetry transformations on the resulted discrete lattices. We find the three-dimensional Snyder space to be associated with two distinct Hilbert spaces, which define two reducible representations of the $su$(2) × $su$(2) algebra. This implies the existence of two distinct lattice structures of Snyder space. The difference between the two representations is evident in the spectra of the position operators, which could only be integers in one case and half integers in the other case. We also show that despite the discrete nature of the Snyder space, continuous translations and rotations can be unitarily implemented on the lattices." @default.
• W2565218974 created "2017-01-06" @default.
• W2565218974 creator A5051780136 @default.
• W2565218974 date "2016-01-01" @default.
• W2565218974 modified "2023-09-24" @default.
• W2565218974 title "Noncommutative spaces from matrix models." @default.
• W2565218974 cites W1510428393 @default.
• W2565218974 cites W1558456204 @default.
• W2565218974 cites W2011550080 @default.
• W2565218974 cites W2014609793 @default.
• W2565218974 cites W2015548884 @default.
• W2565218974 cites W2017302958 @default.
• W2565218974 cites W2026661162 @default.
• W2565218974 cites W2036622549 @default.
• W2565218974 cites W2038472256 @default.
• W2565218974 cites W2041353773 @default.
• W2565218974 cites W2044284037 @default.
• W2565218974 cites W2056822923 @default.
• W2565218974 cites W2071639987 @default.
• W2565218974 cites W2083695524 @default.
• W2565218974 cites W2088787357 @default.
• W2565218974 cites W2090754168 @default.
• W2565218974 cites W2092029373 @default.
• W2565218974 cites W2093311580 @default.
• W2565218974 cites W2095479563 @default.
• W2565218974 cites W2096971640 @default.
• W2565218974 cites W2105192668 @default.
• W2565218974 cites W2111925124 @default.
• W2565218974 cites W2117709364 @default.
• W2565218974 cites W2119740538 @default.
• W2565218974 cites W2161875554 @default.
• W2565218974 cites W2225001832 @default.
• W2565218974 cites W2594363316 @default.
• W2565218974 cites W2950670151 @default.
• W2565218974 cites W3003520087 @default.
• W2565218974 hasPublicationYear "2016" @default.
• W2565218974 type Work @default.
• W2565218974 sameAs 2565218974 @default.
• W2565218974 citedByCount "0" @default.
• W2565218974 crossrefType "dissertation" @default.
• W2565218974 hasAuthorship W2565218974A5051780136 @default.
• W2565218974 hasConcept C104682228 @default.
• W2565218974 hasConcept C106487976 @default.
• W2565218974 hasConcept C134306372 @default.
• W2565218974 hasConcept C159985019 @default.
• W2565218974 hasConcept C183778304 @default.
• W2565218974 hasConcept C192562407 @default.
• W2565218974 hasConcept C202444582 @default.
• W2565218974 hasConcept C2524010 @default.
• W2565218974 hasConcept C33923547 @default.
• W2565218974 hasConcept C68797384 @default.
• W2565218974 hasConcept C79464548 @default.
• W2565218974 hasConceptScore W2565218974C104682228 @default.
• W2565218974 hasConceptScore W2565218974C106487976 @default.
• W2565218974 hasConceptScore W2565218974C134306372 @default.
• W2565218974 hasConceptScore W2565218974C159985019 @default.
• W2565218974 hasConceptScore W2565218974C183778304 @default.
• W2565218974 hasConceptScore W2565218974C192562407 @default.
• W2565218974 hasConceptScore W2565218974C202444582 @default.
• W2565218974 hasConceptScore W2565218974C2524010 @default.
• W2565218974 hasConceptScore W2565218974C33923547 @default.
• W2565218974 hasConceptScore W2565218974C68797384 @default.
• W2565218974 hasConceptScore W2565218974C79464548 @default.
• W2565218974 hasLocation W25652189741 @default.
• W2565218974 hasOpenAccess W2565218974 @default.
• W2565218974 hasPrimaryLocation W25652189741 @default.
• W2565218974 hasRelatedWork W1581807686 @default.
• W2565218974 hasRelatedWork W1586426004 @default.
• W2565218974 hasRelatedWork W1606969880 @default.
• W2565218974 hasRelatedWork W1615857297 @default.
• W2565218974 hasRelatedWork W1898087511 @default.
• W2565218974 hasRelatedWork W2006459736 @default.
• W2565218974 hasRelatedWork W2032656674 @default.
• W2565218974 hasRelatedWork W2040145131 @default.
• W2565218974 hasRelatedWork W2052339150 @default.
• W2565218974 hasRelatedWork W2093534095 @default.
• W2565218974 hasRelatedWork W2100280674 @default.
• W2565218974 hasRelatedWork W2100657516 @default.
• W2565218974 hasRelatedWork W2316389422 @default.
• W2565218974 hasRelatedWork W2983816558 @default.
• W2565218974 hasRelatedWork W3098359374 @default.
• W2565218974 hasRelatedWork W3098635574 @default.
• W2565218974 hasRelatedWork W3101789055 @default.
• W2565218974 hasRelatedWork W3105021281 @default.
• W2565218974 hasRelatedWork W3121398014 @default.
• W2565218974 hasRelatedWork W180631247 @default.
• W2565218974 isParatext "false" @default.
• W2565218974 isRetracted "false" @default.
• W2565218974 magId "2565218974" @default.
• W2565218974 workType "dissertation" @default.