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- In connection with the Schr\"odinger [[../CategoricalGroupRepresentation/|representation]], one defines ...ath>\mathcal{H}_{\alpha}</math>, unitarily equivalent to the Schr\"odinger representation <math>\left\{Q^S_j,P^S_j\right\} ^d_{j =1},</math> <ref name='PCR67'/>. ...4 KB (594 words) - 04:51, 12 September 2020
- ...ein|''Albert Einstein'']] whose [[w:special theory of relativity|''special theory of relativity'']] is the main source of application. Photo taken by [[w:Pau ...'"If it turned out that a system could not be described by a quantum field theory, it would be a sensation; if it turned out it did not obey the rules of qua ...202 KB (29,362 words) - 01:43, 7 November 2020
- ...up'']] is named and [[Albert Einstein]] whose [[special relativity|special theory of relativity]] is the main source of application. Photo taken by [[w:Paul ...'"If it turned out that a system could not be described by a quantum field theory, it would be a sensation; if it turned out it did not obey the rules of qua ...201 KB (29,231 words) - 05:06, 16 December 2020
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- ...]] of the basis elements. This theorem is fundamental in [[representation theory]]. It gives an concrete description of <math>U(\mathfrak{g})</math>; And, *James. E. Humphreys, ''Introduction to Lie algebras and representation theory'', pp.91-93 (detailed) ...1 KB (135 words) - 18:34, 16 November 2014
- ...f orientation-preserving diffeomorphisms of the circle. The representation theory of Virasoro algebra is rich, and has diverse applications in Mathematics an ==Representation Theory== ...2 KB (251 words) - 23:03, 26 July 2017
- ...ilinear form]] ([[w:Cartan-Killing form]]) and is pivotal in the structure theory of representations of Lie algebras. *James Humphreys: ''Introduction to Lie algebras and representation theory'', {{ISBN|9780387900537}} , pp.27,118 ...969 bytes (135 words) - 03:38, 1 May 2017
- ...[[matrix product]] for the [[adjoint representation (Lie algebra)|adjoint representation]] of ''x'' and ''y''. For a [[simple Lie algebra]], the invariant bilinear *J.E.Humphreys, ''Introduction to Lie algebras and representation theory'',{{ISBN|9780387900537}}, pp.21- ...1 KB (187 words) - 03:09, 1 May 2017
- In connection with the Schr\"odinger [[../CategoricalGroupRepresentation/|representation]], one defines ...ath>\mathcal{H}_{\alpha}</math>, unitarily equivalent to the Schr\"odinger representation <math>\left\{Q^S_j,P^S_j\right\} ^d_{j =1},</math> <ref name='PCR67'/>. ...4 KB (594 words) - 04:51, 12 September 2020
- ...ath> is itself free (or admits a Fock [[../CategoricalGroupRepresentation/|representation]]). This basic assumption is expressed in a mathematically precise form by ...eorem in [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantum field theory]]) ...2 KB (295 words) - 06:20, 11 October 2023
- This is a mathematical [[../CategoricalGroupRepresentation/|representation]] of chemical reaction [[../SimilarityAndAnalogousSystemsDynamicAdjointness Bartholomay, A. F.: 1960. Molecular Set Theory. A mathematical representation for chemical reaction mechanisms. ''Bull. Math. Biophys.'' , '''22''' : 285 ...3 KB (381 words) - 16:08, 12 September 2020
- ...tion]] and [[../Momentum/|momentum]] operators, for example) is called a ''representation of the canonical commutation relations (CCR) with <math>d</math> degrees of A standard representation of the CCR is the well-known Schr\"odinger representation <math>\left\{Q^S_j,P_j^S \right\}^d_j=1 </math> which is given by: ...5 KB (694 words) - 04:54, 12 September 2020
- ===Organismic Set Theory and Relational Biology=== ...ells, <math>S_1</math>. Attempts were then made by Rashevsky to expand his theory of organismic sets to organizational models of human societies. Results fro ...3 KB (387 words) - 15:48, 12 September 2020
- ===Organismic Set Theory and Relational Biology=== ...pts were then made by Rashevsky to expand his [[../TheoryOfOrganismicSets/|theory of organismic sets]] to organizational models of human societies. Results f ...3 KB (392 words) - 15:48, 12 September 2020
- ===Groupoid representation theorem=== Any [[../CategoricalGroupRepresentation/|representation]] of a groupoid <math>\grp</math> with [[../HigherDimensionalQuantumAlgebro ...4 KB (624 words) - 12:52, 23 October 2023
- ...ational central charge. In which cases is it possible to write a recursive representation at rational central charge? ...cks are the basic special functions of [[w:two-dimensional conformal field theory]]. They are essential ingredients for computing correlation functions, whic ...5 KB (813 words) - 10:17, 30 October 2024
- ...dia:two-dimensional conformal field theory|two-dimensional conformal field theory]]. Understanding their analytic properties, and computing them efficiently, ...hances of success seem quite good, at least with Zamolodchikov's recursive representation, which is reasonably simple and explicit. ...6 KB (816 words) - 08:18, 28 September 2020
- ...some familiarity with {{W|first-order logic}} is assumed. The goal of this theory is not to prove anything useful or unexpected, but to describe the structur According to this theory, the structure of causal systems is probably that of a {{W|directed acyclic ...6 KB (894 words) - 01:56, 9 July 2024
- ...tyTheories/|quantum field theories]] (AQFT), [[../SR/|general relativity]] theory, unified physical theories, general [[../NewtonianMechanics/|dynamics]] [[. ...math> does not contain any other theories. Valid statements made in a meta-theory are called ''meta-theorems'' or ''metatheorems'' . ...8 KB (1,064 words) - 15:26, 12 September 2020
- ===Natural exponents - algebraic representation=== All elements of a finite subgroup of the multiplicative [[w:en:Unit (ring theory)|group of units]] <math display="inline"> ...7 KB (1,039 words) - 09:55, 6 November 2024
- This is a mathematical [[../CategoricalGroupRepresentation/|representation]] of chemical reaction [[../SimilarityAndAnalogousSystemsDynamicAdjointness Bartholomay, A. F.: 1960. Molecular Set Theory. A mathematical representation for chemical reaction mechanisms. ''Bull. Math. Biophys.'' , '''22''' : 285 ...5 KB (750 words) - 03:15, 13 September 2020
- This is a mathematical [[../CategoricalGroupRepresentation/|representation]] of chemical reaction [[../SimilarityAndAnalogousSystemsDynamicAdjointness Bartholomay, A. F.: 1960. Molecular Set Theory. A mathematical representation for chemical reaction mechanisms. ''Bull. Math. Biophys.'' , '''22''' : 285 ...5 KB (753 words) - 03:15, 13 September 2020
- This is a mathematical [[../CategoricalGroupRepresentation/|representation]] of chemical reaction [[../SimilarityAndAnalogousSystemsDynamicAdjointness AMS MSC: 18D35 ([[../TrivialGroupoid/|category theory]]; homological algebra :: [[../TrivialGroupoid/|categories with structure]] ...6 KB (832 words) - 03:15, 13 September 2020
- ...ive period he developed a categorical [[../CategoricalGroupRepresentation/|representation]] of Metabolic-Repair [[../SimilarityAndAnalogousSystemsDynamicAdjointnessA ...SystemsCategory/|organismic sets]] that he developed over two decades as a representation of both biological and social `organisms'. ...7 KB (1,054 words) - 16:03, 12 September 2020