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- ==Quantum operator algebras(QOA)== defined as the algebras of [[../QuantumSpinNetworkFunctor2/|observable]] [[../QuantumOperatorAlgebr ...22 KB (3,360 words) - 03:41, 13 September 2020
- ==Topical References for Operator Algebras in Theoretical Physics and Algebraic Quantum Field Theories (AQFT):== Banica, T. (1998). Hopf algebras and subfactors associated to vertex models. ...69 KB (9,396 words) - 14:50, 20 October 2023
- This is a topic entry that introduces [[../Groupoid/|quantum operator algebras]] and presents concisely the important ...um operator algebras'' (QOA) in quantum field theories are defined as the algebras of [[../QuantumSpinNetworkFunctor2/|observable]] [[../QuantumOperatorAlgebr ...22 KB (3,397 words) - 03:42, 13 September 2020
- ===Bibliography for Operator Algebras in Mathematical Physics and Algebraic Quantum Field Theories (AQFT):=== Banica, T. (1998). Hopf algebras and subfactors associated to vertex models. ...69 KB (9,405 words) - 14:50, 20 October 2023
- Tensor structures arising from affine Lie algebras. ''Infinite dimensional Lie algebras and groups'' , (Ka\v c, ...30 KB (4,190 words) - 14:51, 20 October 2023
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- ===Examples of nuclear C*-algebras=== *All commutative C*-algebras and all finite-dimensional C*-algebras ...3 KB (409 words) - 15:47, 12 September 2020
- #Alg(1),(algebras with one unary [[../QuantumSpinNetworkFunctor2/|operator]]) #Alg(S2),(binary algebras) ...3 KB (248 words) - 16:10, 12 September 2020
- ...lgebra. Actually, quantum groups are constructed by employing certain Hopf algebras as "building blocks"; and in the case of finite [[../TrivialGroupoid/|group ...d [[../CoIntersections/|algebraic]] properties distinct from those of Hopf algebras. ...7 KB (982 words) - 15:55, 12 September 2020
- ...fact ''non-commutative'' [[../TrivialGroupoid/|algebraic structures]], or algebras of [[../Bijective/|functions]]). ...ialGroupoid/|groups]]; other examples are non-commutative <math>C^*</math>-algebras of [[../QuantumOperatorAlgebra4/|operators]] defined on [[../NormInducedByI ...3 KB (399 words) - 15:46, 12 September 2020
- ===Lie algebras in quantum theories=== ...duct/|vector space]]''. It is also perhaps this feature that makes the Lie algebras somewhat compatible, or consistent, with [[../LQG2/|quantum logics]] that a ...4 KB (496 words) - 08:36, 11 March 2023
- ...up/|Hopf algebra]]'' or coalgebra. Actually, the duals of commutative Hopf algebras obtained by Fourier transformation are finite [[../CompactQuantumGroups/|co ...d [[../CoIntersections/|algebraic]] properties distinct from those of Hopf algebras. ...7 KB (972 words) - 15:35, 12 September 2020
- ...ged Hilbert spaces]] <math>\Re_G</math> of quantum states and [[../Quantum Operator Algebra 5|quantum operators]] on the [[../Norm Induced By Inner Product|Hil ...Hilbert space or a rigged Hilbert space of quantum states and [[../Quantum Operator Algebra 4|operators]] acting on ...3 KB (424 words) - 20:08, 9 September 2020
- ===C*- and von Neumann algebras: Quantum operator algebra in quantum theories=== C*-algebra has evolved as a key [[../PreciseIdea/|concept]] in Quantum Operator Algebra after the introduction of the von Neumann algebra for the mathemati ...11 KB (1,607 words) - 05:03, 12 September 2020
- Hamiltonian operator. Some of the early formulations of [[../QuantumParadox/|quantum mechanics]] ...ors]], (such as the [[../HamiltonianOperator3/|Hamiltonian operators]]) or algebras (such as Lie or Poisson (brackets)), with the classical ones being in the r ...4 KB (656 words) - 03:13, 13 September 2020
- #[[../PoissonRing/|Poisson algebras]], [[../QuantizationMethods/|quantization methods]] and [[../Algebroids/|Ha #Logic lattice algebras and many-valued (MV) logic algebras ...8 KB (1,052 words) - 16:13, 12 September 2020
- ...ationInQuantumGravityTheories/|quantum field theories]] are defined as the algebras of observable operators, and as such, they are also related to the von Neum ...encyclopedia/CategoricalGroupRepresentation.html} of Banach <math>*</math>-algebras} (that are defined on Hilbert spaces) are closely related to C* -algebra re ...9 KB (1,262 words) - 03:39, 13 September 2020
- #[[../MetaTheorems/|meta-theorems]] #Duality between spaces and algebras ...*-algebras, or <math>*</math>-algebras, [[../CoordinateSpace/|von Neumann algebras]], ...10 KB (1,003 words) - 12:39, 6 May 2023
- \subsubsection{Jordan-Banach, Jordan-Lie, and Jordan-Banach-Lie algebras: Definitions and Relationships to Poisson and C*-algebras} ...10 KB (1,513 words) - 15:39, 12 September 2020
- ...gebroid3/|supersymmetry superalgebras]] (or graded `[[../BilinearMap/|Lie' algebras]]), see, for example, their full development in a recent QFT textbook <ref Operator Algebras}, Birkh\"auser, Boston--Basel--Berlin (2003). ...4 KB (535 words) - 04:56, 12 September 2020
- ...ey do not cover the entire field. In the most general sense, ''categorical algebras'' -- as introduced by Mac Lane in 1965 -- can be described as the study of ...uced above can be still further extended by introducing ''supercategorical algebras as interpretations of [[../ETACAxioms/|ETAS]]'', as explained next. ...5 KB (674 words) - 03:14, 13 September 2020
- ...and 2-Lie algebras, as well as their categories of 2-Lie groups and 2-Lie algebras. ...as such as: categorical logics, [[../LM_nLogicAlgebra/|many-valued logic]] algebras, model theory and many specific [[../CosmologicalConstant/|fields]] of math ...8 KB (1,064 words) - 15:26, 12 September 2020
- #[[../PoissonRing/|Poisson algebras]], [[../QuantizationMethods/|quantization methods]] and [[../HamiltonianAlg #Logic Lattice algebras or Many-Valued (MV) Logic algebras ...10 KB (1,384 words) - 16:14, 12 September 2020
- ...] <math>[X,P] = i\hbar I~,</math> where the [[../QuantumParticle/|identity operator]] <math>I</math> ...math>\mathbf{x}</math> with its conjugate [[../QuantumSpinNetworkFunctor2/|operator]] <math>\mathbf{p}</math> is simply <math>[\mathbf{x}, \mathbf{p}] = i</mat ...8 KB (1,066 words) - 08:36, 11 March 2023
- ...es beyond canonical quantization revolve around using ''\htmladdnormallink{operator'' {http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html} kerne the following family of operator kernels ...6 KB (1,029 words) - 16:21, 12 September 2020
- ..../LQG2/|quantum gravity]] #[[../LQG2/|quantum logics]], including LM-logic algebras #Quantum Operator Algebra (QOA) in [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantu ...5 KB (444 words) - 14:10, 6 May 2023