| Description |
1 online resource (x, 373 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
De Gruyter studies in mathematics ; 22
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De Gruyter studies in mathematics ; 22.
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| Bibliography |
Includes bibliographical references and index. |
| Contents |
""Preface""; ""I Elementary Notions of Noncommutative Analysis""; ""1 Some Situations where Functions of Noncommuting Operators Arise""; ""1.1 Nonautonomous Linear Differential Equations of First Order. T-Exponentials""; ""1.2 Operators of Quantum Mechanics. Creation and Annihilation Operators""; ""1.3 Differential and Integral Operators""; ""1.4 Problems of Perturbation Theory""; ""1.5 Multiplication Law in Lie Groups""; ""1.6 Eigenfunctions and Eigenvalues of the Quantum Oscillator""; ""1.7 T-Exponentials, Trotter Formulas, and Path Integrals"" |
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""2 Functions of Noncommuting Operators: the Construction and Main Properties""""2.1 Motivations""; ""2.2 The Definition and the Uniqueness Theorem""; ""2.3 Basic Properties""; ""2.4 Tempered Symbols and Generators of Tempered Groups""; ""2.5 The Influence of the Symbol Classes on the Properties of Generators""; ""2.6 Weyl Quantization""; ""3 Noncommutative Differential Calculus""; ""3.1 The Derivation Formula""; ""3.2 The Daletskii-Krein Formula""; ""3.3 Higher-Order Expansions""; ""3.4 Permutation of Feynman Indices""; ""3.5 The Composite Function Formula"" |
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""4 The Campbell-Hausdorff Theorem and Dynkin�s Formula""""4.1 Statement of the Problem""; ""4.2 The Commutation Operation""; ""4.3 A Closed Formula for In (eBeA)""; ""4.4 A Closed Formula for the Logarithm of a T-Exponential""; ""5 Summary: Rules of “Operator Arithmetic� and Some Standard Techniques""; ""5.1 Notation""; ""5.2 Rules""; ""5.3 Standard Techniques""; ""II Method of Ordered Representation""; ""1 Ordered Representation: Definition and Main Property""; ""1.1 Wick Normal Form""; ""1.2 Ordered Representation and Theorem on Products""; ""1.3 Reduction to Normal Form"" |
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""2 Some Examples""""2.1 Functions of the Operators x and â€? ihÓ?/dÓ?""; ""2.2 Perturbed Heisenberg Relations""; ""2.3 Examples of Nonlinear Commutation Relations""; ""2.4 Lie Commutation Relations""; ""2.5 Graded Lie Algebras""; ""3 Evaluation of the Ordered Representation Operators""; ""3.1 Equations for the Ordered Representation Operators""; ""3.2 How to Obtain the Solution""; ""3.3 Semilinear Commutation Relations""; ""4 The Jacobi Condition and Poincaré-Birkhoff-Witt Theorem""; ""4.1 Ordered Representation of Relation Systems and the Jacobi Condition"" |
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""4.2 The Poincaré-Birkhoff-Witt Theorem""""4.3 Verification of the Jacobi Condition: Two Examples""; ""5 The Ordered Representations, Jacobi Condition, and the Yang-Baxter Equation""; ""6 Representations of Lie Groups and Functions of Their Generators""; ""6.1 Conditions on the Representation""; ""6.2 Hilbert Scales""; ""6.3 Symbol Spaces""; ""6.4 Symbol Classes: More Suitable for Asymptotic Problems""; ""III Noncommutative Analysis and Differential Equations""; ""1 Preliminaries""; ""1.1 Heaviside�s Operator Method for Differential Equations with Constant Coefficients"" |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Geometry, Differential.
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Geometry, Differential. |
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Noncommutative algebras.
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Noncommutative algebras. |
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Mathematical physics.
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Mathematical physics. |
| Genre/Form |
Electronic books.
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| Added Author |
Shatalov, V. E. (Viktor Evgenʹevich)
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Sternin, B. I͡U.
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| Other Form: |
Print version: 9781306275262 |
| ISBN |
9783110813548 (electronic book) |
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3110813548 (electronic book) |
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1306275261 (e-book) |
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9781306275262 (e-book) |
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3110146320 |
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9783110146325 |
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