Lie algebras and quantum mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Benjamin
1970
|
| Series: | Mathematics lecture note series
46 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 320 S. |
| ISBN: | 0805339426 0805339434 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lie algebras and quantum mechanics |c Robert Hermann |
| 264 | 1 | |a New York, NY |b Benjamin |c 1970 | |
| 300 | |a XVI, 320 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics lecture note series |v 46 | |
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| 650 | 4 | |a Lie, Algèbres de | |
| 650 | 7 | |a Lie-algebra's |2 gtt | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 7 | |a Toepassingen |2 gtt | |
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| 650 | 4 | |a Quantum field theory | |
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Record in the Search Index
| _version_ | 1805070251929370624 |
|---|---|
| adam_text |
CONTENTS
Page
I. THE LIE ALGEBRA APPROACH TO CLASSICAL
AND QUANTUM MECHANICS 1
1. States and Observables 2
2. Lie Algebra Approach . 7
3. States and Observables in
Quantum Mechanics 11
4. Relations Between Classical
and Quantum Mechanics 18
5. Classical and Quantum Systems
With Constraints 22
Bibliography 27
II. QUANTIZATION OP CONSTRAINED SYSTEMS . 29
1. Introduction 29
2. The Poisson Bracket Defined by
a Closed Differential Form 31
3. Behavior of Poisson Bracket
Under Mappings 36
4. Poisson Bracket for Systems
With Constraints 45
5. Poisson Brackets Subject
to Constraints 48
6. Lie Algebra Structures on
Quotients of Algebras 53
7. Constraint Problems in Particle
Quantum Mechanics on a
Riemannian Manifold 60
Bibliography 71
xiii
xiv CONTENTS
III. CURRENT ALGEBRAS AND GAUGE GROUPS 73
1. Introduction 73
2. The Gauge Group of a Vector
Bundle, Its Lie Algebra, and
The Algebra of Currents 75
3 Some "Non Trivial" Represen¬
tations 83
4. An Algebraic Construction of
Certain Representations of
The Algebra of Currents 91
Bibliography 97
IV. REPRESENTATIONS OF THE ALGEBRA OF
CURRENTS, AND ALGEBRAIC CONSTRUCTION
OF SCHWINGER TERMS 99
1. Introduction 99
2. Deformation of The Current
Algebra Commutation Relations
and Schwinger Terms 104
3. A Systematic Method for Finding
the Sufficient Conditions 110
4. Are The Cocycles Cohomologous
to Zero? 118
5. Normalization of Cocycles 127
6. Representations of The Algebra
of Currents With Schwinger
Terms 135
7. Vanishing of Certain Cohomology
Products 138
Bibliography 144
V. A DIFFERENTIAL GEOMETRIC FORMALISM FOR
MULTIPLE INTEGRAL VARIATIONAL PROBLEMS;
APPLICATIONS TO QUANTUM FIELD THEORY . 145
1. Introduction 145
CONTENTS xv
2. An Extended Variational
Formalism 146
3. The Euler Equations of The
Extremals 149
4. Noether's Theorem and The
Goldberger Treiman Relation 157
5. A Poisson Bracket Formalism
Associated With An Arbitrary
Differential Form 167
6. A Hamiltonian Formalism For
Regular Variational Problems . 178
Bibliography 189
VI. QUANTIZATION OF CLASSICAL FIELD THEORIES
USING DIFFERENTIAL FORMS 191
1. Introduction 191
2. A Poisson Bracket on The Space
of Integral Maps . 195
3. Study of The Hamiltonian
Formalism 205
4. Calculation of Currents 211
Bibliography 215
VII. PROPAGATORS AND SCATTERING 217
1. Introduction 217
2. Propagators Associated With
Second Order Differential
Operators 219
3. Extension of the Propagators . 225
4. Equations for Perturbed
Propagators 230
5. Scattering 235
Bibliography 245
xvi CONTENTS
VIII. A GEOMETRIC VIEWPOINT IN QUANTUM
FIELD THEORY 247
1. Introduction 247
2. Poisson Bracket and Quanti¬
zation 250
3. The Poisson Bracket on The Space
of Solutions of Partial Differ¬
ential Equations 254
4. The Poisson Bracket Defined by
A Variational Problem 261
Bibliography 269
IX. SCATTERING THEORY IN GENERALIZED
FUNCTION SPACES AND ON MANIFOLDS 271
1. Introduction 271
2. Hilbert and Dirac Spaces 272
3. In and Out State, and The
Lippman Schwinger Equation 277
4. The Lippman Schwinger Equation
in Terms of Propagators 284
5. Scattering Theory on Riemannian
Manifolds 291
6. Scattering by a Central
Potential 298
7. The Scattering Map 303
8. Differentiability Properties . 309
Bibliography 320 |
| any_adam_object | 1 |
| author | Hermann, Robert 1931-2020 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 SK 950 |
| ctrlnum | (OCoLC)99193 (DE-599)BVBBV005687809 |
| dewey-full | 530.14/3/0151289 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/3/0151289 |
| dewey-search | 530.14/3/0151289 |
| dewey-sort | 3530.14 13 6151289 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV005687809 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T04:18:58Z |
| institution | BVB |
| isbn | 0805339426 0805339434 |
| language | English |
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| physical | XVI, 320 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Benjamin |
| record_format | marc |
| series | Mathematics lecture note series |
| series2 | Mathematics lecture note series |
| spelling | Hermann, Robert 1931-2020 Verfasser (DE-588)102586333X aut Lie algebras and quantum mechanics Robert Hermann New York, NY Benjamin 1970 XVI, 320 S. txt rdacontent n rdamedia nc rdacarrier Mathematics lecture note series 46 Kwantumveldentheorie gtt Lie, Algèbres de Lie-algebra's gtt Théorie quantique Toepassingen gtt Lie algebras Quantum field theory Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Lie-Algebra (DE-588)4130355-6 s DE-604 Quantenmechanik (DE-588)4047989-4 s Mathematics lecture note series 46 (DE-604)BV001899001 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003552631&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hermann, Robert 1931-2020 Lie algebras and quantum mechanics Mathematics lecture note series Kwantumveldentheorie gtt Lie, Algèbres de Lie-algebra's gtt Théorie quantique Toepassingen gtt Lie algebras Quantum field theory Lie-Algebra (DE-588)4130355-6 gnd Quantenmechanik (DE-588)4047989-4 gnd Quantentheorie (DE-588)4047992-4 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4047989-4 (DE-588)4047992-4 |
| title | Lie algebras and quantum mechanics |
| title_auth | Lie algebras and quantum mechanics |
| title_exact_search | Lie algebras and quantum mechanics |
| title_full | Lie algebras and quantum mechanics Robert Hermann |
| title_fullStr | Lie algebras and quantum mechanics Robert Hermann |
| title_full_unstemmed | Lie algebras and quantum mechanics Robert Hermann |
| title_short | Lie algebras and quantum mechanics |
| title_sort | lie algebras and quantum mechanics |
| topic | Kwantumveldentheorie gtt Lie, Algèbres de Lie-algebra's gtt Théorie quantique Toepassingen gtt Lie algebras Quantum field theory Lie-Algebra (DE-588)4130355-6 gnd Quantenmechanik (DE-588)4047989-4 gnd Quantentheorie (DE-588)4047992-4 gnd |
| topic_facet | Kwantumveldentheorie Lie, Algèbres de Lie-algebra's Théorie quantique Toepassingen Lie algebras Quantum field theory Lie-Algebra Quantenmechanik Quantentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003552631&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT hermannrobert liealgebrasandquantummechanics |