P-adic analysis and mathematical physics
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1994
|
| Schriftenreihe: | Series on Soviet and East European mathematics
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Vladimirov, Vasilij S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a P-adic analysis and mathematical physics |c V. S. Vladimirov, I. V. Volovich and E. I. Zelenov |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1994 | |
| 300 | |a XVIII, 319 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on Soviet and East European mathematics |v 1 | |
| 650 | 7 | |a Analyse p-adique |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a P-adic analysis | |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a p-adische Analysis |0 (DE-588)4252360-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a p-adische Analysis |0 (DE-588)4252360-6 |D s |
| 689 | 0 | 1 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Volovič, Igorʹ V. |e Verfasser |4 aut | |
| 700 | 1 | |a Zelenov, E. I. |e Verfasser |4 aut | |
| 830 | 0 | |a Series on Soviet and East European mathematics |v 1 |w (DE-604)BV007228526 |9 1 | |
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| 940 | 1 | |n oe | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006445686 | |
Datensatz im Suchindex
| _version_ | 1819689260983255040 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION be
Chapter 1
ANALYSIS ON THE FIELD OF p ADIC NUMBERS
I. The Field of p Adic Numbers 1
1. p adic norm 1
2. p adic numbers 3
3. Non Archimedean topology of the field Qp of p adic 5
numbers
4. Quadratic extensions of the field Qp 9
5. Polar coordinates and circles in the field Qp(i/F) 12
6. Qp and M 13
7. Space Q^ 16
II. Analytic Functions 17
1. Power series 17
2. Analytic functions 20
3. Algebra of analytic functions 22
4. Functions tx, ln(l + x), sin a:, cos a; 23
5. Theorem on inverse function 28
III. Additive and Multiplicative Characters 30
1. Additive characters of the field Qp 30
2. Multiplicative characters of the field Qp 34
3. Multiplicative characters of the field Qp(y/e) 37
IV. Integration Theory 38
1. Invariant measure on the field Qp 38
2. Change of variables in integrals 39
3. Some examples of calculation of integrals 42
4. Integration in Qp 48
V
vi Contents
V. The Gaussian Integrals 54
1. The Gaussian integrals on the circles 57 55
2. The Gaussian integrals on the discs By 65
3. The Gaussian integrals on Qp 67
4. Further properties of the function Ap(a). 68
5. Example 72
6. Analysis of the function S(a, q) 77
VI. Generalized Functions (Distributions) 78
1. Locally constant functions 79
2. Test functions, n = 1 81
3. Generalized functions (distributions), n = 1 84
4. Linear operators in V 86
5. Test and generalized functions (distributions), n 1 89
6. The direct product of generalized functions 90
7. The kernel Theorem 91
8. Adeles 92
VII. Convolution and the Fourier Transformation 94
1. Convolution of generalized functions 94
2. The Fourier transform of test functions 99
3. The Fourier transform of generalized functions 106
4. The space L2 110
5. Multiplication of generalized functions 112
VIII. Homogeneous Generalized Functions 116
1. Homogeneous generalized functions 116
2. The Fourier transform of homogeneous generalized 122
functions and F function
3. Convolution of homogeneous generalized functions and 131
^ function
4. Homogeneous generalized functions of several variables 134
Chapter 2
PSEUDO DIFFERENTIAL OPERATORS
ON THE FIELD OF p ADIC NUMBERS
IX. The Operator D° 143
1. The operator Da,a £ 1 144
2. Operator D~l 147
Contents vii
3. Equation Daip g 154
4. Spectrum of the operator Da in Qp, a 0 156
5. Orthonormal basis of eigenfunctions of the operator Da 158
6. Expansions on eigen functions 165
X. p Adic Schrodinger Operators 167
1. Bounded from below selfadjoint operators 167
2. Compactness in Lp(Qn) 170
3. The operator a* + V 171
4. Operator Da, a 0 in Br 176
5. Operator Da, a 0 in 5r 179
6. Operator Da + V{ x p), a 0 in Qp, p ^ 2 181
7. Operator £ * + Vd^lp), a 0 in Lj (Qp) (p ^ 2) 183
8. The lowest eigen value Ao 184
9. Operator Da + V( x p), a 0 in Qp, p ^ 2 (continuation) 188
10. Example. Potential |z|£, a 0 (p ^ 2) 190
11. Operator Da + V( x p), a 0 outside of a disc (p / 2) 192
12. Justification of the method of Sec. 10.11 195
13. Further results on the spectrum of the operator Da + 198
V( x p)
14. Non stationary p adic Schrodinger equation 200
Chapter 3
p ADIC QUANTUM THEORY
XL p Adic Quantum Mechanics 204
1. Classical mechanics over Qp 205
2. The Weyl representation 207
3. Free particle 210
4. Harmonic oscillator 212
5. Lagrangian formalism 215
6. Feynman path integral 220
7. Quantum mechanics with p adic valued functions 224
XII. Spectral Theory in p Adic Quantum Mechanics 226
1. Harmonic analysis 227
2. Operator theory 229
3. The theorem about dimensions of invariant subspaces 229
4. Study of the eigenfunctions 236
5. Weyl systems and coherent states 241
viii Contents
6. Symplectic group 250
7. Investigation of eigen functions for p = 3 (mod 4) 253
XIII. Weyl Systems. Infinite Dimensional Case 262
1. Weyl algebras 262
2. Positive functionals 263
3. Fock representation 265
4. Equivalence of Z Fock representations 270
XIV. p Adic Strings 272
1. Dual amplitudes 272
2. p Adic amplitudes 275
3. Adelic products 278
4. String action 281
5. Moduli space and theta functions 282
6. Multiloop amplitudes 284
7. Rigid analytic geometry and p adic strings 287
XV. q Analysis (Quantum Groups) and p Adic Analysis 290
1. p Adic and g integrals 290
2. Differential operators 292
3. Spectra of the g deformed oscillator and the p adic model 292
XVI. Stochastic Processes over the Field of p Adic Numbers 293
1. Random maps and Markov processes 293
2. Brownian motion on the p adic line 297
3. Generalized stochastic processes 299
4. Quantum field theory 300
Bibliography 302
References 309
|
| any_adam_object | 1 |
| author | Vladimirov, Vasilij S. Volovič, Igorʹ V. Zelenov, E. I. |
| author_facet | Vladimirov, Vasilij S. Volovič, Igorʹ V. Zelenov, E. I. |
| author_role | aut aut aut |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 512/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009745540 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T13:34:34Z |
| institution | BVB |
| isbn | 9810208804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006445686 |
| oclc_num | 30907657 |
| open_access_boolean | |
| owner | DE-384 DE-12 DE-634 DE-83 DE-11 |
| owner_facet | DE-384 DE-12 DE-634 DE-83 DE-11 |
| physical | XVIII, 319 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on Soviet and East European mathematics |
| series2 | Series on Soviet and East European mathematics |
| spellingShingle | Vladimirov, Vasilij S. Volovič, Igorʹ V. Zelenov, E. I. P-adic analysis and mathematical physics Series on Soviet and East European mathematics Analyse p-adique ram Physique mathématique ram Mathematische Physik Mathematical physics P-adic analysis Quantenmechanik (DE-588)4047989-4 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4252360-6 |
| title | P-adic analysis and mathematical physics |
| title_auth | P-adic analysis and mathematical physics |
| title_exact_search | P-adic analysis and mathematical physics |
| title_full | P-adic analysis and mathematical physics V. S. Vladimirov, I. V. Volovich and E. I. Zelenov |
| title_fullStr | P-adic analysis and mathematical physics V. S. Vladimirov, I. V. Volovich and E. I. Zelenov |
| title_full_unstemmed | P-adic analysis and mathematical physics V. S. Vladimirov, I. V. Volovich and E. I. Zelenov |
| title_short | P-adic analysis and mathematical physics |
| title_sort | p adic analysis and mathematical physics |
| topic | Analyse p-adique ram Physique mathématique ram Mathematische Physik Mathematical physics P-adic analysis Quantenmechanik (DE-588)4047989-4 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| topic_facet | Analyse p-adique Physique mathématique Mathematische Physik Mathematical physics P-adic analysis Quantenmechanik p-adische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006445686&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007228526 |
| work_keys_str_mv | AT vladimirovvasilijs padicanalysisandmathematicalphysics AT volovicigorʹv padicanalysisandmathematicalphysics AT zelenovei padicanalysisandmathematicalphysics |