Ten physical applications of spectral zeta functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1995
|
| Schriftenreihe: | [Lecture notes in physics / M]
35 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 224 S. graph. Darst. |
| ISBN: | 3540602305 |
Internformat
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| 100 | 1 | |a Elizalde, Emilio |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ten physical applications of spectral zeta functions |c Emilio Elizalde |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
| 300 | |a XII, 224 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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| adam_text | EMILIO ELIZALDE
TEN PHYSICAL APPLICATIONS
OF SPECTRAL ZETA FUNCTIONS
SPRINGER
CONTENTS
INTRODUCTIO
N AN
D OUTLOO
K 1
1.1 ZETA FUNCTIONS 1
1.1.1 THE RIEMANN ZETA FUNCTION 1
1.1.2 THE HURWITZ ZETA FUNCTION 3
1.1.3 THE EPSTEIN ZETA FUNCTION 4
1.1.4 A WORD ON RELATED BIBLIOGRAPHY 6
1.2 ZETA FUNCTION REGULARIZATION 6
1.2.1 THE ZETA FUNCTION OF A DIFFERENTIAL OPERATOR 6
1.2.2 REGULARIZATION OF TH
E VACUUM ENERGY 7
1.2.3 REGULARIZATION OF ONE-LOOP GRAPHS 8
1.3 EXAMPLES AND A COMPARISON WITH OTHER PROCEDURES 9
1.3.1 SOME EXPLICIT EXAMPLES 9
1.3.2 COMPARISON WITH OTHER REGULARIZATION METHODS 11
1.3.3 A WORD OF WARNING 14
1.4 PRESENT DEVELOPMENTS AND A POINT ON RIGOR 15
1.4.1 CALCULATION OF HEAT-KERNEL COEFFICIENTS ,1
5
1.4.2 DETERMINANT OF TH
E LAPLACIAN 17
1.4.3 PROPER DEFINITION OF TH
E ZETA FUNCTION OF A PARTIA
L
DIFFERENTIAL OPERATOR 19
MATHEMATICA
L FORMULA
S INVOLVIN
G TH
E
DIFFEREN
T ZETA FUNCTION
S 21
2.1 A SIMPLE RECURRENCE FOR TH
E HIGHER DERIVATIVES OF TH
E HURWITZ
ZETA FUNCTION 21
2.2 THE ZETA-FUNCTION REGULARIZATION THEOREM . . ..
. 28
2.2.1 THE THEOREM (SPECIAL FORM) 30
2.3 IMMEDIATE APPLICATION OF TH
E THEOREM 38
2.4 EXPRESSIONS FOR MULTI-SERIES ON COMBINATIONS INVOLVING
ARBITRARY CONSTANTS AND EXPONENTS 41
X
3 A TREATMEN
T O
F TH
E NON-POLYNOMIA
L CONTRI
-
BUTIONS
: APPLICATIO
N T
O CALCULAT
E PARTITIO
N
FUNCTION
S O
F STRING
S AN
D MEMBRANE
S 5
1
3.1 DEALING WITH TH
E NON-POLYNOMICAL TER
M
AER
51
3.1.1 PROOF OF ASYMPTOTICIT
Y OF TH
E SERIES 53
3.1.2 TH
E REMAINDER TER
M AND TH
E POISSON RESUMMATIO
N
FORMULA 58
3.2 NUMERICAL ESTIMATE
S OF TH
E REMAINDER . 60
3.3 APPLICATION: SUMMATIO
N OF TH
E STRING PARTITIO
N FUNCTION FOR
DIFFERENT RANGES OF TH
E TEMPERATUR
E 64
4 ANALYTICA
L AN
D NUMERICA
L STUD
Y O
F INHOMO
-
GENEOU
S EPSTEI
N AN
D EPSTEIN-HURWIT
Z ZET
A
FUNCTION
S 7
3
4.1 EXPLICIT ANALYTICAL CONTINUATION OF INHOMOGENEOUS
EPSTEIN ZETA FUNCTIONS 74
4.1.1 TH
E PARTICULA
R CASE OF TH
E BASIC ONE-DIMENSIONAL
EPSTEIN-HURWIT
Z SERIES 76
4.1.2 TH
E HOMOGENEOUS CASE: CHOWLA-SELBERG S FORMULA ..
. 79
4.1.3 DERIVATION OF TH
E GENERAL FORMULA 80
4.2 NUMERICAL ANALYSIS OF TH
E INHOMOGENEOUS GENERALIZED
EPSTEIN-HURWITZ ZET
A FUNCTION 84
4.2.1 ASYMPTOTI
C EXPANSIONS OF TH
E FUNCTION AN
D IT
S
DERIVATIVES WITH RESPECT T
O TH
E VARIABLE AND
PARAMETER
S 85
5 PHYSICA
L APPLICATION
: TH
E CASIMI
R EFFEC
T 9
7
5.1 ESSENTIALS OF TH
E CASIMIR EFFECT 97
5.1.1 TH
E CLASSICAL CASIMIR EFFECT . . 97
5.1.2 CONNECTION WITH TH
E VAN DER WAALS FORCES AND
TH
E LONDON THEORY 98
5.1.3 TH
E SPECIFIC CONTRIBUTION OF CASIMIR AND POLDER:
RETARDE
D VAN DER WAALS FORCES 99
5.1.4 TH
E LIFSCHITZ THEORY 101
5.2 EXPERIMENTA
L VERIFICATION 103
5.2.1 TH
E FIRST DIRECT EXPERIMENTS
: ABRIKOSOVA & DERYAGIN,
KITCHENER & PROSSER, SPARNAAY ET AL 103
XI
5.2.2 TH
E EXPERIMENT OF TABOR AND WINTERTON
: TRANSITIO
N
FROM NORMAL T
O RETARDE
D VAN DER WAALS FORCES 103
5.2.3 TH
E EXPERIMENT OF SABISKI AND ANDERSON 104
5.2.4 A CONTEMPORAR
Y EXPERIMENT 105
5.3 TH
E CASIMIR EFFECT IN QUANTU
M FIELD THEORY 106
5.3.1 TH
E LOCAL FORMULATION OF TH
E CASIMIR EFFECT 106
5.3.2 TH
E MYSTER
Y OF THE CASIMI
R EFFECT 107
5.3.3 TH
E CONCEPT OF TH
E VACUUM ENERGY 108
5.3.4 TH
E EXPLICIT, REGULARIZED DEFINITION
OF TH
E CASIMIR ENERGY 110
5.3.5 DEFINITION OF TH
E CASIMIR ENERGY DENSITY
AND IT
S RELATION WITH TH
E VACUUM ENERGY IL
L
5.4 A VERY SIMPLE COMPUTATIO
N OF TH
E CASIMIR EFFECT 113
5.4.1 TH
E CASIMIR EFFECT FOR A FREE MASSLESS SCALAR FIELD IN
S
1
X
R
D
AND IN T
2
X R
2
SPACETIMES 114
. 5.4.2 TH
E CASE OF A MASSLESS SCALAR FIELD BETWEEN
P
PERPENDICULAR PAIRS OF PARALLEL WALLS WITH
DIRICHLET BOUNDAR
Y CONDITIONS 117
5.4.3 MASSLESS SCALAR FIELD WITH PERIODIC AND NEUMANN
BOUNDAR
Y CONDITIONS, AND ELECTROMAGNETIC FIELD 122
FOU
R PHYSICA
L APPLICATION
S O
F TH
E
INHOMOGENEOU
S GENERALIZE
D
EPSTEIN-HURWIT
Z ZET
A FUNCTION
S !L2
9
6.1
V
APPLICATION: TH
E CASIMIR ENERGY OVER RIEMANN SURFACES ....,
130
6.2 APPLICATION: KALUZA-KLEI
N MODEL WITH SPHERICAL
COMPACTIFICATION
.
136
6.3 CRITICAL BEHAVIOR OF A FIELD THEORY A
T NON-ZERO TEMPERATUR
E . .14
3
6.4 APPLICATION T
O QUANTIZING THROUG
H TH
E WHEELER-D
E WIT
T
EQUATION 146
6.4.1 EXPLICIT ZETA-FUNCTION CALCULATION OF TH
E ESSENTIAL
DETERMINAN
T AND EXTREM
A OF TH
E POTENTIA
L 147
6.4.2 AN ALTERNATIV
E TREATMEN
T BY MEANS OF EISENSTEIN SERIES 153
XII
7 MISCELLANEOU
S APPLICATION
S COMBININ
G ZET
A
WIT
H OTHE
R REGULARIZATIO
N PROCEDURE
S 15
7
7.1 RELATION BETWEEN TH
E GENERALIZED PAULI-VILLAR
S AND TH
E
COVARIANT REGULARIZATIONS 157
7.2 TH
E CASIMIR ENERGY CORRESPONDING T
O A PIECEWISE
UNIFORM STRING 163
7.2.1 TH
E ZERO TEMPERATUR
E THEORY 166
7.2.2 REGULARIZED CASIMIR ENERGY AND NUMERICAL RESULTS . . . 169
7.2.3 TH
E FINITE TEMPERATUR
E THEORY 173
8 APPLICATION
S T
O GRAVITY
, STRING
S
AN
D P-BRANE
S 17
9
8.1 APPLICATION T
O SPONTANEOUS COMPACTIFICATION
IN TWO-DIMENSIONAL QUANTU
M GRAVITY 180
8.2 APPLICATION T
O TH
E STUD
Y OF TH
E STABILIT
Y
OF TH
E RIGID MEMBRANE . 183
8.2.1 CALCULATION OF TH
E POTENTIA
L 184
8.2.2 TH
E LIMIT OF LARGE SPACETIME DIMENSIONALITY 185
8.2.3 A SADDLE POINT ANALYSIS . 187
8.2.4 EXPLICIT EXPRESSIONS FOR TH
E ZETA-FUNCTION
REGULARIZATION OF TH
E EFFECTIVE POTENTIA
L 188
8.2.5 DISCUSSION OF TH
E GENERAL CASE 190
9 LAS
T APPLICATION
: TOPOLOGICA
L SYMMETR
Y
BREAKIN
G I
N SELF-INTERACTIN
G THEORIE
S 19
3
9.1 GENERAL CONSIDERATIONS 193
9.2 TH
E ONE-LOOP EFFECTIVE POTENTIA
L FOR TH
E SELF-INTERACTING THEOR
Y 195
9.3 TH
E ONE-LOOP TOPOLOGICAL MASS 199
9.4 RENORMALIZATION OF TH
E THEORY * 202
9.5 SYMMETRY BREAKING MECHANISM FOR A MASSLESS SCALAR FIELD . . . 204
REFERENCE
S
20
9
INDE
X 22
1
|
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| author_facet | Elizalde, Emilio |
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| ctrlnum | (OCoLC)246855577 (DE-599)BVBBV010332077 |
| discipline | Physik Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:40Z |
| institution | BVB |
| isbn | 3540602305 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006876670 |
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| physical | XII, 224 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
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| series2 | [Lecture notes in physics / M] |
| spelling | Elizalde, Emilio Verfasser aut Ten physical applications of spectral zeta functions Emilio Elizalde Berlin [u.a.] Springer 1995 XII, 224 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Lecture notes in physics / M] 35 Zetafunktion (DE-588)4190764-4 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s DE-604 Mathematische Physik (DE-588)4037952-8 s M] [Lecture notes in physics 35 (DE-604)BV021852221 35 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006876670&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elizalde, Emilio Ten physical applications of spectral zeta functions Zetafunktion (DE-588)4190764-4 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4190764-4 (DE-588)4037952-8 |
| title | Ten physical applications of spectral zeta functions |
| title_auth | Ten physical applications of spectral zeta functions |
| title_exact_search | Ten physical applications of spectral zeta functions |
| title_full | Ten physical applications of spectral zeta functions Emilio Elizalde |
| title_fullStr | Ten physical applications of spectral zeta functions Emilio Elizalde |
| title_full_unstemmed | Ten physical applications of spectral zeta functions Emilio Elizalde |
| title_short | Ten physical applications of spectral zeta functions |
| title_sort | ten physical applications of spectral zeta functions |
| topic | Zetafunktion (DE-588)4190764-4 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Zetafunktion Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006876670&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021852221 |
| work_keys_str_mv | AT elizaldeemilio tenphysicalapplicationsofspectralzetafunctions |