Deformations of space-time symmetries: gravity, group-valued momenta and non-commutative fields
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
[2021]
|
| Schriftenreihe: | Lecture Notes in Physics
Volume 986 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis |
| Beschreibung: | XIII, 191 Seiten Illustrationen 23.5 cm x 15.5 cm |
| ISBN: | 9783662630952 |
Internformat
MARC
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| 100 | 1 | |a Arzano, Michele |e Verfasser |0 (DE-588)1237698480 |4 aut | |
| 245 | 1 | 0 | |a Deformations of space-time symmetries |b gravity, group-valued momenta and non-commutative fields |c Michele Arzano, Jerzy Kowalski-Glikman |
| 264 | 1 | |a Berlin |b Springer |c [2021] | |
| 300 | |a XIII, 191 Seiten |b Illustrationen |c 23.5 cm x 15.5 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture Notes in Physics |v Volume 986 | |
| 650 | 0 | 7 | |a Fundamentalgruppe |0 (DE-588)4155638-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Raum-Zeit |0 (DE-588)4302626-6 |2 gnd |9 rswk-swf |
| 653 | |a Discrete Spacetime Symmetries | ||
| 653 | |a Gravity in 2+1 Dimensions | ||
| 653 | |a Hopf Algebras | ||
| 653 | |a Quantum Gravity Phenomenology | ||
| 653 | |a Quantum-deformed Symmetries | ||
| 653 | |a Relativistic Particles and Fields | ||
| 689 | 0 | 0 | |a Raum-Zeit |0 (DE-588)4302626-6 |D s |
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
PART
I
FROM
GRAVITY
TO
CURVED
MOMENTUM
SPACE
AND
NON-COMMUTATIVE
SPACETIME
1
INVITATION:
GRAVITY,
POINT
PARTICLES,
AND
GROUP-VALUED
MOMENTA
.
3
1.1
INTRODUCTION
.
3
1.2
2+1
GRAVITY,
PARTICLES,
AND
CURVATURE
OF
MOMENTUM
SPACE
.
7
REFERENCES
.
13
2
GRAVITY
IN
2+1
DIMENSIONS
AS
A
CHEM-SIMONS
THEORY
.
15
2.1
PURE
GRAVITY
IN
2+1
DIMENSIONS
.
15
2.2
PARTICLE
COUPLING
.
21
2.3
EFFECTIVE
DEFORMED
SINGLE
PARTICLE
ACTION
.
26
2.4
PROPERTIES
OF
THE
DEFORMED
LAGRANGIAN
.
31
2.5
THE
CASE
OF
MANY
PARTICLES
.
34
2.6
K-CARROLLIAN
DEFORMATION
.
37
2.7
DEFORMED
SPACETIME
SYMMETRIES
OF
2+1
QUANTUM
GRAVITY
.
42
REFERENCES
.
47
3
GRAVITY
IN
3+1
DIMENSIONS,
PARTICLES,
AND
TOPOLOGICAL
LIMIT
.
49
3.1
FROM
3+1
TO
2+1
DIMENSIONS
VIA
DIMENSIONAL
REDUCTION
.
49
3.2
GRAVITY
AS
A
CONSTRAINED
BF
THEORY
.
52
3.3
PARTICLES
COUPLED
TO
GRAVITY
.
59
3.4
EQUATIONS
FOR
THE
PARTICLE-GRAVITY
SYSTEM
.
62
3.5
THE
TOPOLOGICAL
VACUUM
.
65
3.6
EFFECTIVE
DEFORMED
PARTICLE
.
67
REFERENCES
.
70
PART
II
DEFORMED
PARTICLES
AND
THEIR
SYMMETRIES
4
DEFORMED
CLASSICAL
PARTICLES:
PHASE
SPACE
AND
KINEMATICS
.
73
4.1
FROM
SYMPLECTIC
MANIFOLDS
TO
POISSON-LIE
GROUPS
.
73
4.1.1
FROM
SYMPLECTIC
MANIFOLDS
TO
POISSON
MANIFOLDS
.
74
4.1.2
LIE
GROUPS
AS
PHASE
SPACES
.
75
XII
CONTENTS
4.1.3
DEFORMING
PHASE
SPACES:
THE
CLASSICAL
DOUBLES
.
82
4.2
RELATIVISTIC
SPINLESS
PARTICLE:
FLAT
MOMENTUM
SPACE
.
84
4.3
DEFORMING
MOMENTUM
SPACE
TO
THE
AN
(NJ
GROUP
.
86
4.4
DEFORMING
MOMENTUM
SPACE
TO
THE
GROUP
SL(2,R)
.
91
4.5
RELATIVISTIC
HAMILTONIAN
MECHANICS
WITH
CURVED
MOMENTUM
SPACE
.
95
4.6
ZC-POINCARE
PARTICLE
-
THE
FREE
CASE
.
101
4.7
THE
SYSTEM
OF
TWO
ZC-DEFORMED
PARTICLES
.
107
4.7.1
TRANSLATIONS
.
109
4.7.2
LORENTZ
SYMMETRY
.
ILL
REFERENCES
.
114
5
HOPF
ALGEBRA
RELATIVISTIC
SYMMETRIES:
THE
ZC-POINCARE
ALGEBRA.
.
115
5.1
HOPF
ALGEBRA
STRUCTURES
IN
QUANTUM
THEORY
.
115
5.2
THE
ZC-POINCARE
HOPF
ALGEBRA
.
127
REFERENCES
.
139
PART
III
AN
INTRODUCTION
TO
K
-DEFORMED
FIELDS
6
CLASSICAL
FIELDS,
SYMMETRIES,
AND
CONSERVED
CHARGES
.
143
6.1
PRELIMINARIES
.
143
6.1.1
MORE
ON
THE
K-POINCARE
ALGEBRA
.
147
6.1.2
NON-COMMUTATIVE
CALCULUS
.
151
6.1.3
WEYL
MAPS
AND
YY-PRODUCT
.
154
6.1.4
SUMMARY
OF
THE
TECHNICAL
TOOLS
.
155
6.2
ACTION
AND
FIELD
EQUATIONS
.
158
6.3
COMPLEX
SCALAR
FIELD
AND
MOMENTUM
SPACE
ACTION
.
161
6.4
POINCARE
SYMMETRY
OF
THE
ACTION
.
165
6.5
SYMPLECTIC
STRUCTURE
.
166
6.6
CONSERVED
CHARGES
.
169
REFERENCES
.
171
7
FREE
QUANTUM
FIELDS
AND
DISCRETE
SYMMETRIES
.
173
7.1
FREE
ZC-DEFORMED
QUANTUM
FIELDS:
THE
FEYNMAN
PROPAGATOR
.
173
7.1.1
THE
ZC-DEFORMED
FREE
FIELD
PARTITION
FUNCTION
.
173
7.1.2
THE
FEYNMAN
PROPAGATOR
.
176
7.2
CREATION/ANNIHILATION
OPERATORS
ALGEBRA
.
180
7.3
DISCRETE
SYMMETRIES
.
183
7.3.1
PARITY
&
.
183
7.3.2
TIME
REVERSAL
ST
.
184
7.3.3
CHARGE
CONJUGATION
.
185
7.4
PROPERTIES
OF
ONE-PARTICLE
STATES
.
186
REFERENCES
.
188
INDEX
.
189 |
| adam_txt |
CONTENTS
PART
I
FROM
GRAVITY
TO
CURVED
MOMENTUM
SPACE
AND
NON-COMMUTATIVE
SPACETIME
1
INVITATION:
GRAVITY,
POINT
PARTICLES,
AND
GROUP-VALUED
MOMENTA
.
3
1.1
INTRODUCTION
.
3
1.2
2+1
GRAVITY,
PARTICLES,
AND
CURVATURE
OF
MOMENTUM
SPACE
.
7
REFERENCES
.
13
2
GRAVITY
IN
2+1
DIMENSIONS
AS
A
CHEM-SIMONS
THEORY
.
15
2.1
PURE
GRAVITY
IN
2+1
DIMENSIONS
.
15
2.2
PARTICLE
COUPLING
.
21
2.3
EFFECTIVE
DEFORMED
SINGLE
PARTICLE
ACTION
.
26
2.4
PROPERTIES
OF
THE
DEFORMED
LAGRANGIAN
.
31
2.5
THE
CASE
OF
MANY
PARTICLES
.
34
2.6
K-CARROLLIAN
DEFORMATION
.
37
2.7
DEFORMED
SPACETIME
SYMMETRIES
OF
2+1
QUANTUM
GRAVITY
.
42
REFERENCES
.
47
3
GRAVITY
IN
3+1
DIMENSIONS,
PARTICLES,
AND
TOPOLOGICAL
LIMIT
.
49
3.1
FROM
3+1
TO
2+1
DIMENSIONS
VIA
DIMENSIONAL
REDUCTION
.
49
3.2
GRAVITY
AS
A
CONSTRAINED
BF
THEORY
.
52
3.3
PARTICLES
COUPLED
TO
GRAVITY
.
59
3.4
EQUATIONS
FOR
THE
PARTICLE-GRAVITY
SYSTEM
.
62
3.5
THE
TOPOLOGICAL
VACUUM
.
65
3.6
EFFECTIVE
DEFORMED
PARTICLE
.
67
REFERENCES
.
70
PART
II
DEFORMED
PARTICLES
AND
THEIR
SYMMETRIES
4
DEFORMED
CLASSICAL
PARTICLES:
PHASE
SPACE
AND
KINEMATICS
.
73
4.1
FROM
SYMPLECTIC
MANIFOLDS
TO
POISSON-LIE
GROUPS
.
73
4.1.1
FROM
SYMPLECTIC
MANIFOLDS
TO
POISSON
MANIFOLDS
.
74
4.1.2
LIE
GROUPS
AS
PHASE
SPACES
.
75
XII
CONTENTS
4.1.3
DEFORMING
PHASE
SPACES:
THE
CLASSICAL
DOUBLES
.
82
4.2
RELATIVISTIC
SPINLESS
PARTICLE:
FLAT
MOMENTUM
SPACE
.
84
4.3
DEFORMING
MOMENTUM
SPACE
TO
THE
AN
(NJ
GROUP
.
86
4.4
DEFORMING
MOMENTUM
SPACE
TO
THE
GROUP
SL(2,R)
.
91
4.5
RELATIVISTIC
HAMILTONIAN
MECHANICS
WITH
CURVED
MOMENTUM
SPACE
.
95
4.6
ZC-POINCARE
PARTICLE
-
THE
FREE
CASE
.
101
4.7
THE
SYSTEM
OF
TWO
ZC-DEFORMED
PARTICLES
.
107
4.7.1
TRANSLATIONS
.
109
4.7.2
LORENTZ
SYMMETRY
.
ILL
REFERENCES
.
114
5
HOPF
ALGEBRA
RELATIVISTIC
SYMMETRIES:
THE
ZC-POINCARE
ALGEBRA.
.
115
5.1
HOPF
ALGEBRA
STRUCTURES
IN
QUANTUM
THEORY
.
115
5.2
THE
ZC-POINCARE
HOPF
ALGEBRA
.
127
REFERENCES
.
139
PART
III
AN
INTRODUCTION
TO
K
-DEFORMED
FIELDS
6
CLASSICAL
FIELDS,
SYMMETRIES,
AND
CONSERVED
CHARGES
.
143
6.1
PRELIMINARIES
.
143
6.1.1
MORE
ON
THE
K-POINCARE
ALGEBRA
.
147
6.1.2
NON-COMMUTATIVE
CALCULUS
.
151
6.1.3
WEYL
MAPS
AND
YY-PRODUCT
.
154
6.1.4
SUMMARY
OF
THE
TECHNICAL
TOOLS
.
155
6.2
ACTION
AND
FIELD
EQUATIONS
.
158
6.3
COMPLEX
SCALAR
FIELD
AND
MOMENTUM
SPACE
ACTION
.
161
6.4
POINCARE
SYMMETRY
OF
THE
ACTION
.
165
6.5
SYMPLECTIC
STRUCTURE
.
166
6.6
CONSERVED
CHARGES
.
169
REFERENCES
.
171
7
FREE
QUANTUM
FIELDS
AND
DISCRETE
SYMMETRIES
.
173
7.1
FREE
ZC-DEFORMED
QUANTUM
FIELDS:
THE
FEYNMAN
PROPAGATOR
.
173
7.1.1
THE
ZC-DEFORMED
FREE
FIELD
PARTITION
FUNCTION
.
173
7.1.2
THE
FEYNMAN
PROPAGATOR
.
176
7.2
CREATION/ANNIHILATION
OPERATORS
ALGEBRA
.
180
7.3
DISCRETE
SYMMETRIES
.
183
7.3.1
PARITY
&
.
183
7.3.2
TIME
REVERSAL
ST
.
184
7.3.3
CHARGE
CONJUGATION
.
185
7.4
PROPERTIES
OF
ONE-PARTICLE
STATES
.
186
REFERENCES
.
188
INDEX
.
189 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Arzano, Michele Kowalski-Glikman, Jerzy 1957- |
| author_GND | (DE-588)1237698480 (DE-588)121622142 |
| author_facet | Arzano, Michele Kowalski-Glikman, Jerzy 1957- |
| author_role | aut aut |
| author_sort | Arzano, Michele |
| author_variant | m a ma j k g jkg |
| building | Verbundindex |
| bvnumber | BV047382834 |
| ctrlnum | (OCoLC)1235993203 (DE-599)DNB1226055907 |
| format | Book |
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| id | DE-604.BV047382834 |
| illustrated | Illustrated |
| index_date | 2024-07-03T17:48:06Z |
| indexdate | 2024-12-09T13:06:17Z |
| institution | BVB |
| institution_GND | (DE-588)1065168780 |
| isbn | 9783662630952 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032784348 |
| oclc_num | 1235993203 |
| open_access_boolean | |
| owner | DE-29T DE-83 DE-384 |
| owner_facet | DE-29T DE-83 DE-384 |
| physical | XIII, 191 Seiten Illustrationen 23.5 cm x 15.5 cm |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Springer |
| record_format | marc |
| series | Lecture Notes in Physics |
| series2 | Lecture Notes in Physics |
| spelling | Arzano, Michele Verfasser (DE-588)1237698480 aut Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields Michele Arzano, Jerzy Kowalski-Glikman Berlin Springer [2021] XIII, 191 Seiten Illustrationen 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Physics Volume 986 Fundamentalgruppe (DE-588)4155638-0 gnd rswk-swf Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Discrete Spacetime Symmetries Gravity in 2+1 Dimensions Hopf Algebras Quantum Gravity Phenomenology Quantum-deformed Symmetries Relativistic Particles and Fields Raum-Zeit (DE-588)4302626-6 s Fundamentalgruppe (DE-588)4155638-0 s DE-604 Kowalski-Glikman, Jerzy 1957- Verfasser (DE-588)121622142 aut Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe 9783662630976 Lecture Notes in Physics Volume 986 (DE-604)BV000003166 986 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=551eed8f21214bd784ee5fe4cb65fa7d&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032784348&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20210131 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Arzano, Michele Kowalski-Glikman, Jerzy 1957- Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields Lecture Notes in Physics Fundamentalgruppe (DE-588)4155638-0 gnd Raum-Zeit (DE-588)4302626-6 gnd |
| subject_GND | (DE-588)4155638-0 (DE-588)4302626-6 |
| title | Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields |
| title_auth | Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields |
| title_exact_search | Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields |
| title_exact_search_txtP | Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields |
| title_full | Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields Michele Arzano, Jerzy Kowalski-Glikman |
| title_fullStr | Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields Michele Arzano, Jerzy Kowalski-Glikman |
| title_full_unstemmed | Deformations of space-time symmetries gravity, group-valued momenta and non-commutative fields Michele Arzano, Jerzy Kowalski-Glikman |
| title_short | Deformations of space-time symmetries |
| title_sort | deformations of space time symmetries gravity group valued momenta and non commutative fields |
| title_sub | gravity, group-valued momenta and non-commutative fields |
| topic | Fundamentalgruppe (DE-588)4155638-0 gnd Raum-Zeit (DE-588)4302626-6 gnd |
| topic_facet | Fundamentalgruppe Raum-Zeit |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=551eed8f21214bd784ee5fe4cb65fa7d&prov=M&dok_var=1&dok_ext=htm http://www.springer.com/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032784348&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
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