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The Resource Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces, by Abraham A. Ungar, (electronic resource)

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces, by Abraham A. Ungar, (electronic resource)

Creator
Author
Summary
"I cannot define coincidence [in mathematics]. But 1 shall argue that coincidence can always be elevated or organized into a superstructure which perfonns a unification along the coincidental elements. The existence of a coincidence is strong evidence for the existence of a covering theory. " -Philip 1. Davis [Dav81] Alluding to the Thomas gyration, this book presents the Theory of gy­ rogroups and gyrovector spaces, taking the reader to the immensity of hyper­ bolic geometry that lies beyond the Einstein special theory of relativity. Soon after its introduction by Einstein in 1905 [Ein05], special relativity theory (as named by Einstein ten years later) became overshadowed by the ap­ pearance of general relativity. Subsequently, the exposition of special relativity followed the lines laid down by Minkowski, in which the role of hyperbolic ge­ ometry is not emphasized. This can doubtlessly be explained by the strangeness and unfamiliarity of hyperbolic geometry [Bar98]. The aim of this book is to reverse the trend of neglecting the role of hy­ perbolic geometry in the special theory of relativity, initiated by Minkowski, by emphasizing the central role that hyperbolic geometry plays in the theory
Language
  • eng
  • eng
Work
Publication
Edition
1st ed. 2001.
Extent
1 online resource (XLII, 419 p. 25 illus.)
Note
Bibliographic Level Mode of Issuance: Monograph
Contents
  • 1. Thomas Precession: The Missing Link
  • 2. Gyrogroups: Modeled on Einstein’s Addition
  • 3. The Einstein Gyrovector Space
  • 4. Hyperbolic Geometry of Gyrovector Spaces
  • 5. The Ungar Gyrovector Space
  • 6. The Möbius Gyrovector Space
  • 7. Gyrogeometry
  • 8. Gyrooperations — The SL(2, C) Approach
  • 9. The Cocycle Form
  • 10.The Lorentz Group and Its Abstraction
  • 11.The Lorentz Transformation Link
  • 12.Other Lorentz Groups
  • 13.References
  • About the Author
  • Topic Index
  • Author Index
Isbn
9789401091220
Instance
Label
Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces
Title
Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession
Title remainder
The Theory of Gyrogroups and Gyrovector Spaces
Statement of responsibility
by Abraham A. Ungar
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
"I cannot define coincidence [in mathematics]. But 1 shall argue that coincidence can always be elevated or organized into a superstructure which perfonns a unification along the coincidental elements. The existence of a coincidence is strong evidence for the existence of a covering theory. " -Philip 1. Davis [Dav81] Alluding to the Thomas gyration, this book presents the Theory of gy­ rogroups and gyrovector spaces, taking the reader to the immensity of hyper­ bolic geometry that lies beyond the Einstein special theory of relativity. Soon after its introduction by Einstein in 1905 [Ein05], special relativity theory (as named by Einstein ten years later) became overshadowed by the ap­ pearance of general relativity. Subsequently, the exposition of special relativity followed the lines laid down by Minkowski, in which the role of hyperbolic ge­ ometry is not emphasized. This can doubtlessly be explained by the strangeness and unfamiliarity of hyperbolic geometry [Bar98]. The aim of this book is to reverse the trend of neglecting the role of hy­ perbolic geometry in the special theory of relativity, initiated by Minkowski, by emphasizing the central role that hyperbolic geometry plays in the theory
Member of
http://library.link/vocab/creatorName
Ungar, Abraham A
Dewey number
530.1
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
jyPAuBS1Ags
Image bit depth
0
Language note
English
LC call number
QC19.2-20.85
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Fundamental Theories of Physics,
Series volume
117
http://library.link/vocab/subjectName
  • Algebra
  • Theoretical, Mathematical and Computational Physics
  • Astronomy, Observations and Techniques
  • Non-associative Rings and Algebras
Label
Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces, by Abraham A. Ungar, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1. Thomas Precession: The Missing Link -- 2. Gyrogroups: Modeled on Einstein’s Addition -- 3. The Einstein Gyrovector Space -- 4. Hyperbolic Geometry of Gyrovector Spaces -- 5. The Ungar Gyrovector Space -- 6. The Möbius Gyrovector Space -- 7. Gyrogeometry -- 8. Gyrooperations — The SL(2, C) Approach -- 9. The Cocycle Form -- 10.The Lorentz Group and Its Abstraction -- 11.The Lorentz Transformation Link -- 12.Other Lorentz Groups -- 13.References -- About the Author -- Topic Index -- Author Index
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (XLII, 419 p. 25 illus.)
File format
multiple file formats
Form of item
online
Isbn
9789401091220
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-94-010-9122-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000120988
  • (SSID)ssj0001240527
  • (PQKBManifestationID)11723872
  • (PQKBTitleCode)TC0001240527
  • (PQKBWorkID)11207827
  • (PQKB)11596306
  • (DE-He213)978-94-010-9122-0
  • (MiAaPQ)EBC3109606
  • (EXLCZ)993400000000120988
Label
Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces, by Abraham A. Ungar, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1. Thomas Precession: The Missing Link -- 2. Gyrogroups: Modeled on Einstein’s Addition -- 3. The Einstein Gyrovector Space -- 4. Hyperbolic Geometry of Gyrovector Spaces -- 5. The Ungar Gyrovector Space -- 6. The Möbius Gyrovector Space -- 7. Gyrogeometry -- 8. Gyrooperations — The SL(2, C) Approach -- 9. The Cocycle Form -- 10.The Lorentz Group and Its Abstraction -- 11.The Lorentz Transformation Link -- 12.Other Lorentz Groups -- 13.References -- About the Author -- Topic Index -- Author Index
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (XLII, 419 p. 25 illus.)
File format
multiple file formats
Form of item
online
Isbn
9789401091220
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-94-010-9122-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000120988
  • (SSID)ssj0001240527
  • (PQKBManifestationID)11723872
  • (PQKBTitleCode)TC0001240527
  • (PQKBWorkID)11207827
  • (PQKB)11596306
  • (DE-He213)978-94-010-9122-0
  • (MiAaPQ)EBC3109606
  • (EXLCZ)993400000000120988

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