The mathematics of Minkowski space time: with an introduction to commutative hypercomplex numbers
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Basel ; Boston, Mass. ; Berlin
Birkhäuser Verlag
2008
|
| Series: | Frontiers in Mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seiten 245 - 250 |
| Physical Description: | XVIII, 255 Seiten graph. Darst. 24 cm |
| ISBN: | 9783764386139 3764386134 |
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| 245 | 1 | 0 | |a The mathematics of Minkowski space time |b with an introduction to commutative hypercomplex numbers |c Francesco Catoni [und 5 andere] |
| 264 | 1 | |a Basel ; Boston, Mass. ; Berlin |b Birkhäuser Verlag |c 2008 | |
| 300 | |a XVIII, 255 Seiten |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Frontiers in Mathematics | |
| 500 | |a Literaturverzeichnis Seiten 245 - 250 | ||
| 650 | 4 | |a Espaces généralisés | |
| 650 | 4 | |a Relativité restreinte (Physique) | |
| 650 | 4 | |a Generalized spaces | |
| 650 | 4 | |a Special relativity (Physics) | |
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| 700 | 1 | |a Catoni, Francesco |e Sonstige |4 oth | |
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| adam_text |
Contents
Preface
vii
1
Introduction
1
2
N-Dimensional
Commutative Hypercomplex
Numbers
5
2.1
N-Dimensional Hypercomplex
Numbers.
5
2.1.1
Equality and Sum
. 5
2.1.2
The Product Operation
. 6
2.1.3
Characteristic Matrix and Characteristic Determinant
. 7
2.1.4
Invariant Quantities for Hypercomplex Numbers
. 9
2.1.5
The Division Operation
. 10
2.1.6
Characteristic Equation and Principal Conjugations
. 10
2.1.7
Decomposable Systems
. 12
2.2
The General Two-Dimensional System
. 12
2.2.1
Canonical Two-Dimensional Systems
. 16
2.2.2
The Two-Dimensional Hyperbolic System
. 16
3
The Geometries Generated by Hypercomplex Numbers
19
3.1
Linear Transformations and Geometries
. 19
3.1.1
The Continuous Lie Groups
. 19
3.1.2
Klein's
Erlanger
Programm. 19
3.2
Groups Associated with Hypercomplex Numbers
. 20
3.2.1
Geometries Generated by Complex and Hyperbolic
Numbers
. 23
3.3
Conclusions
. 24
4
Trigonometry in the Minkowski Plane
27
4.1
Geometrical Representation of Hyperbolic Numbers
. 28
4.1.1
Hyperbolic Exponential Function and Hyperbolic Polar
Transformation
. 28
4.1.2
Hyperbolic Rotations as
Lorentz
Transformations of Special
Relativity
. 30
4.2
Basics of Hyperbolic Trigonometry
. 31
4.2.1
Complex Numbers and Euclidean Trigonometry
. 31
4.2.2
Hyperbolic Rotation Invariants in Pseudo-Euclidean Plane
Geometry
. 32
4.2.3
Fjelstad's Extension of Hyperbolic Trigonometric Functions
35
4.3
Geometry in the Pseudo-Euclidean Cartesian Plane
. 37
Contents
4.4 Goniometry
and Trigonometry in the Pseudo-Euclidean
Plane . 40
4.4.1
Analytical Definitions of Hyperbolic Trigonometric
Functions
. 41
4.4.2
Trigonometric Laws in the Pseudo-Euclidean Plane
. 42
4.4.3
The Triangle's Angles Sum
. 43
4.5
Theorems on Equilateral Hyperbolas in the Pseudo-Euclidean
Plane
. 44
4.6
Examples of Triangle Solutions in the Minkowski Plane
. 52
Uniform and Accelerated Motions in the Minkowski Space-Time
(Twin Paradox)
57
5.1
Inerţial
Motions
. 58
5.2
Inerţial
and Uniformly Accelerated Motions
. 61
5.3
Non-uniformly Accelerated Motions
. 69
5.3.1
Prenet's Formulas in the Minkowski Space-Time
. 70
5.3.2
Proper Time in Non-Uniformly Accelerated Motions
. 70
General Two-Dimensional Hypercomplex Numbers
73
6.1
Geometrical Representation
. 73
6.2
Geometry and Trigonometry in Two-Dimensional Algebras
. 76
6.2.1
The "Circle" for Three Points
. 76
6.2.2
Hero's Formula and Pythagoras' Theorem
. 77
6.2.3
Properties of "Orthogonal" Lines in General Algebras
. 79
6.3
Some Properties of Fundamental Conic Sections
. 79
6.3.1
"Incircles" and "Excircles" of a Triangle
. 79
6.3.2
The Tangent Lines to the Fundamental Conic Section
. 82
6.4
Numerical Examples
. 83
Functions of a Hyperbolic Variable
87
7.1
Some Remarks on Functions of a Complex Variable
. 87
7.2
Functions of Hypercomplex Variables
. 89
7.2.1
Generalized Cauchy-Riemann Conditions
. 89
7.2.2
The Principal Transformation
. 91
7.2.3
Functions of a Hypercomplex Variable as
Infinite-Dimensional Lie Groups
. 92
7.3
The Functions of a Hyperbolic Variable
. 93
7.3.1
Cauchy-Riemann Conditions for General Two-Dimensional
Systems
. 93
7.3.2
The Derivative of Functions of a Canonical Hyperbolic
Variable
. 94
7.3.3
The Properties of H-Analytic Functions
. 95
7.3.4
The Analytic Functions of Decomposable Systems
. 95
7.4
The Elementary Functions of a Canonical Hyperbolic Variable
. . 96
Contents xiii
7.5 H-Conformal
Mappings .
97
7.5.1 H-Conformal
Mappings by Means of Elementary Functions
99
7.5.2
Hyperbolic Linear-Fractional Mapping
. 109
7.6
Commutative Hypercomplex Systems with Three Unities
. 114
7.6.1
Some Properties of the Three-Units Separable Systems
. . . 115
8
Hyperbolic Variables on
Lorentz
Surfaces
119
8.1
Introduction
. 119
8.2
Gauss:
Conformai
Mapping of Surfaces
. 121
8.2.1
Mapping of a Spherical Surface on a Plane
. 123
8.2.2
Conclusions
. 124
8.3
Extension of Gauss Theorem:
Conformai
Mapping of
Lorentz
Surfaces
. 125
8.4
Beltrami: Complex Variables on a Surface
. 126
8.4.1
Beltrami's Equation
. 127
8.5
Beltrami's Integration of Geodesic Equations
. 130
8.5.1
Differential Parameter and Geodesic Equations
. 130
8.6
Extension of Beltrami's Equation to Non-Definite Differential
Forms
. 133
9
Constant Curvature
Lorentz
Surfaces
137
9.1
Introduction
. 137
9.2
Constant Curvature Riemann Surfaces
. 140
9.2.1
Rotation Surfaces
. 140
9.2.2
Positive Constant Curvature Surface
. 143
9.2.3
Negative Constant Curvature Surface
. 148
9.2.4
Motions
. 149
9.2.5
Two-Sheets
Hyperboloid
in a Semi-Riemannian Space
. . . 151
9.3
Constant Curvature
Lorentz
Surfaces
. 153
9.3.1
Line Element
. 153
9.3.2
Isometric Forms of the Line Elements
. 153
9.3.3
Equations of the Geodesies
. 154
9.3.4
Motions
. 156
9.4
Geodesies and Geodesic Distances on Riemann and
Lorentz
Surfaces
. 157
9.4.1
The Equation of the Geodesic
. 157
9.4.2
Geodesic Distance
. 159
10
Generalization of Two-Dimensional Special Relativity
(Hyperbolic Transformations and the Equivalence Principle)
161
10.1
The Physical Meaning of Transformations by Hyperbolic
Functions
. 161
xiv Contents
10.2
Physical
Interpretation
of Geodesies on Riemann and
Lorentz
Surfaces with Positive Constant Curvature
. 164
10.2.1
The Sphere
. 165
10.2.2
The
Lorentz
Surfaces
. 165
10.3
Einstein's Way to General Relativity
. 166
10.4
Conclusions
. 167
Appendices
A Commutative Segre's Quaternions
169
A.I Hypercomplex Systems with Four Units
. 170
A.I.I Historical Introduction of Segre's Quaternions
. 171
A.
1.2
Generalized Segre's Quaternions
. 171
A.2 Algebraic Properties
. 172
A.2.1 Quaternions as a Composed System
. 176
A.3 Functions of a Quaternion Vaxiable
. 177
A.3.1 Holomorphic Functions
. 178
A.
3.2
Algebraic Reconstruction of Quaternion Functions Given a
Component
. 182
A.
4
Mapping by Means of Quaternion Functions
. 183
A.4.1 The "Polar" Representation of Elliptic and Hyperbolic
Quaternions
. 183
A.4.2
Conformai
Mapping
. 185
A.4.3 Some Considerations About Scalar and Vector Potentials
. 186
A.
5
Elementary Functions of Quaternions
. 187
A.
6
Elliptic-Hyperbolic Quaternions
. 191
A.
6.1
Generalized Cauchy-Riemann Conditions
. 193
A.6.2 Elementary Functions
. 193
A.
7
Elliptic-Parabolic Generalized Segre's Quaternions
. 194
A.7.1 Generalized Cauchy-Riemann conditions
. 195
A.7.2 Elementary Functions
. 196
В
Constant Curvature Segre's Quaternion Spaces
199
B.I Quaternion Differential Geometry
. 200
B.2 Euler's Equations for Geodesies
. 201
B.3 Constant Curvature Quaternion Spaces
. 203
B.3.1 Line Element for Positive Constant Curvature
. 204
B.4 Geodesic Equations in Quaternion Space
. 206
B.4.1 Positive Constant Curvature Quaternion Space
. 210
С
Matrix Formalization for Commutative Numbers
213
C.I Mathematical Operations
. 213
C.I.I Equality, Sum, and Scalar Multiplication
. 214
C.1.2 Product and Related Operations
. 215
Contents xv
С.
1.3 Division
Between Hypercomplex Numbers
. 218
С.
2
Two-dimensional Hypercomplex Numbers
. 221
C.3 Properties of the Characteristic Matrix M.
. 222
C.3.1 Algebraic Properties
. 223
C.3.2 Spectral Properties
. 223
C.3.3 More About Divisors of Zero
. 227
C.3.
4
Modulus of a Hypercomplex Number
. 227
C.3.
5
Conjugations of a Hypercomplex Number
. 227
C.4 Functions of a Hypercomplex Variable
. 228
C.4.1 Analytic Continuation
. 228
C.4.
2
Properties of Hypercomplex Functions
. 229
C.5 Functions of a Two-dimensional Hypercomplex Variable
. 230
C.5.1 Function of
2x2
Matrices
. 231
C.5.2 The Derivative of the Functions of a Real Variable
. 233
C.6 Derivatives of a Hypercomplex Function
. 236
C.6.1 Derivative with Respect to a Hypercomplex Variable
. 236
C.6.
2
Partial Derivatives
. 237
C.6.3 Components of the Derivative Operator
. 238
C.6.
4
Derivative with Respect to the Conjugated Variables
. 239
C.7 Characteristic Differential Equation
. 239
С
7.1
Characteristic Equation for Two-dimensional Numbers
. 241
C.8 Equivalence Between the Formalizations of Hypercomplex
Numbers
. 242
Bibliography
245
Index
251 |
| adam_txt |
Contents
Preface
vii
1
Introduction
1
2
N-Dimensional
Commutative Hypercomplex
Numbers
5
2.1
N-Dimensional Hypercomplex
Numbers.
5
2.1.1
Equality and Sum
. 5
2.1.2
The Product Operation
. 6
2.1.3
Characteristic Matrix and Characteristic Determinant
. 7
2.1.4
Invariant Quantities for Hypercomplex Numbers
. 9
2.1.5
The Division Operation
. 10
2.1.6
Characteristic Equation and Principal Conjugations
. 10
2.1.7
Decomposable Systems
. 12
2.2
The General Two-Dimensional System
. 12
2.2.1
Canonical Two-Dimensional Systems
. 16
2.2.2
The Two-Dimensional Hyperbolic System
. 16
3
The Geometries Generated by Hypercomplex Numbers
19
3.1
Linear Transformations and Geometries
. 19
3.1.1
The Continuous Lie Groups
. 19
3.1.2
Klein's
Erlanger
Programm. 19
3.2
Groups Associated with Hypercomplex Numbers
. 20
3.2.1
Geometries Generated by Complex and Hyperbolic
Numbers
. 23
3.3
Conclusions
. 24
4
Trigonometry in the Minkowski Plane
27
4.1
Geometrical Representation of Hyperbolic Numbers
. 28
4.1.1
Hyperbolic Exponential Function and Hyperbolic Polar
Transformation
. 28
4.1.2
Hyperbolic Rotations as
Lorentz
Transformations of Special
Relativity
. 30
4.2
Basics of Hyperbolic Trigonometry
. 31
4.2.1
Complex Numbers and Euclidean Trigonometry
. 31
4.2.2
Hyperbolic Rotation Invariants in Pseudo-Euclidean Plane
Geometry
. 32
4.2.3
Fjelstad's Extension of Hyperbolic Trigonometric Functions
35
4.3
Geometry in the Pseudo-Euclidean Cartesian Plane
. 37
Contents
4.4 Goniometry
and Trigonometry in the Pseudo-Euclidean
Plane . 40
4.4.1
Analytical Definitions of Hyperbolic Trigonometric
Functions
. 41
4.4.2
Trigonometric Laws in the Pseudo-Euclidean Plane
. 42
4.4.3
The Triangle's Angles Sum
. 43
4.5
Theorems on Equilateral Hyperbolas in the Pseudo-Euclidean
Plane
. 44
4.6
Examples of Triangle Solutions in the Minkowski Plane
. 52
Uniform and Accelerated Motions in the Minkowski Space-Time
(Twin Paradox)
57
5.1
Inerţial
Motions
. 58
5.2
Inerţial
and Uniformly Accelerated Motions
. 61
5.3
Non-uniformly Accelerated Motions
. 69
5.3.1
Prenet's Formulas in the Minkowski Space-Time
. 70
5.3.2
Proper Time in Non-Uniformly Accelerated Motions
. 70
General Two-Dimensional Hypercomplex Numbers
73
6.1
Geometrical Representation
. 73
6.2
Geometry and Trigonometry in Two-Dimensional Algebras
. 76
6.2.1
The "Circle" for Three Points
. 76
6.2.2
Hero's Formula and Pythagoras' Theorem
. 77
6.2.3
Properties of "Orthogonal" Lines in General Algebras
. 79
6.3
Some Properties of Fundamental Conic Sections
. 79
6.3.1
"Incircles" and "Excircles" of a Triangle
. 79
6.3.2
The Tangent Lines to the Fundamental Conic Section
. 82
6.4
Numerical Examples
. 83
Functions of a Hyperbolic Variable
87
7.1
Some Remarks on Functions of a Complex Variable
. 87
7.2
Functions of Hypercomplex Variables
. 89
7.2.1
Generalized Cauchy-Riemann Conditions
. 89
7.2.2
The Principal Transformation
. 91
7.2.3
Functions of a Hypercomplex Variable as
Infinite-Dimensional Lie Groups
. 92
7.3
The Functions of a Hyperbolic Variable
. 93
7.3.1
Cauchy-Riemann Conditions for General Two-Dimensional
Systems
. 93
7.3.2
The Derivative of Functions of a Canonical Hyperbolic
Variable
. 94
7.3.3
The Properties of H-Analytic Functions
. 95
7.3.4
The Analytic Functions of Decomposable Systems
. 95
7.4
The Elementary Functions of a Canonical Hyperbolic Variable
. . 96
Contents xiii
7.5 H-Conformal
Mappings .
97
7.5.1 H-Conformal
Mappings by Means of Elementary Functions
99
7.5.2
Hyperbolic Linear-Fractional Mapping
. 109
7.6
Commutative Hypercomplex Systems with Three Unities
. 114
7.6.1
Some Properties of the Three-Units Separable Systems
. . . 115
8
Hyperbolic Variables on
Lorentz
Surfaces
119
8.1
Introduction
. 119
8.2
Gauss:
Conformai
Mapping of Surfaces
. 121
8.2.1
Mapping of a Spherical Surface on a Plane
. 123
8.2.2
Conclusions
. 124
8.3
Extension of Gauss Theorem:
Conformai
Mapping of
Lorentz
Surfaces
. 125
8.4
Beltrami: Complex Variables on a Surface
. 126
8.4.1
Beltrami's Equation
. 127
8.5
Beltrami's Integration of Geodesic Equations
. 130
8.5.1
Differential Parameter and Geodesic Equations
. 130
8.6
Extension of Beltrami's Equation to Non-Definite Differential
Forms
. 133
9
Constant Curvature
Lorentz
Surfaces
137
9.1
Introduction
. 137
9.2
Constant Curvature Riemann Surfaces
. 140
9.2.1
Rotation Surfaces
. 140
9.2.2
Positive Constant Curvature Surface
. 143
9.2.3
Negative Constant Curvature Surface
. 148
9.2.4
Motions
. 149
9.2.5
Two-Sheets
Hyperboloid
in a Semi-Riemannian Space
. . . 151
9.3
Constant Curvature
Lorentz
Surfaces
. 153
9.3.1
Line Element
. 153
9.3.2
Isometric Forms of the Line Elements
. 153
9.3.3
Equations of the Geodesies
. 154
9.3.4
Motions
. 156
9.4
Geodesies and Geodesic Distances on Riemann and
Lorentz
Surfaces
. 157
9.4.1
The Equation of the Geodesic
. 157
9.4.2
Geodesic Distance
. 159
10
Generalization of Two-Dimensional Special Relativity
(Hyperbolic Transformations and the Equivalence Principle)
161
10.1
The Physical Meaning of Transformations by Hyperbolic
Functions
. 161
xiv Contents
10.2
Physical
Interpretation
of Geodesies on Riemann and
Lorentz
Surfaces with Positive Constant Curvature
. 164
10.2.1
The Sphere
. 165
10.2.2
The
Lorentz
Surfaces
. 165
10.3
Einstein's Way to General Relativity
. 166
10.4
Conclusions
. 167
Appendices
A Commutative Segre's Quaternions
169
A.I Hypercomplex Systems with Four Units
. 170
A.I.I Historical Introduction of Segre's Quaternions
. 171
A.
1.2
Generalized Segre's Quaternions
. 171
A.2 Algebraic Properties
. 172
A.2.1 Quaternions as a Composed System
. 176
A.3 Functions of a Quaternion Vaxiable
. 177
A.3.1 Holomorphic Functions
. 178
A.
3.2
Algebraic Reconstruction of Quaternion Functions Given a
Component
. 182
A.
4
Mapping by Means of Quaternion Functions
. 183
A.4.1 The "Polar" Representation of Elliptic and Hyperbolic
Quaternions
. 183
A.4.2
Conformai
Mapping
. 185
A.4.3 Some Considerations About Scalar and Vector Potentials
. 186
A.
5
Elementary Functions of Quaternions
. 187
A.
6
Elliptic-Hyperbolic Quaternions
. 191
A.
6.1
Generalized Cauchy-Riemann Conditions
. 193
A.6.2 Elementary Functions
. 193
A.
7
Elliptic-Parabolic Generalized Segre's Quaternions
. 194
A.7.1 Generalized Cauchy-Riemann conditions
. 195
A.7.2 Elementary Functions
. 196
В
Constant Curvature Segre's Quaternion Spaces
199
B.I Quaternion Differential Geometry
. 200
B.2 Euler's Equations for Geodesies
. 201
B.3 Constant Curvature Quaternion Spaces
. 203
B.3.1 Line Element for Positive Constant Curvature
. 204
B.4 Geodesic Equations in Quaternion Space
. 206
B.4.1 Positive Constant Curvature Quaternion Space
. 210
С
Matrix Formalization for Commutative Numbers
213
C.I Mathematical Operations
. 213
C.I.I Equality, Sum, and Scalar Multiplication
. 214
C.1.2 Product and Related Operations
. 215
Contents xv
С.
1.3 Division
Between Hypercomplex Numbers
. 218
С.
2
Two-dimensional Hypercomplex Numbers
. 221
C.3 Properties of the Characteristic Matrix M.
. 222
C.3.1 Algebraic Properties
. 223
C.3.2 Spectral Properties
. 223
C.3.3 More About Divisors of Zero
. 227
C.3.
4
Modulus of a Hypercomplex Number
. 227
C.3.
5
Conjugations of a Hypercomplex Number
. 227
C.4 Functions of a Hypercomplex Variable
. 228
C.4.1 Analytic Continuation
. 228
C.4.
2
Properties of Hypercomplex Functions
. 229
C.5 Functions of a Two-dimensional Hypercomplex Variable
. 230
C.5.1 Function of
2x2
Matrices
. 231
C.5.2 The Derivative of the Functions of a Real Variable
. 233
C.6 Derivatives of a Hypercomplex Function
. 236
C.6.1 Derivative with Respect to a Hypercomplex Variable
. 236
C.6.
2
Partial Derivatives
. 237
C.6.3 Components of the Derivative Operator
. 238
C.6.
4
Derivative with Respect to the Conjugated Variables
. 239
C.7 Characteristic Differential Equation
. 239
С
7.1
Characteristic Equation for Two-dimensional Numbers
. 241
C.8 Equivalence Between the Formalizations of Hypercomplex
Numbers
. 242
Bibliography
245
Index
251 |
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| ctrlnum | (OCoLC)187294662 (DE-599)DNB985454393 |
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| discipline_str_mv | Physik Mathematik |
| format | Book |
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| id | DE-604.BV023356316 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:07:12Z |
| indexdate | 2025-03-18T09:01:59Z |
| institution | BVB |
| isbn | 9783764386139 3764386134 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016539851 |
| oclc_num | 187294662 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-11 DE-188 |
| physical | XVIII, 255 Seiten graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser Verlag |
| record_format | marc |
| series2 | Frontiers in Mathematics |
| spelling | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers Francesco Catoni [und 5 andere] Basel ; Boston, Mass. ; Berlin Birkhäuser Verlag 2008 XVIII, 255 Seiten graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Frontiers in Mathematics Literaturverzeichnis Seiten 245 - 250 Espaces généralisés Relativité restreinte (Physique) Generalized spaces Special relativity (Physics) Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Hyperkomplexe Zahl (DE-588)4215212-4 gnd rswk-swf Hyperkomplexe Zahl (DE-588)4215212-4 s Raum-Zeit (DE-588)4302626-6 s DE-604 Catoni, Francesco Sonstige oth http://d-nb.info/985454393/04 Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers Espaces généralisés Relativité restreinte (Physique) Generalized spaces Special relativity (Physics) Raum-Zeit (DE-588)4302626-6 gnd Hyperkomplexe Zahl (DE-588)4215212-4 gnd |
| subject_GND | (DE-588)4302626-6 (DE-588)4215212-4 |
| title | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers |
| title_auth | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers |
| title_exact_search | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers |
| title_exact_search_txtP | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers |
| title_full | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers Francesco Catoni [und 5 andere] |
| title_fullStr | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers Francesco Catoni [und 5 andere] |
| title_full_unstemmed | The mathematics of Minkowski space time with an introduction to commutative hypercomplex numbers Francesco Catoni [und 5 andere] |
| title_short | The mathematics of Minkowski space time |
| title_sort | the mathematics of minkowski space time with an introduction to commutative hypercomplex numbers |
| title_sub | with an introduction to commutative hypercomplex numbers |
| topic | Espaces généralisés Relativité restreinte (Physique) Generalized spaces Special relativity (Physics) Raum-Zeit (DE-588)4302626-6 gnd Hyperkomplexe Zahl (DE-588)4215212-4 gnd |
| topic_facet | Espaces généralisés Relativité restreinte (Physique) Generalized spaces Special relativity (Physics) Raum-Zeit Hyperkomplexe Zahl |
| url | http://d-nb.info/985454393/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT catonifrancesco themathematicsofminkowskispacetimewithanintroductiontocommutativehypercomplexnumbers |
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