The book provides readers with an understanding of the mutual conditioning of spacetime and interactions and matter. The spacetime manifold will be looked at to be a reservoir for the parametrization of operation Lie groups or subgroup classes of Lie groups. With basic operation groups or Lie algebras, all physical structures can be interpreted in terms of corresponding realizations or representations. Physical properties are related eigenvalues or invariants. As an explicit example of operational spacetime is proposed, called electroweak spacetime, parametrizing the classes of the internal hypercharge - isospin group in the general linear group in two complex dimensions, i.e., the Lorentz cover group, extended by the casual (dilation) and phase group. Its representations and invariants will be investigated with the aim to connect them, qualitatively and numerically, with the properties of interactions and particles as arising in the representations of its tangent Minkowski spaces.

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Saller, Heinrich

Springer Nature

Fundamental Theories of Physics, 163, New York, NY, 2010

United States, United States of America

Springer Nature, New York, 2010

1, 20091028

sm41108506

producers:
Acrobat Distiller 8.0.0 (Windows)

Operational Spacetime: Interactions and Particles provides readers with a basic understanding of the mutual conditioning of spacetime and interactions and matter. The spacetime manifold will be looked at to be a reservoir for the parametrization of operation Lie groups or subgroup classes of Lie groups. With basic operation groups or Lie algebras, all physical structures can be interpreted in terms of corresponding realizations or representations. Physical properties are related eigenvalues or invariants. As an explicit example, an operational spacetime is proposed, called electroweak spacetime, parametrizing the classes of the internal hypercharge-isospin group in the general linear group in two complex dimensions, i.e., the Lorentz cover group, extended by the causal (dilation) and phase group. Its representations and invariants will be investigated with the aim to connect them, qualitatively and numerically, with the properties of interactions and particles as arising in the representations of its tangent Minkowski spaces. Heinrich Saller is the author of Operational Quantum Theory I: Nonrelativistic Structures (Springer, 2006) and Operational Quantum Theory II: Relativistic Structures (Springer, 2006)

Operational Spacetime 2
0 Introduction and Orientation 12
1 Einstein's Gravity 27
2 Riemannian Manifolds 39
3 Mass Points 91
4 Quantum Mechanics 103
5 Quantum Fields of Flat Spacetime 121
6 External and Internal Operations 156
7 Relativities and Homogeneous Spaces 181
8 Representation Coeffficients 209
9 Convolutions and Product Representations 262
10 Interactions and Kernels 284
11 Electroweak Spacetime 302
12 Masses and Coupling Constants 323
Bibliography 338
Index 342

2015-08-03