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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.
List of contents
Introduction and Orientation.- Einstein's Gravity.- Riemannian Manifolds.- Mass Points.- Quantum Mechanics.- Quantum Fields of Flat Spacetime.- External and Internal Operations.- Relativities and Homogeneous Spaces.- Representation Coefficients.- Convolutions and Product Representations.- Interactions and Kernels.- Electroweak Spacetime.- Masses and Coupling Constants.
Summary
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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From the reviews:
“This book provides a basic understanding of the fundamental connections between the properties of spacetime interactions and matter. … it provides a deeper and more radical view of the fundamental principles of physics. … The book addresses graduate students and scientists with an interest in the structure of those basic physical theories that have some experimental justification.” (Gheorghe Zet, Mathematical Reviews, Issue 2011 a)
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From the reviews:
"This book provides a basic understanding of the fundamental connections between the properties of spacetime interactions and matter. ... it provides a deeper and more radical view of the fundamental principles of physics. ... The book addresses graduate students and scientists with an interest in the structure of those basic physical theories that have some experimental justification." (Gheorghe Zet, Mathematical Reviews, Issue 2011 a)
