and Orientation.- Einstein#x2019;s Gravity.- Riemannian Manifolds.- Mass Points.- Quantum Mechanics.- Quantum Fields of Flat Spacetime.- External and Internal Operations.- Relativities and Homogeneous Spaces.- Representation Coeffficients.- Convolutions and Product Representations.- Interactions and Kernels.- Electroweak Spacetime.- Masses and Coupling Constants.
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.
Provides readers with interactive examples on how to connect quantum structure with spacetime
Gives a unique overview of group theoretical foundation of interactions and particles
Presents latest techniques in understanding the mutual conditions of operational spacetime and particles