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Electroweak Spacetime

Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 163)

Abstract

Unitary relativity in two complex dimensions is parametrized by electroweak spacetime \( \mathbb{D}(2) \cong \bf{\rm {GL}}(\mathbb{C}^2)/ \rm{U}(2) \) as the noncompact real four-dimensional base manifold of a coset bundle \( {\bf{U}}(2)= {\bf U}(1_2) \circ {\bf SU}{(2)} \) for the global group \( {\bf GL}(\mathbb{C}^2) \) with the typical fiber \( {\bf{U}}(2)= {\bf U}(1_2) \circ {\bf SU}{(2)} \) as local group, i.e., the real four-dimensional internal (chargelike) hyperisospin operations (see Chapter 6). In the classical manifold interpretation, electroweak spacetime \( {\bf D}(1) \times y^3 \) is a flat Friedmann universe with a hyperbolically curved position. Its representations are characterized by two continuous invariants for causal time \( {\bf D}(1) \cong \mathbb{R}_+ \) and hyperbolic position \( y^3 \cong \mathbb{R}_3 \). The Hilbert representations, as used for quantum theory, are infinite-dimensional for a nontrivial action of the external operations \( {\bf D}(1) \times {\bf SO}_0 (1, 3)\). They will be related to spacetime particles and interactions in Chapter 12.

Keywords

Hardy Space Lorentz Group Continuous Invariant Spacetime Representation Friedmann Universe 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.MPI für Physik Werner-Heisenberg-InstitutMünchenGermany

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