Operational Spacetime pp 295-315 | Cite as

# Electroweak Spacetime

## 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## Preview

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