Masses and Coupling Constants

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


The nonrelativistic hydrogen atom and the atomic spectrum characterize cyclic Hilbert representations for the analysis of hyperbolic position Y 3, i.e., of the homogeneous space SO 0(1, 3)/SO(3) for rotation relativity. The particle spectrum is proposed to arise in an analysis of electroweak spacetime \( \mathcal{D}^4 \) as the homogeneous space for unitary relativity \( {\bf D}(1) \times y^3 \cong {\bf GL}(\mathbb{C}^2)/ {\bf U}(2) \) i.e., for position Y 3 with additional causal (dilation) operations D(1).

The particle spectrum \( \left( {m^2 , J, z} \right) \in \mathbb{R}_+ \times \frac{{\rm N}} {2} \times \mathbb{Z} \) for flat spacetime is characterized by the continuous mass as invariant for translations \( \mathbb{R}^4 \) in the D(1) × U(1)-extended Poincaré group \( {\bf GL} (\mathbb{C}^2) \vec \times \mathbb{R}^4 \), by (half-)integer spin or polarization for rotations SU(2) or SO(2) as translation fixgroup in the Lorentz cover group \( {\bf SL} (\mathbb{C}^2)\), and by an integer charge number for electro-magnetic windings U(1). The basic interactions are implemented by massless fields with characteristic coupling constants.

The eigentime \( {\bf D}(1) \cong \mathbb{R}\) invariants for the representations of electroweak spacetime \( \mathcal{D}^4 \cong {\bf D}(1) \times y^3 \cong \mathbb{R}^4_+ \) are proposed to determine the mass of relativistic particles. Since the causal spacetime group \( {\bf GL} (\mathbb{C}^2)\) has real rank 2, i.e., two characterizing continuous invariants \( \left\{ {m^2 ,\,M^2 } \right\} \), the translation invariants are related to both the embedded causal group D(1) and Lorentz group SO 0(1, 3)-representations of 3-position Y 3.


Lorentz Group Product Representation Goldstone Mode Real Rank Dilation Property 
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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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