Contribution to Book
American Mathematical Society
Mark J. Gotay, Jerold E. Marsden, Vincent Moncrief
SUe 4) x SU(2) is shown to characterize the possible choices of spacetime metric constructible from the gauge fields of the conformal group. When this symmetry is broken by the choice of metric, exactly the SU(3) x SU(2) x U(l) symmetry of the standard model remains. The conformal group consists of Lorentz transformations, translations, inverse translations and dilations. Treated in the standard way, conformal symmetry fails as a unifying gauge group: dilations make the mass spectrum continuous, and the inverse translational gauge field is auxiliary. The theory reduces back to the Poincare group.
Wheeler, J. T., SU(3) x SU(2) x U(1)SU(3): The residual symmetry of conformal gravity, Mathematical Aspects of Classical Field Theory, Contemporary Mathematics, Am. Math. Soc., Edited by Mark J. Gotay, Jerold E. Marsden, & Vincent Moncrief (1992) 635-644. http://arxiv.org/pdf/hep-th/9109033