The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial homogeneity. A parameter dependent decomposition of the metric variables adapted to the symmetry breaking effects of the nonabelian Bianchi types on the “free dynamics...

I discuss some new trends in Particle Theory beyond the Standard Model. Some topics which are briefly covered include electroweak baryogenesis, gauge versus non-gauge discrete symmetries, the strong-CP problem, dynamical symmetry breaking scenarios, supersymmetric grand unification, new aspects in low-energy supersymmetry and superstring phe-

When 4-dimensional general relativity is extended by a 3-dimensional grav-itational Chern-Simons term an apparent violation of diffeormorphism invari-ance is extinguished by the dynamical equations of motion for the modified theory. The physical predictions of this recently proposed model show little evidence of symmetry breaking, but require the vanishing of the Pontryagin density.

We study finite groups that occur as combinatorial automorphism or geometric symmetry of convex polytopes. When $\Gamma$ is a subgroup the group $d$-polytope, $d\geq 3$, then there exists $d$-polytope related to original polytope with exactly $\Gamma$. both and These symmetry-breaking results are applied show for every abelian even order involution $\sigma$ $\Gamma$, centrally symmetric such co...

We analyze a gauge-Higgs unification model which is based on a gauge theory defined on a six-dimensional spacetime with an S2 extra-space. We impose a symmetry condition for a gauge field and non-trivial boundary conditions of the S2. We provide the scheme for constructing a four-dimensional theory from the six-dimensional gauge theory under these conditions. We then construct a concrete model ...

Recent developments of physics at the TeV energy scale, especially physics related to the e + e − linear colliders are briefly reviewed. The topics include the present status of the standard model, Higgs physics, supersym-metry, strongly interacting electroweak symmetry breaking mechanism, and top quark physics.

Norbert Stoop, Romain Lagrange, Denis Terwagne2∗, Pedro M. Reis, and Jörn Dunkel Department of Mathematics, Massachussetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA Department of Civil & Environmental Engineering, Massachussetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA Department of Mechanical Engineering, Massachusset...