Scalar Quotes
Inflation is a simple idea: imagine that the universe begins in a tiny patch of space dominated by the potential energy of some scalar field, a kind of super-dense dark energy. This causes that patch to expand at a terrifically accelerated rate, smoothing out the density and diluting away any unwanted relics. Eventually the scalar field decays into ordinary matter and radiation, reheating the universe into a conventional Big Bang state, after which things proceed as normal.
Sean M. Carroll
At the most abstract level, the relation between urbanism and microelectronics is scalar (fractal). The coming computers are closer to miniature cities than to artificial brains, dominated by traffic problems (congestion), migration / communications, zoning issues (mixed use), the engineering potential of new materials, questions of dimensionality (3D solutions to density constraints), entropy or heat / waste dissipation (recycling / reversible computation), and disease control.
Nick Land
Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar fields of the theory in question parametrize a symmetric space. Thus, if the non-compact symmetry group is G, and its maximal compact subgroup is H, the scalar fields map the space-time into the symmetric space G/H, and the number of scalar fields is dim G – dim H. The first supergravity example of this type to be found, N = 4 supergravity is one of the most interesting. In this case there are two scalar fields and the symmetric space is SL(2,R)/SO(2).
John Henry Schwarz
In 1917 Levi-Civita discovered his celebrated parallelism which is an infinitesimal transportation of tangent vectors preserving the scalar product and is the first example of a connection. The salient fact about the Levi-Civita parallelism is the result that it is the parallelism, and not the Riemannian metric, which accounts for most of the properties concerning curvature.
Shiing-Shen Chern
In a previous paper we showed that a static (nonrotating) black hole cannot be endowed with exterior scalar-meson or massive vector-meson fields. Here we show that the same is true for massive spin-2 meson fields. We also extend the above results to the case of a rotating stationary black hole. We conclude from our results that a black hole in its final (static or stationary) state cannot interact with the exterior world via the strong interactions which are mediated by meson fields such as the π (scalar), ρ (vector), and ƒ (spin-2). A direct consequence of this is the impossibility of determining the baryon number of the black hole by means of exterior measurements alone. This results in the transcendence of the law of baryon-number conservation as originally predicted by Wheeler.
Jacob Bekenstein
