On Weyl's Gauge Field

Abstract

A new scalar field, called a measure field, is proposed which plays a role of measure assigned to each world point. By measuring all the quantities with a standard given by the above mentioned measure field, it is shown to be possible to write all the field equations in a manifestly gauge-invariant manner. Weyl's gauge field, when it is written in this fashion, is proved to have a negative energy density and has a tachyon-like property inside material particles. It is shown, however, that such a strange field can not come out of the matter.