Subtleties of Lorentz Invariance in Relativistic Constituent Quark Models of the Nucleon and the Spin-Dependent Quark Density

Abstract

We study the effects of a barely perceivable violation of Lorentz invariance on results computed using a relativistic constituent quark model wave function. The model nucleon wave function of Gross {\it et al.} is constructed such thatthere is no orbital angular momentum and that the spin-dependent density is spherical. This model wave function is claimed to be manifestly covariant, but we show that this is not so. In particular,the seeming covariance of the matrix elements of the electromagnetic current arises from using the Breit frame. Matrix elements have a different appearance in any other frame.