Lorentz-covariant four-vector formalism for two-measure theory

In the conventional two-measure theory, the scalar density function Φ is taken to be Φ≡ÏμμνρσÏμ _abcd(∂_μφa)(∂_νφb) (∂_ρφc)(∂_σφd), where the indices a,b,c,d=1, 2, 3, 4 are internal-space indices. It is more natural to replace the four scalars φa by a Lorentz-covariant four-vector φm with a local Lorentz index m=(0), (1), (2), (3). We entertain this possibility, and show that the newly proposed Lagrangian respects not only Lorentz covariance, but also global-scale invariance. The crucial equation ∂_μL=0 in the conventional two-measure theory also arises in our new formulation, as the φm-field equation.