A Born–Infeld scalar and a dynamical violation of the scale invariance from the modified measure action

Starting with a simple two-scalar field system coupled to a modified measure that is independent of the metric, we, first, find a Born–Infeld dynamics sector of the theory for a scalar field and second, show that the initial scale invariance of the action is dynamically broken and leads to a scale charge nonconservation, although there is still a conserved dilatation current.

FIELD THEORY OF MASSIVE AND MASSLESS VECTOR PARTICLES IN THE DUFFIN–KEMMER–PETIAU FORMALISM

Field theory of massive and massless vector particles is considered in the first-order formalism. The Hamiltonian form of equations is obtained after the exclusion of nondynamical components. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken in the massive case but in the massless case the modified dilatation current is conserved. The canonical quantization is performed and the propagator of the massive fields is found in the Duffin–Kemmer–Petiau formalism.

KALB–RAMOND FIELDS IN THE PETIAU–DUFFIN–KEMMER FORMALISM AND SCALE INVARIANCE

Kalb–Ramond equations for massive and massless particles are considered in the framework of the Petiau–Duffin–Kemmer formalism. We obtain 10×10 matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy–momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.