SCALE SYMMETRY BREAKING FROM THE DYNAMICS OF MAXIMAL RANK GAUGE FIELD STRENGTHS

Abstract

Scale invariant theories which contain maximal rank gauge field strengths (of D indices in D dimensions) are studied. The integration of the equations of motion of these gauge fields leads to the scale symmetry breaking of scale invariance. The cases in study are (i) the spontaneous generation of r-1 potentials in particle mechanics in a theory that contains only r-2 potentials in the scale invariant phase, (ii) mass generation in scalar field theories, (iii) generation of nontrivial dilaton potentials in generally covariant theories, and (iv) spontaneous generation of confining behavior in gauge theories. The possible origin of these models is discussed.