ON THE FORM OF LOCAL CONSERVATION-LAWS FOR SOME RELATIVISTIC FIELD-THEORIES IN 1+1 DIMENSIONS

We investigate the possible form of local translation-invariant conser vation laws associated with the relativistic field equations partial d erivativepartial-differential-equationphi(i) = -v(i)(phi) for a multic omponent field phi. Under the assumptions that (i) the v(i)'s can be e xpressed as linear combinations of partial derivatives partial derivat ivew(j)/partial derivativephi(k) of a set of functions w(j) (phi), (ii ) the space of functions spanned by the w(j)'s is closed under partial derivations, and (iii) the fields phi take values in a simply connect ed space, the local conservation laws can be transformed either to the form partial-derivativePBAR = partial-differential-equation SIGMA(j) w(j) Q(j) (where PBAR and Q(j) are homogeneous polynomials in the vari ables partial-differential-equationphi(i), partial-differential-equati on2phi(i),...), or to the parity-transformed version of this expressio n, partial derivative = (partial derivative(t) + partial derivative(x) )/square-root2 reversible partial-differential-equation = (partial der ivative(t) - partial derivative(x))/square-root2.