Algebric generalization of symmetry Dirac bracket. Application to field theory

The A set of observable of a physical system with finite e infinite number of degrees of freedom and submitted to certain constraint conditions, is considered. Using jordan algebra structure on A in relation to bymmetric Poisson bracket obtained by Droz-Vincent, a jordan product is obtained on the A/I quocient set with regard to I ideal generated by constraints of second class. It is shown that this product on A/I corresponds to symmetric Dirac bracket. The developed formulation is applied to a system corresponding to harmonic oscillators, non relativistic field, Rarita-Schwinger field and the possibility of its utilization in fermionic string theories is discussed. (M.C.K.)