Constraint Superalgebras and Their Application to Gauge Field Theories and String Theories

We show that with every classical system possessing first class constraints that form a natural Lie algebra, we can associate a superalgebra that admits the constraint Lie algebra as a subalgebra. An odd generator of this superalgebra that commutes with the constraints is shown to be the BRST operator whose form follows from a non linear coset representation of the superalgebra. We further show the existence of the superalgebra for all Yang-Mills theories and for 26-dimensional bosonic strings.