Basics in Conformal Field Theory

The approach for studying Conformal Field Theories is somewhat different from the usual approach for Quantum Field Theories. Because, instead of starting with a classical action for the fields and quantising them via the canonical quantisation or the path integral method, one employs the symmetries of the theory. In the spirit of the so-called boot-strap approach, for CFTs one defines and for certain cases even solves the theory just by exploiting the consequences of the symmetries. Such a procedure is possible in two dimensions because the algebra of infinitesimal conformal transformations in this case is very special: it is infinite dimensional.