Thus, sum of introduced occupation number operators. This operator is well defined in the constructed space of states. One can also add to an arbitrary constant It includes possible terms, which appear if some finite number of products in the sum were not ordered normally. First prove relation . Then calculate commutator where is the dimension of Minkowski space.
Solution is here .
Thus, quantum Virasoro algebra in given representation has anomaly. Coefficient in anomaly term is called central charge . Presence of anomaly implies that and for all k cannot be simultaneously satisfied.