Quantum Vacuum and Anomalies

Chiral, conformal and ghost number anomalies are discussed from the viewpoint of the quantum vacuum in Hamiltonian formalism. After introducing the energy cut-off, we derive known anomalies in a new way. We show that the physical origin of the anomalies is the zero point fluctuation of bosonic or fermionic field. We first point out that the chiral U(1) anomaly is understood as the creation of the chirality at the bottom of the regularized Dirac sea in classical electromagnetic field. In the study of the (1+1) dimensional quantum vacuum of matter field coupled to the gravity, we give a physically intuitive picture of the conformal anomaly. The central charges are evaluated from the vacuum energy. We clarify that the non-Hermitian regularization factor of the vacuum energy is responsible for the ghost number anomaly.