Quantum Vacuum and Anomalies

TL;DR

This paper explores the origins of quantum anomalies through the vacuum fluctuations in Hamiltonian formalism, providing new derivations and physical insights into chiral, conformal, and ghost number anomalies.

Contribution

It offers a novel perspective on anomalies by linking them to zero point fluctuations and introduces a new derivation method using energy cut-off in Hamiltonian formalism.

Findings

Chiral U(1) anomaly arises from chirality creation at the Dirac sea bottom.

Conformal anomaly is explained via vacuum energy in (1+1)D quantum gravity.

Ghost number anomaly is linked to non-Hermitian regularization of vacuum energy.

Abstract

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.