Hamiltonian approach to the torsional anomalies and its dimensional ladder

Torsion can cause various anomalies in various dimensions, including the (3 + 1)-dimensional [(3 1)D] Nieh-Yan anomaly, the (2 + 1)D Hughes-Leigh-Fradkin (HLF) parity anomaly, and the (3 + 1)D, (1 + 1)D chiral energy-momentum anomaly. We study these anomalies from the Hamiltonian approach. We derive the (1 + 1)D chiral energy-momentum anomaly from the single-body Hamiltonian. We then show how other torsional anomalies can be related to the (1 + 1)D chiral energy-momentum anomaly in a straightforward way. Finally, the Nieh-Yan anomaly and the (3 + 1)D chiral energy-momentum anomaly are obtained from the parity anomaly and the HLF effective action, respectively. Hence, we have constructed the dimensional ladder for the torsional anomalies from the single-body Hamiltonian picture.