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+1D Hughes-Leigh-Fradkin (HLF) parity anomaly, and the 3+1D, 1+1D chiral energy-momentum anomaly. We study these anomalies from the Hamiltonian approach. We derive the 1+1D chiral energy-momentum anomaly from the single-body Hamiltonian. We then show how other torsional anomalies can be related to the 1+1D chiral energy-momentum anomaly in a straightforward way. Finally, the Nieh-Yan anomaly and the 3+1D 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.