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Hamiltonian approach to the torsional anomalies and its dimensional ladder

Torsion can cause various anomalies in various dimensions, including the $\left(3+1\right)$-dimensional $[(3+1)D]$ Nieh-Yan anomaly, the $\left(2+1\right)$D Hughes-Leigh-Fradkin (HLF) parity anomaly, and the $\left(3+1\right)$D, $\left(1+1\right)$D chiral energy-momentum anomaly. We study these anomalies from the Hamiltonian approach. We derive the $\left(1+1\right)$D chiral energy-momentum anomaly from the single-body Hamiltonian. We then show how other torsional anomalies can be related to the $\left(1+1\right)$D chiral energy-momentum anomaly in a straightforward way. Finally, the Nieh-Yan anomaly and the $\left(3+1\right)$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.