A Quantum Anomaly For Rigid Particles

TL;DR

This paper investigates the canonical quantisation of rigid particles, revealing a Lorentz-gravitational anomaly that affects the invariance of physical states under Lorentz transformations, with implications for rigid strings.

Contribution

It identifies a mixed Lorentz-gravitational anomaly in the quantisation of rigid particles, highlighting a fundamental symmetry breaking in the gauge-invariant subspace.

Findings

Discovery of a Lorentz-gravitational anomaly in the commutator of boosts and reparametrisations

Physical state subspace is not Lorentz invariant due to the anomaly

Implications for the quantisation of rigid strings

Abstract

Canonical quantisation of rigid particles is considered paying special attention to the restriction on phase space due to causal propagation. A mixed Lorentz-gravitational anomaly is found in the commutator of Lorentz boosts with world-line reparametrisations. The subspace of gauge invariant physical states is therefore not invariant under Lorentz transformations. The analysis applies for an arbitrary extrinsic curvature dependence with the exception of only one case to be studied separately. Consequences for rigid strings are also discussed.