Relativistic Rigid Particles: Classical Tachyons and Quantum Anomalies

TL;DR

This paper explores classical and quantum properties of relativistic rigid particles with arbitrary extrinsic curvature dependence, revealing causal tachyonic solutions, gauge symmetries, and a Lorentz anomaly affecting physical state invariance.

Contribution

It provides a detailed Hamiltonian formulation, identifies gauge symmetries, and performs canonical quantization, uncovering a Lorentz-gravitational anomaly in rigid particle models.

Findings

Existence of causal tachyonic solutions.

Identification of gauge symmetries and phase space structure.

Discovery of a Lorentz anomaly affecting physical states.

Abstract

Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian formulation is developed in detail except for one degenerate situation for which only partial results are given and requiring a separate analysis. However, for otherwise generic rigid particles, the precise specification of Hamiltonian gauge symmetries is obtained with in particular the identification of the Teichm$\ddot{\rm u}$ller and modular spaces for these systems. Finally, canonical quantisation of the generic case is performed paying special attention to the phase space restriction 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. Consequences for rigid strings and membranes are also discussed.