Generalized Conformal Symmetry and Extended Objects from the Free Particle

TL;DR

This paper explores how quantizing free particles and harmonic oscillators reveals a new spin-like degree of freedom linked to extended symmetries, with implications for understanding extended objects in physics.

Contribution

It introduces a novel degree of freedom arising from anomaly quantization and connects it to extended objects via generalized diffeomorphism algebras.

Findings

Identification of a new spin-like degree of freedom

Connection to Weyl-symplectic group transformations

Potential implications for extended object theories

Abstract

The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group $WSp(6,\Re)$. The physical meaning of this new degree of freedom can be established, with a major scope, only by analysing the quantization of an infinite-dimensional algebra of diffeomorphisms generalizing string symmetry and leading to more general extended objects.