Theory of metaparticles

We introduce and develop the theory of metaparticles. At the classical level, this is a world-line theory with the usual reparametrization invariance and two additional features. The theory is motivated by string theory on compact targets and can be thought of, at least at the noninteracting level, as a theory of particles at a given string level, or as a particle model for Born geometries. The first additional feature of the model is the presence of an additional local symmetry, which from the string point of view corresponds to the completion of worldsheet diffeomorphism invariance. From the particle world-line point of view, this symmetry is associated with an additional local constraint. The second feature is the presence of a nontrivial symplectic form on the metaparticle phase space, also motivated by string theory [L. Freidel, R. G. Leigh, and D. Minic, Noncommutativity of closed string zero modes, Phys. Rev. D 96, 066003 (2017)., L. Freidel, R. G. Leigh, and D. Minic, Intrinsic non-commutativity of closed string theory, J. High Energy Phys. 09 (2017) 060.]. Because of its interpretation as a particle model on Born geometry, the spacetime on which the metaparticle propagates is ambiguous, with different choices related by what, in string theory, we would call T-duality. In this paper, we define the model and explore some of its principle classical and quantum properties, including causality and unitarity.

Figure 1

The world line is discretized, with points labelled by $r$, each point on a world line mapping to (${\ell }_r$, ${\tilde{\ell }}_r$). In the continuum limit, we choose to take $r\to \tau$, $x_r\to x(\tau )$, etc. Typical paths, projected to $e$, $\tilde{e}$, are shown for the Feynman propagator and the Hadamard propagator, respectively.