Abstract
We introduce and develop the theory of metaparticles. At the classical level, this is a world-line theory with the usual reparameterization invariance and two additional features. The theory is motivated by string theory on compact targets, and can be thought of, at least at the non-interacting 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 non-trivial symplectic form on the metaparticle phase space, also motivated by string theory [1, 2]. Because of its interpretation as a particle model on Born geometry, the space-time 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.
Highlights
The advent of Born geometry [1,2], as describing a target geometry of string theory upon which T-duality acts as a linear symmetry [3], presents us with many deep conceptual issues
Born geometries [3,4] may be viewed as the proper generalization of double field theory and generalized geometry [6] and has recently been understood in terms of globally well-defined para-Hermitian structures [7,8,9]
With such structure,strings propagate generally on a target space for which our usual notion of spacetime is a subspace, usually of half-dimension; under suitable circumstances, this subspace is a Lagrangian subspace with respect to a symplectic form which is part of the defining structure of a para-Hermitian geometry and whose presence and significance in string theory has only recently been realized
Summary
The advent of Born geometry [1,2], as describing a target geometry of string theory upon which T-duality acts as a linear symmetry [3], presents us with many deep conceptual issues. Much as for an ordinary relativistic free particle propagating in spacetime, there is an equivalent phase space formulation in which reparametrization invariance of the world line is ensured by the presence of a Hamiltonian constraint, which generates a corresponding canonical transformation on the phase space variables XAðτÞ, PAðτÞ. At first sight, such a model must surely be sick, as there are two timelike directions, x0 and x0. In addition to the Hamiltonian constraint, which reads
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