A Non-Trivial Zero Length Limit of the Nambu-Goto String

Abstract

We show that a Nambu-Goto string has a nontrivial zero length limit which corresponds to a massless particle with extrinsic curvature. The system has the set of six first class constraints, which restrict the phase space variables so that the spin vanishes. Upon quantization, we obtain six conditions on the state, which can be represented as a wave function of position coordinates, $x^{\mu }$, and velocities, $q^{\mu }$. We have found a wave function $\psi (x,q)$ that turns out to be a general solution of the corresponding system of six differential equations, if the dimensionality of spacetime is eight. Though classically the system is just a point particle with vanishing extrinsic curvature and spin, the quantized system is not trivial, because it is consistent in eight, but not in arbitrary, dimensions.

arXiv comment13 pages; Improved Section 3

References in corpus (11)

• Avoiding Dark Energy with 1/R Modifications of Gravity
• Stable Self-Interacting Pais-Uhlenbeck Oscillator
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• Dynamics of relativistic particle with Lagrangian dependent on acceleration
• W-symmetry and the rigid particle
• Some Comments on Ghosts and Unitarity: The Pais-Uhlenbeck Oscillator Revisited
• Pais-Uhlenbeck Oscillator with a Benign Friction Force
• Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
• Gauge symmetry and W-algebra in higher derivative systems
• Zitterbewegung and reduction: 4D spinning particles and 3D anyons on light-like curves
• Rigid Particle and its Spin Revisited