Semiclassical Strings in (2+1)-Dimensional Backgrounds

Abstract

This study analyzes the geometrical relationship between a classical string and its semi-classical quantum model. From an arbitrary (2 + 1)−dimensional geometry, a specific ansatz for a classical string is used to generate a semi-classical quantum model. In this framework, examples of quantum oscillations and quantum free particles are presented that uniquely determine a classical string and the spacetime geometry where its motion takes place.

The Static String

“…Quantum fluctuation depends on the function g, which determines the geometry of the space and the momentum operatorΠ. Some possibilities for g have already been discussed in the context of moving strings [3], and we bring them to the context of the static string in the next section.…”

“…where E = √ λṫ andṫ = κ have been used as the classical energy of the string andṫ 2 = g 2 y ′ 2 has been used from (3). Thus, the quantum solutions are free particles whose squared energy is given by the difference between the squared classical energy E 2 and the squared quantum…”

“…The possibility of a classical string being used to construct a quantum model enables us to establish a relation between string theory and quantum mechanics. The quantum harmonic oscillator has already been obtained from a classical pulsating string [1] in Minkowski spacetime, and a generalization of this method has obtained a variety of quantum models in different space times [3]. In this article we go further and determine that the quantum free particle may be obtained from a classical static string.…”

“…We develop this point further by calculating the differences in the quantum fluctuations of a static string in a (2 + 1)−dimensional space both with and without the effect of the other coordinates of the space. This idea has already been explored in the case of pulsating strings and of free falling strings [3], and in this article we propose to extend it to static strings. The results indicate that the dimension of the space may indeed contribute to quantum fluctuations, but the (2 + 1)−dimensional is interesting as a toy model in order to conceptualize an understanding of the problem.…”

Axisymmmetric Empty Space: Light Propagation, Orbits and Dark Matter

“…When the parameter is set to zero, the deformed sphere becomes the usual five dimensional sphere and consequently the Lunin-Maldacena space recovers AdS 5 × S 5 in this limit. Some other axisymmetric space-times have been used in semi-classical string theory [2,3].…”