Second Order Perturbations of a Macroscopic String; Covariant Approach

Details Second Order Perturbations of a Macroscopic String; Covariant Approach Second Order Perturbations of a Macroscopic String; Covariant Approach

2000-09-20

arxiv.org/abs/hep-th/0009151v2

Phys.Rev. D63 (2001) 125006

Physics

High Energy Physics

High Energy Physics - Theory

New discussion about the quantum mass-spectrum in chapter 4

Scientific paper

10.1103/PhysRevD.63.125006

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessaary for a consistent computation of the energy. We also quantize the perturbations and derive the mass-formula up to second order in perturbations for an observer using world-sheet time $\tau $. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be non-diagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass-spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.

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