Quantum Einstein-Rosen waves: Coherent states and n-point functions

TL;DR

This paper investigates the quantization of Einstein-Rosen waves, analyzing the use of coherent states for system dynamics and examining the structure of n-point functions, revealing deviations from standard quantum field theory behavior.

Contribution

It demonstrates the limitations of coherent states for full dynamics and characterizes the unique structure of n-point functions in quantum Einstein-Rosen waves.

Findings

Coherent states approximate full dynamics only near the vacuum.

N-point functions differ from standard perturbative quantum field theory.

The relevant approximation scheme is asymptotic, not a power series.

Abstract

We discuss two different types of issues concerning the quantization of Einstein-Rosen waves. First of all we study in detail the possibility of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian appearing in the description of the model to study the full dynamics of the system. For time periods of arbitrary length we show that this is only possible for states that are close, in a precise mathematical sense, to the vacuum. We do this by comparing the quantum evolutions defined by the auxiliary and physical Hamiltonians on the class of coherent states. In the second part of the paper we study the structure of n-point functions. As we will show their detailed behavior differs from the one corresponding to standard perturbative quantum field theories. We take this as a manifestation of the fact that the correct approximation scheme for physically interesting objects in these models does not lead to a power series expansion in the relevant coupling constant but to a more complicated asymptotic behavior.