Unitarity through PT symmetry in Quantum Quadratic Gravity

TL;DR

This paper shows how quantum quadratic gravity can be reformulated as a PT-symmetric non-Hermitian theory, leading to a unitary quantum framework that avoids ghost issues present in the Hermitian version.

Contribution

It introduces a complex deformation of quantum quadratic gravity into a PT-symmetric form, ensuring unitarity and ghost-free behavior.

Findings

Quantum quadratic gravity can be PT-symmetrized to restore unitarity.

The PT-symmetric formulation avoids the ghost problem.

The theory admits a consistent quantum probability interpretation.

Abstract

Theories described by non-Hermitian Hamiltonians are known to possess strictly positive energy eigenvalues and exhibit unitary time evolution if the Hamiltonian is symmetric under discrete parity and time (PT) transformation. In this work, we demonstrate how quantum quadratic gravity, a theory that generally violates unitarity when viewed as a Hermitian quantum field theory, can be complex-deformed into such a PT-symmetric theory with an action that consists of a ghost-less Hermitian free part and non-Hermitian interactions. Paying special attention to the gauge symmetry present in the theory, we quantize in the covariant operator formalism after suggesting how the framework might be extended to the pseudo-Hermitian picture. We find compelling evidence that the resulting quantum theory possesses a unitary inner product and a sensible interpretation of quantum probability, thus avoiding the ghost problem present in the Hermitian formulation of quadratic gravity.