Correlators for pseudo Hermitian systems

TL;DR

This paper develops a formalism to compute cosmological correlators in pseudo-Hermitian systems, specifically analyzing a model with symplectic fermions, and finds that one-loop corrections are indistinguishable from scalar bosons in certain cases.

Contribution

It introduces in-in and Schwinger Keldysh formalisms for pseudo-Hermitian systems and applies them to a cosmological model involving symplectic fermions.

Findings

One-loop three-point functions differ by a minus sign from scalar boson models.

The correction cannot distinguish between scalar bosons and symplectic fermions.

Discussion on potential methods to differentiate these particles.

Abstract

Pseudo-Hermitian system is a class of non-Hermitian system with Hamiltonian satisfying the condition $\eta^{-1}H^\dagger\eta=H$. We develop the in-in and Schwinger Keldysh formalism to calculate cosmological correlators for pseudo-Hermitian systems. We study a model consists of massive symplectic fermions coupled to the primordial curvature perturbation. The three-point function for the primordial curvature perturbation is computed up to one-loop and compared to earlier work where the loop correction comes from a massive scalar boson. The two results differ by a minus sign. Therefore, the one loop correction to the three-point function cannot be used to distinguished scalar bosons and symplectic fermions. To conclude, we discuss possibilities where the scalar bosons and symplectic fermions may be distinguished.