Proof of the most general multiple-scalar field theory in Minkowski space-time free of Ostrogradski Ghost

TL;DR

This paper proves the most general multi-scalar field theory in flat space-time that avoids Ostrogradski ghosts, ensuring stability by constraining the derivative order of the field equations.

Contribution

It establishes the complete form of multi-scalar theories in Minkowski space free of Ostrogradski instabilities, including all physically viable models.

Findings

Identifies the most general scalar field theory with second-order equations.

Ensures the absence of Ostrogradski ghosts in the constructed theories.

Provides a foundational framework for stable multi-scalar field models.

Abstract

We give a proof of the most general multiple scalar field theory in flat space-time free of Ostrogradski ghosts. We start from the assumption that the action is a functional of the scalar fields and their derivatives of order upto two (which in general can have field equations of derivative order up to four), and arrive at the most-general field theory that can be constructed such that the field equations are of derivative order up to two. Naturally, this theory includes all physically viable multi-scalar field theories in flat space-time, in the sense that they don't suffer from Ostrogradski instability \cite{ostro}.