Higher Derivative Scalar Quantum Field Theory in Curved Spacetime

Abstract

We study a free scalar field $\varphi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(\square )\varphi =0$, where $F$ is a polynomial of the form $F(\square )={\prod }_i(\square -m_i^2)$ and all masses $m_i$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantisation and briefly discuss the issue of negative energy versus negative norm and its relation to Reflection Positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish non-existence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background, and show how the Hubble friction may eliminate what would otherwise be unstable behaviour when interactions are included.

41 pages

References in corpus (11)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Metastability in Quadratic Gravity
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• Pais-Uhlenbeck Oscillator and Negative Energies
• Inflation with a Weyl term, or ghosts at work
• Quantum Field Theory on Curved Backgrounds, I. The Euclidean Functional Integral
• Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants
• Reflection Positivity and Monotonicity
• Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries
• Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and their cosmological applications
• Higher time derivatives in the microcanonical ensemble describe dynamics of flux-coupled classical and quantum oscillators

Cited by in corpus (20)

• Massive gravity generalization of $T\overline{T}$ deformations
• Quasinormal Modes of C-metric from SCFTs
• Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories
• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
• On the initial value problem for semiclassical gravity without and with quantum state collapses
• Resonance and stability of higher derivative theories of derived type
• Anomalies in Covariant Fracton Theories
• Opus on conformal symmetry of the Nambu-Goto versus Polyakov strings
• World-line Path integral for the Propagator expressed as an ordinary integral: Concept and Applications
• A class of QFTs with higher derivative field equations leading to standard dispersion relation for the particle excitations
• Generalized Abelian Gauge Field Theory under Rotor Model
• Cosmology in $R^2$-gravity: Effects of a Higher Derivative Scalar Condensate Background
• Quantum fluctuation of stress tensor in a higher-derivative scalar field theory around a cosmic string
• Generalized Yang-Mills Theory under Rotor Mechanism
• Configurable photonic simulator for quantum field dynamics
• Calculations in induced gravity from higher-derivative field theories
• Pseudodifferential calculus in Schwinger--DeWitt formalism: UV and IR parts
• A classical mechanical model of two interacting massless particles in de Sitter space and its quantization
• Quantization of Generalized Abelian Gauge Field Theory under Rotor Model
• Extended Chern-Simons model for a vector multiplet