Classical and Quantum Dynamics of Higher-Derivative Systems

Abstract

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however: ghosts are benign. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe represents then a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

29 pages, 6 figures. Final version published in IJMPA

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Cited by in corpus (37)

• Quadratic Gravity
• Unitarity, stability and loops of unstable ghosts
• General Relativity solutions with stealth scalar hair in quadratic higher-order scalar-tensor theories
• Dimensional Transmutation in Gravity and Cosmology
• Gauge Assisted Quadratic Gravity: A Framework for UV Complete Quantum Gravity
• Dynamics of the generalized unimodular gravity theory
• Stable interactions in higher derivative field theories of derived type
• Massive poles in Lee-Wick quantum field theory
• Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants
• One-loop beta-functions in 4-derivative gauge theory in 6 dimensions
• Dynamical systems with benign ghosts
• Foundations of ghost stability
• Effective field theory of degenerate higher-order inflation
• Ghost from constraints: a generalization of Ostrogradsky theorem
• On exactly solvable higher-derivative systems
• Resonance and stability of higher derivative theories of derived type
• Stable interactions between the extended Chern-Simons theory and a charged scalar field with higher derivatives: Hamiltonian formalism
• Conservation Laws and Stability of Field Theories of Derived Type
• The renormalization structure of $6D$, $\mathcal{N}=(1,0)$ supersymmetric higher-derivative gauge theory
• Boundaries in Free Higher Derivative Conformal Field Theories
• Conservation laws and stability of higher derivative extended Chern-Simons
• Higher time-derivative theories from space-time interchanged integrable field theories
• Dark energy with a shift-symmetric scalar field: obstacles, loophole hunting and dead ends
• Stable interactions between higher derivative extended Chern-Simons and charged scalar field
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• Path Integrals in Quadratic Gravity
• Various disguises of the Pais-Uhlenbeck oscillator
• Vacuum radiation and frequency-mixing in linear light-matter systems
• Quantum field theories of relativistic Luttinger fermions
• Witten index for weak supersymmetric systems: invariance under deformations
• Arnold's potentials and quantum catastrophes II
• Lagrangian Formulation of an Infinite Derivative Real Scalar Field Theory in the Framework of the Covariant Kempf-Mangano Algebra in a $(D+1)$-dimensional Minkowski Space-time
• Renormalizable and unitary Lorentz invariant model of quantum gravity
• Gauss-Bonnet Gravity and Spacetime Singularities
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator
• Quasi-isospectral higher-order Hamiltonians via a reversed Lax pair construction