Higher Derivative Field Theories: Degeneracy Conditions and Classes
arXiv:1703.01623 · doi:10.1007/JHEP06(2017)124
Abstract
We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.
26 pages, 1 figure. v2: minor changes, references added, matches version published in JHEP
References in corpus (15)
- Resummation of Massive Gravity
- Covariant Galileon
- Healthy theories beyond Horndeski
- Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
- Exploring gravitational theories beyond Horndeski
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Multi-field galileons and higher co-dimension branes
- Bi-galileon theory I: motivation and formulation
- Third order equations of motion and the Ostrogradsky instability
- Degrees of Freedom in Massive Gravity
- Generalized Galileon Duality
- Lagrangian approach to the physical degree of freedom count
- Field redefinitions in theories beyond Einstein gravity using the language of differential forms
- Tensor Galileons and Gravity
- New terms for scalar multi-Galileon models and application to SO(N) and SU(N) group representations
Cited by in corpus (49)
- Horndeski theory and beyond: a review
- Dark Energy and Modified Gravity in Degenerate Higher-Order Scalar-Tensor (DHOST) theories: a review
- Dark Energy in light of Multi-Messenger Gravitational-Wave astronomy
- Vainshtein mechanism after GW170817
- Beyond Lovelock gravity: Higher derivative metric theories
- Self-accelerating universe in scalar-tensor theories after GW170817
- Extended Cuscuton: Formulation
- Mimetic gravity as DHOST theories
- Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories
- Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
- Ghost-free theory with third-order time derivatives
- Ghost-free theories with arbitrary higher-order time derivatives
- Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
- Effective loop quantum cosmology as a higher-derivative scalar-tensor theory
- On avoiding Ostrogradski instabilities within Asymptotic Safety
- First-order thermodynamics of Horndeski gravity
- Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis
- Cosmological perturbations and stability of nonsingular cosmologies with limiting curvature
- Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
- Cosmological evolution in DHOST theories
- A Lagrangian constraint analysis of first order classical field theories with an application to gravity
- Geometric Lagrangian approach to the physical degree of freedom count in field theory
- Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy
- Minimally modified theories of gravity: a playground for testing the uniqueness of general relativity
- Spontaneously Broken Spacetime Symmetries and the Role of Inessential Goldstones
- Spatially covariant gravity: Perturbative analysis and field transformations
- Higher derivative scalar-tensor theory through a non-dynamical scalar field
- Wave propagation and shock formation in the most general scalar-tensor theories
- More on the first-order thermodynamics of scalar-tensor and Horndeski gravity
- Foundations of ghost stability
- Reflection positivity in higher derivative scalar theories
- Tackling non-linearities with the effective field theory of dark energy and modified gravity
- Perturbative reduction of derivative order in EFT
- Constraint characterization and degree of freedom counting in Lagrangian field theory
- Disformal mappings of spherical DHOST geometries
- Ghost free boson-fermion co-existence system
- Reconciling tensor and scalar observables in G-inflation
- To Half--Be or Not To Be?
- Ghost-free scalar-fermion interactions
- On Lorentz-invariant spin-2 theories
- Canonical aspects of pregeometric vector-based first order gauge theory
- Ghosts in higher derivative Maxwell-Chern-Simon's theory and symmetry
- Avoiding Big Rip Singularities in Phantom Scalar Field theory with Gauss-Bonnet term
- Degenerate Horava gravity
- New time-dependent solutions of viable Horndeski gravity
- Higher time derivatives in the microcanonical ensemble describe dynamics of flux-coupled classical and quantum oscillators
- Symplectic quantization of multi-field Generalized Proca electrodynamics
- Reducing the O(3) model as an effective field theory
- Construction of consistent interactions in higher derivative Yang-Mills gauge theory with matter fields