Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)
arXiv:2204.04742 · doi:10.1140/epjp/s13360-022-03348-5
Abstract
The article is devoted to the investigation of the Noether currents and integrals of motion in the special subclass of theories with higher field derivatives -- theories under differential field transformations in action (DFTA). Under fairly general assertions, we derive a simple representation for the integrals as sums of "old" integrals of motion, terms, that vanishes on the "old" equations of motion and surface integrals. We show that for some cosmological theories of that kind with high order derivatives the last contribution can violate gauge invariance, specifically, diffeomorphisms. Then we investigate ambiguity of the Noether procedure for higher derivative theories and fix it in the way the problem resolves in quite general setting. The obtained results are discussed for the several extensions of the General Relativity, which are obtained by DFTA, in particular, for mimetic, disformal and Regge-Teitelboim theories of gravity.
References in corpus (64)
- f(R) Theories Of Gravity
- Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
- Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
- Black Hole Entropy is Noether Charge
- Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
- The Gravitational Hamiltonian, Action, Entropy, and Surface Terms
- Covariant theory of asymptotic symmetries, conservation laws and central charges
- Local BRST cohomology in gauge theories
- The Relation between Physical and Gravitational Geometry
- Testing General Relativity in Cosmology
- Mimetic Dark Matter
- Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
- Cosmology with Mimetic Matter
- Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
- Mimetic gravity: inflation, dark energy and bounce
- On the recently proposed Mimetic Dark Matter
- Covariant phase space with boundaries
- Relativistic conservation laws and integral constraints for large cosmological perturbations
- Higher derivative theories with constraints : Exorcising Ostrogradski's Ghost
- Disformal Transformations, Veiled General Relativity and Mimetic Gravity
- Cosmological perturbations in modified teleparallel gravity models
- Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
- The Energy-Momentum Tensor for the Gravitational Field
- Energy-Momentum Conservation in General Relativity
- Covariant Horava-like and mimetic Horndeski gravity: cosmological solutions and perturbations
- Local BRST cohomology in Einstein--Yang--Mills theory
- Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach
- Alive and well: mimetic gravity and a higher-order extension in light of GW170817
- Recovering a MOND-like acceleration law in mimetic gravity
- The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
- Correspondence of Gravity Singularities in Jordan and Einstein Frames
- Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
- Accelerating Cosmology and Phase Structure of F(R) Gravity with Lagrange Multiplier Constraint: Mimetic Approach
- Geodetic Brane Gravity
- Noether's Second Theorem and Ward Identities for Gauge Symmetries
- Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity
- On the quantisation of gravity by embedding spacetime in a higher dimensional space
- Ghost-Free Gravity with Lagrange Multiplier Constraint
- New Modified Mimetic Gravity
- Geometric formulation of the Covariant Phase Space methods with boundaries
- Mimetic Black Holes
- Gauge Field Mimetic Cosmology
- Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity
- Embeddings for Schwarzschild metric: classification and new results
- Constraint algebra for Regge-Teitelboim formulation of gravity
- On covariant phase space methods
- Cosmology in Mimetic SU(2) Gauge Theory
- Asymptotically Free Mimetic Gravity
- Forms of action for perfect fluid in General Relativity and mimetic gravity
- Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity
- Non-relativistic limit of embedding gravity as General Relativity with dark matter
- Hamiltonian dynamics of extended objects
- Modifications of gravity via differential transformations of field variables
- Energy-Momentum of the Gravitational Field: Crucial Point for Gravitation Physics and Cosmology
- Invariant conserved currents in generalized gravity
- Noether currents for the Teukolsky Master Equation
- Noether's theorems and conserved currents in gauge theories in the presence of fixed fields
- Comments on conformal masses, asymptotics backgrounds and conservation laws
- Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space
- External time canonical formalism for gravity in terms of embedding theory
- Hamilton-Jacobi approach for Regge-Teitelboim cosmology
- Gravitational energy in the framework of embedding and splitting theories
- The problem of motion in gauge theories of gravity
- Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form