New Dynamical Degrees of Freedom from Invertible Transformations

Abstract

We show that invertible transformations of dynamical variables can change the number of dynamical degrees of freedom. Moreover, even in cases when the number of dynamical degrees of freedom remains unchanged, the resulting dynamics can be essentially different from the one of the system prior to transformation. After giving concrete examples in point particle cases, we discuss changes in dynamics due to invertible disformal transformations of the metric in gravitational theories

21 pages, plus references, plus 2 figures, added a discussion on spontaneous symmetry breaking

References in corpus (15)

• Avoiding Dark Energy with 1/R Modifications of Gravity
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Cosmology with Mimetic Matter
• On causality and superluminal behavior in classical field theories. Applications to k-essence theories and MOND-like theories of gravity
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
• Imperfect Dark Matter
• Invertible disformal transformations with higher derivatives
• Modified Dust and the Small Scale Crisis in CDM
• Generalized disformal Horndeski theories: cosmological perturbations and consistent matter coupling
• Losing the trace to find dynamical Newton or Planck constants
• Disforming to Conformal Symmetry
• Invertibility conditions for field transformations with derivatives: toward extensions of disformal transformation with higher derivatives
• The Variational principle, Conformal and Disformal transformations, and the degrees of freedom
• Generalized unimodular gravity as a form of k-essence

Cited by in corpus (4)

• Generalisation of Conformal-Disformal Transformations of the Metric in Scalar-Tensor Theories
• On the degrees of freedom count on singular phase space submanifolds
• Collapsing scenarios of K-essence generalized Vaidya spacetime under $f(\bar{R},\bar{T})$ gravity
• Jackiw-Teitelboim Gravity Generates Horndeski via Disformal Transformations