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K-nonizing

Jose Beltrán Jiménez, Teodor Borislavov Vasilev, Darío Jaramillo-Garrido, Antonio L. Maroto, Prado Martín-Moruno

Abstract

We unveil the dynamical equivalence of field theories with non-canonical kinetic terms and canonical theories with a volume element invariant under transverse diffeomorphisms. The proof of the equivalence also reveals a subtle connection between the standard Legendre transformation and the so-called Clairaut equation. Explicit examples of canonizable theories include classes of $k$-essence, non-linear electrodynamics, or $f(R)$ theories. The equivalence can also be extended to the class of mimetic theories.

K-nonizing

Abstract

We unveil the dynamical equivalence of field theories with non-canonical kinetic terms and canonical theories with a volume element invariant under transverse diffeomorphisms. The proof of the equivalence also reveals a subtle connection between the standard Legendre transformation and the so-called Clairaut equation. Explicit examples of canonizable theories include classes of -essence, non-linear electrodynamics, or theories. The equivalence can also be extended to the class of mimetic theories.

Paper Structure

This paper contains 33 equations, 1 figure.

Figures (1)

  • Figure 1: Solutions of Clairaut's equation for the Born-Infeld model $K(X) = -\sqrt{1 - X}$. The straight line solutions generate the envelope (singular) solution $H(Y)$. The solid black line denotes the branch $X\geq 0$ of the singular solution, whereas the $X<0$ branch is shown in dashed black.