Invertibility conditions for field transformations with derivatives: Toward extensions of disformal transformation with higher derivatives
| Autor: | Masahide Yamaguchi, Norihiro Tanahashi, Eugeny Babichev, Keisuke Izumi |
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| Přispěvatelé: | Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Cosmology and Nongalactic Astrophysics (astro-ph.CO) Differential equation FOS: Physical sciences General Physics and Astronomy Field (mathematics) General Relativity and Quantum Cosmology (gr-qc) derivative: high Type (model theory) 01 natural sciences General Relativity and Quantum Cosmology law.invention law 0103 physical sciences 010306 general physics Mathematical Physics Physics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] 010308 nuclear & particles physics Degrees of freedom differential equations Mathematical Physics (math-ph) Simple extension field theory: scalar Invertible matrix Transformation (function) High Energy Physics - Theory (hep-th) [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph] Scalar field Astrophysics - Cosmology and Nongalactic Astrophysics |
| Zdroj: | Progress of Theoretical and Experimental Physics |
| ISSN: | 2050-3911 |
| Popis: | We discuss a field transformation from fields $\psi_a$ to other fields $\phi_i$ that involves derivatives, $\phi_i = \bar \phi_i(\psi_a, \partial_\alpha \psi_a, \ldots ;x^\mu)$, and derive conditions for this transformation to be invertible, primarily focusing on the simplest case that the transformation maps between a pair of two fields and involves up to their first derivatives. General field transformation of this type changes number of degrees of freedom, hence for the transformation to be invertible, it must satisfy certain degeneracy conditions so that additional degrees of freedom do not appear. Our derivation of necessary and sufficient conditions for invertible transformation is based on the method of characteristics, which is used to count the number of independent solutions of a given differential equation. As applications of the invertibility conditions, we show some non-trivial examples of the invertible field transformations with derivatives, and also give a rigorous proof that a simple extension of the disformal transformation involving a second derivative of the scalar field is not invertible. Comment: 38 pages. v2: typos corrected, published version |
| Databáze: | OpenAIRE |
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