2020/02/05 by Anton Sheykin, A. A. Sheykin, Dmitry Solovyev +5
Mathematics · Physics and Astronomy · #Action (physics) #Algebraic and Geometric Analysis #Cosmology and Gravitation Theories #Differential (mechanical device) #Embedding #Extension (predicate logic) #Field (mathematics) #Field theory (psychology) #Relativity and Gravitational Theory #Simple (philosophy) #Term (time) #Transformation (genetics) #gr-qc #hep-th
paper · pdf · doi:10.3390/sym12020240
published as Symmetry 2020, 12(2), 240 · 18 pages
arxiv created 2020/02/05 · openalex publication_date 2020/02/05 · arxiv updated 2020/02/06 · openalex created_date 2020/02/14 · openalex updated_date 2026/08/05
We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFTs) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the procedure. In this process, the dynamics of the theory might either change or be conserved. After that, we concentrate on the theories of gravity which appear as a result of various DFTs applied to general relativity, namely the mimetic gravity and Regge–Teitelboim embedding theory. We review the main results related to the extension of dynamics in these theories, as well as the possibility to write down the action of a theory after DFTs as the action of the original theory before DFTs plus an additional term. Such a term usually contains some constraints with Lagrange multipliers and can be interpreted as an action of additional matter, which might be of use in cosmological applications, e.g., for the explanation of the effects of dark matter.