On Canonical Transformation and Tachyon Like "Particles" in Inflationary Cosmology
We examine a classical and quantum dynamics of systems described by the DBItype Lagrangian with tachyon like potentials and corresponding DBI Lagrangians on (non )Archimedean spaces. The dynamic of tachyon fields in spatially homogeneous and in zero dimensional limits is analysed. A formalism for connecting a wide class of potentials and DBI Lagrangians with the locally equivalent canonical Lagrangians is presented. The results for exponentially decaying and inverse cosine hyperbolic are reviewed and for the potentials of the form V (x) x n are discussed in more details. Classical actions and corresponding quantum propagators are calculated for these potentials in the Feynman path integral approach, on both Archimedean and nonArchemedean spaces.