DBI-type tachyons for inverse cosh potential

Abstract

We consider classical and quantum dynamics of a tachyonic system described by a DBI type Lagrangian and inverse cosh potential. This investigation is partially motivated by the string theory and D-brane dynamics, but mostly by their application in cosmological inflation. A formalism for describing dynamics of spatially homogenous tachyon scalar field with this kind of potentials is developed. Classical actions and corresponding quantum propagators in the Feynman path integral approach, both on real and nonarchimedean spaces, are calculated. Possibilities for a quantum adelic generalization of these models are noticed. Cosmological applications are pointed out and discussed.

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

“…We find conditions for the existence of this type of s vacuum state. Investigation of other possible vacuum states and for p = 2 is a rather technical issue and will be presented elsewhere [29].…”

Classicalization and Quantization of Tachyon-like Matter on (non)Archimedean Spaces

“…In the light of the above discussion on tahyonic dynamics on (non)-Archemedean spaces, a natural question arises: is it possible to simplify the equation of motion ( 8) and, if it is possible, in which cases could that be done [23,24,28,29]? Further, is it possible to quantize the models, at least for some particular potentials?…”

“…The necessary conditions for the existence of ground states in the form of the characteristic Ω-function are "dictated" by the expression (52), from which the necessary restriction on the values of the parameters of the theory can be found [29]. For p = 2 the necessary conditions are…”

“…We will show that for certain choices of generating function of canonical transformation the equation of motion simplify significantly. At this point one can involve Lagrangian of the standard type which corresponds to the same equation of motion and which is locally equivalent [28,29]. It allows us to quantize the simplified (toy) model, obtain quantum propagator and vacuum states in p-adic and adelic framework, as well as discuss their basic physical consequences.…”