Propagator for the free relativistic particle on Archimedean and no Archimedean spaces

Abstract

We consider dynamics of a free relativists particle at very short distances treating space-time as Archimedean as well as no Archimedean one. Usual action for the relativistic particle is nonlinear. Meanwhile, in the real case, that system may be treated like a system with quadratic (Hamiltonian) constraint. We perform similar procedure in p-adic case, as the simplest example of a no Archimedean space. The existence of the simplest vacuum state is considered and corresponding Green function is calculated. Similarities and differences between obtained results on both spaces are examined and possible physical implications are discussed.

Non-archimedean quantum cosmology and tachyonic inflation

“…For the review and detailed discussion see Djordjevic et al, 2002a). The nonarchimedean and noncommutative cosmological quantum models with extra dimensions and an accelerating phase have been considered , as well as the relevant models and techniques in a pure quantum mechanical context (Dimitrijevic et al, 2007;Dimitrijevic et al, 2004;. To keep this text to a reasonable size, we will not consider noncommuative cosmology here, and a review would be given elsewhere.…”

Quantum cosmology and tachyons

“…For the review and detailed discussion see [2,16]. The nonarchimedean and noncommutative cosmological quantum models with extra dimensions and an accelerating phase have been considered [17], as well as the relevant models and techniques in pure quantum mechanical context [18,19,20,21].…”