Propagator for the Free Relativistic Particle on Archimedean and Nonarchimedean Spaces

Details Propagator for the Free Relativistic Particle on Archimedean and Nonarchimedean Spaces Propagator for the Free Relativistic Particle on Archimedean and Nonarchimedean Spaces

2004-12-08

arxiv.org/abs/hep-th/0412091v1

Facta Univ.Ser.Phys.Chem.Tech. 3 (2004) 9-21

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

We consider dynamics of a free relativistic particle at very short distances, treating space-time as archimedean as well as nonarchimedean 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 -adic case, as the simplest example of a nonarchimedean 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.

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