arXiv:1011.6589 · P-Adic Numbers Ultrametric Analysis and Applications

Path integrals for quadratic lagrangians on p-adic and adelic spaces

Branko G Dragovich, Zoran Rakić

Published Nov 23, 2010• 8 citations

Abstract

Feynman’s path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes K(x″, t″; x′, t′) for two-dimensional systems with quadratic Lagrangians are evaluated analytically and obtained expressions are generalized to any finite-dimensional spaces. These general formulas are presented in the form which is invariant under interchange of the number fields ℝ ↔ ℚ p and ℚ ↔ ℚ p , p ≠ p′. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum phenomena.

DOI: 10.1134/s2070046610040060

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