Path Integrals for Quadratic Lagrangians on p-Adic and Adelic Spaces

Details Path Integrals for Quadratic Lagrangians on p-Adic and Adelic Spaces Path Integrals for Quadratic Lagrangians on p-Adic and Adelic Spaces

2010-11-30

arxiv.org/abs/1011.6589v1

p-Adic Numbers, Ultrametric Analysis and Applications 2 (4), 322-340 (2010)

Physics

Mathematical Physics

23 pages

Scientific paper

10.1134/S2070046610040060

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 ${\mathbb R} \leftrightarrow {\mathbb Q}_p$ and ${\mathbb Q}_p \leftrightarrow {\mathbb Q}_{p'} \, ,\, p\neq p'$. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum phenomena.

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