  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.
