ABSTRACT
Quantum mechanics is often contrasted with its classical counterpart. This distinction is nearly “washed out” when quantum statistics for bosonic systems are formulated in terms of Feynman’s path integrals [1]. These provide a unique possibility of projecting subtle quantum mechanical properties into the language of classical statistics of closed trajectories in (d+1)-dimensional space. We note, however, that the corresponding projection and an intuition associated with it require that the statistics of path integrals be sign-positive (which is not the case for the generic fermionic system). Indeed, for the positive definite statistics, one can appeal to properties of “typical” configurations contributing to the answer and then estimate probabilities of atypical configurations to occur. If configurations contribute to the statistics with the sign or, in a more general case, with phase factors, then the notion of typical and relevant configurations is misleadingconfigurations with large modulus and opposite sign cancel each other to a large degree in the final answer, and only their combined effect has a physical meaning.
