Correlazioni quantistiche temporali con il formalismo delle storie generalizzate

Quantum mechanics is a well-established theory whose predictions have been confirmed by numerous experimental evidences. Although there is no uniformity among the scientific community as to what is the correct interpretation for this theory, there are, however, several formalisms that describe the same phenomena but, in the right contexts, more adequately than standard quantum mechanics. This is the case of Feynman’s path integrals, which in addition to reproducing already known results have provided a valuable means of understanding others. Following the same idea, we worked in this thesis with a new formalism, referred to as the generalized histories formalism, which through the study of temporal quantum correlations in a variety of examples sheds light on the symmetric nature - in space and time - of quantum mechanics. Our work precisely starts from the path integral formalism, which is then generalized to the concept of generalized histories, whose formalism is introduced and discussed in detail. Subsequently, several examples are considered in which it is pointed out how temporal, as well as spatial, quantum correlations emerge from it in a natural way. Among the original contributions of the thesis are the extension of Schmidt’s decomposition to the time case and the study of the non-locality in time that characterizes the formalism. We then have concluded by showing how the generalized histories formalism is not only perfectly capable of reproducing the results of standard quantum mechanics, but also how it provides a more immediate and diagrammatic way to keep track of all the possible histories of a quantum system and how it is particularly well suited for a symmetric treatment of quantum correlations in space and time. Furthermore, our new language makes certain distinctive features of quantum mechanics more evident, and in addressing two specific examples, we demonstrate that it is capable of providing a concrete explanation for the counterintuitive aspects of quantum theory, thereby eliminating their apparent paradoxes.