Elements of Quantum Mechanics of Infinite Systems

John von Neumann

Rathindra Nath Sen

Rathindra Nath Sen

Vieri Benci, Lorenzo Luperi Baglini, Kyrylo Simonov

Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of ultrafunctions can be used as a richer framework for a description of a physical system in quantum mechanics. In this paper, we provide a discussion of the space of ultrafunctions and its advantages in the applications of quantum mechanics, particularly for the Schrödinger equation for a Hamiltonian with the delta function potential.

Franco Strocchi

This book is a collection of lecture notes discussing the basic features of the Quantum Mechanics of Infinite Systems such as collective phenomena, spontaneous symmetry breaking, etc. The mathematical precision has been reduced to a minimum in order to communicate the main ideas to a larger audience including those who are not mathematically meinded. It is aimed at helping students who have difficulty in finding accessible and compact expositions of the material in standard textbooks.

D.P. Nagpal