Math of QM: 10.1 Motivation for Infinite Tensor Product of Hilbert Spaces

Motivation of need for infinite tensor products, via representations of CCR in the infinite case
This is the first part of Lecture 10 in the lecture series "Mathematical Aspects of Quantum Mechanics" of Roland Speicher in the winter term 2020/21 at Saarland University, Germany. Lecture 10, which is split into 6 parts, addresses the question how to define an infinite tensor product of Hilbert spaces and uses this then to show that there exist inequivalent representations of the CCR in the case of an infinite number of degrees of freedom.