Abstract
Quantum mechanics arguably is one of the most successful physical theories of the past century. Not only has its development led to important results in physics, also many fields in mathematics have their origin in or progressed significantly alongside the development of quantum mechanics, and vice versa (Wigner, Commun Pure Appl Math 13(1):1–14, 1960). Of particular interest also from a mathematical point of view are quantum systems with infinitely many degrees of freedom. This includes quantum field theory, but one can also take infinitely many copies of a finite system, for example a spin-1/2 system. This is the type of systems that we will study in these lecture notes. That is, we will almost exclusively defined on a discrete space (a lattice), rather than with a continuum theory.
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Notes
- 1.
An extensive discussion can be found in the introduction of [2].
- 2.
At least, usually this gives a very good approximation of the “true” dynamics which may be much more complicated. One can compare this for example with gravity: if we are sufficiently far away from earth, the gravitational field due to the earth mass is so small that we can effectively pretend it does not exist.
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Naaijkens, P. (2017). Introduction. In: Quantum Spin Systems on Infinite Lattices. Lecture Notes in Physics, vol 933. Springer, Cham. https://doi.org/10.1007/978-3-319-51458-1_1
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