The Ultraviolet Structure of Quantum Field Theories. Part 1: Quantum
Mechanics
- URL: http://arxiv.org/abs/2105.11470v2
- Date: Fri, 27 Aug 2021 18:33:42 GMT
- Title: The Ultraviolet Structure of Quantum Field Theories. Part 1: Quantum
Mechanics
- Authors: Djordje Radicevic
- Abstract summary: This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence.
The focus will be on quantum field theory in (0+1)D, i.e. quantum mechanics.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: This paper fires the opening salvo in the systematic construction of the
lattice-continuum correspondence, a precise dictionary that describes the
emergence of continuum quantum theories from finite, nonperturbatively defined
models ("lattice theories"). Here the focus will be on quantum field theory in
(0+1)D, i.e. quantum mechanics. The main conceptual achievement is an explicit
and systematic procedure for reducing a theory with a large but finite Hilbert
space to a subtheory in which wavefunctions satisfy prescribed smoothness and
compactness constraints. This reduction, here named taming, in effect defines
quantum mechanics on a continuum target space. When appropriate lattice
theories are tamed, many familiar continuum notions explicitly emerge, e.g.
canonical commutation relations, contact terms in correlation functions,
continuous spacetime symmetries, and supersymmetry algebras. All of these are
thus "put on the lattice" using the present framework. This analysis also leads
to further insights into old subjects: for example, it is proven that any
supersymmetric lattice theory must have a vanishing Witten index.
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