A Quantum Information Geometric Approach to Renormalization
John B. DeBrota
TL;DR
This paper reviews a quantum information geometric approach to renormalization, integrating quantum state distinguishability with geometric and information-theoretic methods for condensed matter and quantum field theory.
Contribution
It provides a noncommutative generalization of information geometry, offering an intuitive geometric and empirical framework for quantum renormalization.
Findings
Unifies condensed matter and quantum field theory approaches
Introduces a geometric interpretation of quantum state distinguishability
Provides a detailed review of Bény and Osborne's work
Abstract
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of information geometry allows one to treat quantum state distinguishability in geometric terms with an intuitive empirical interpretation, allowing for an information theoretic prescription of renormalization which incorporates both the condensed matter and quantum field theoretic approaches.
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Taxonomy
TopicsQuantum Mechanics and Applications · Statistical Mechanics and Entropy · Advanced Thermodynamics and Statistical Mechanics