More on complexity of operators in quantum field theory

A bstract Recently it has been shown that the complexity of SU( n ) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous...

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Bibliographic Details
Published in:The journal of high energy physics 2019-03, Vol.2019 (3), p.1-41, Article 161
Main Authors: Yang, Run-Qiu, An, Yu-Sen, Niu, Chao, Zhang, Cheng-Yong, Kim, Keun-Young
Format: Article
Language:English
Subjects:
Axioms
Classical and Quantum Gravitation
Complexity
Curvature
Elementary Particles
Field theory
Gauge-gravity correspondence
Geometry
High energy physics
Holography and condensed matter physics (AdS/CMT)
Invariants
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
Saturation
String Theory
Topology
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Summary:A bstract Recently it has been shown that the complexity of SU( n ) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten p -norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as k -local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU( n ) groups.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2019)161