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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Published inThe journal of high energy physics Vol. 2019; no. 3; pp. 1 - 41
Main Authors Yang, Run-Qiu, An, Yu-Sen, Niu, Chao, Zhang, Cheng-Yong, Kim, Keun-Young
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2019
Springer Nature B.V
SpringerOpen
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
Gauge-gravity correspondence
Holography and condensed matter physics (AdS/CMT)
Online AccessGet full text
ISSN1029-8479
1029-8479
DOI10.1007/JHEP03(2019)161

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Abstract 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.
AbstractList 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.
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.
Abstract 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.
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.
ArticleNumber 161
Author An, Yu-Sen
Zhang, Cheng-Yong
Yang, Run-Qiu
Kim, Keun-Young
Niu, Chao
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  surname: Zhang
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  givenname: Keun-Young
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Snippet 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...
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...
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...
Abstract 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...
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SubjectTerms 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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Title More on complexity of operators in quantum field theory
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Volume 2019
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