Rational terms in two-loop calculations Article Swipe

PDF

Max F. Zoller , Stefano Pozzorini , Hantian Zhang ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.22323/1.375.0081

We present an extension of the renormalisation procedure based on the R-operation in $D$ dimensions at two-loop level, in which the numerators of all Feynman diagrams can be constructed in four dimensions, and the rational terms stemming from the interplay of $(D-4)$-dimensional numerator parts and UV poles are fully reconstructed from a finite set of universal local counterterms.\nThis represents an extension of the concept of rational terms of type $R_2$ to two loops. We provide a general method to compute one and two-loop rational counterterms from massive one-scale tadpole integrals. \nFinally, we present the full set of rational counterterms of UV origin for QED up to two-loop order.

Related Topics

Concepts

Extension (predicate logic) Feynman diagram Loop (graph theory) Rational function Set (abstract data type) Rational number Tadpole (physics) Order (exchange) Mathematics Propagator Pure mathematics Physics Mathematical physics Computer science Particle physics Combinatorics Programming language Economics Finance

Metadata

Type: preprint
Language: en
Landing Page: https://doi.org/10.22323/1.375.0081
PDF: https://pos.sissa.it/375/081/pdf
OA Status: gold
Cited By: 2
References: 12
Related Works: 10
OpenAlex ID: https://openalex.org/W3001834615

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W3001834615

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.22323/1.375.0081

Digital Object Identifier
Title: Rational terms in two-loop calculations

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2019

Year of publication
Publication date: 2019-12-20

Full publication date if available
Authors: Max F. Zoller, Stefano Pozzorini, Hantian Zhang

List of authors in order
Landing page: https://doi.org/10.22323/1.375.0081

Publisher landing page
PDF URL: https://pos.sissa.it/375/081/pdf

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: gold

Open access status per OpenAlex
OA URL: https://pos.sissa.it/375/081/pdf

Direct OA link when available
Concepts: Extension (predicate logic), Feynman diagram, Loop (graph theory), Rational function, Set (abstract data type), Rational number, Tadpole (physics), Order (exchange), Mathematics, Propagator, Pure mathematics, Physics, Mathematical physics, Computer science, Particle physics, Combinatorics, Programming language, Economics, Finance

Top concepts (fields/topics) attached by OpenAlex
Cited by: 2

Total citation count in OpenAlex
Citations by year (recent): 2022: 1, 2021: 1

Per-year citation counts (last 5 years)
References (count): 12

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W3001834615
doi	https://doi.org/10.22323/1.375.0081
ids.doi	https://doi.org/10.22323/1.375.0081
ids.mag	3001834615
ids.openalex	https://openalex.org/W3001834615
fwci	0.30273321
type	preprint
title	Rational terms in two-loop calculations
biblio.issue
biblio.volume
biblio.last_page	081
biblio.first_page	081
topics[0].id	https://openalex.org/T10048
topics[0].field.id	https://openalex.org/fields/31
topics[0].field.display_name	Physics and Astronomy
topics[0].score	0.9997000098228455
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/3106
topics[0].subfield.display_name	Nuclear and High Energy Physics
topics[0].display_name	Particle physics theoretical and experimental studies
topics[1].id	https://openalex.org/T10025
topics[1].field.id	https://openalex.org/fields/31
topics[1].field.display_name	Physics and Astronomy
topics[1].score	0.9955000281333923
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/3106
topics[1].subfield.display_name	Nuclear and High Energy Physics
topics[1].display_name	Black Holes and Theoretical Physics
topics[2].id	https://openalex.org/T10224
topics[2].field.id	https://openalex.org/fields/31
topics[2].field.display_name	Physics and Astronomy
topics[2].score	0.9726999998092651
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/3106
topics[2].subfield.display_name	Nuclear and High Energy Physics
topics[2].display_name	Quantum Chromodynamics and Particle Interactions
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C2778029271
concepts[0].level	2
concepts[0].score	0.8175121545791626
concepts[0].wikidata	https://www.wikidata.org/wiki/Q5421931
concepts[0].display_name	Extension (predicate logic)
concepts[1].id	https://openalex.org/C65574998
concepts[1].level	2
concepts[1].score	0.7599163055419922
concepts[1].wikidata	https://www.wikidata.org/wiki/Q386272
concepts[1].display_name	Feynman diagram
concepts[2].id	https://openalex.org/C184670325
concepts[2].level	2
concepts[2].score	0.7191537022590637
concepts[2].wikidata	https://www.wikidata.org/wiki/Q512604
concepts[2].display_name	Loop (graph theory)
concepts[3].id	https://openalex.org/C75190567
concepts[3].level	2
concepts[3].score	0.624076783657074
concepts[3].wikidata	https://www.wikidata.org/wiki/Q41237
concepts[3].display_name	Rational function
concepts[4].id	https://openalex.org/C177264268
concepts[4].level	2
concepts[4].score	0.552659273147583
concepts[4].wikidata	https://www.wikidata.org/wiki/Q1514741
concepts[4].display_name	Set (abstract data type)
concepts[5].id	https://openalex.org/C46875033
concepts[5].level	2
concepts[5].score	0.5434685945510864
concepts[5].wikidata	https://www.wikidata.org/wiki/Q1244890
concepts[5].display_name	Rational number
concepts[6].id	https://openalex.org/C2778311813
concepts[6].level	2
concepts[6].score	0.49925756454467773
concepts[6].wikidata	https://www.wikidata.org/wiki/Q7674671
concepts[6].display_name	Tadpole (physics)
concepts[7].id	https://openalex.org/C182306322
concepts[7].level	2
concepts[7].score	0.4608532786369324
concepts[7].wikidata	https://www.wikidata.org/wiki/Q1779371
concepts[7].display_name	Order (exchange)
concepts[8].id	https://openalex.org/C33923547
concepts[8].level	0
concepts[8].score	0.4281442165374756
concepts[8].wikidata	https://www.wikidata.org/wiki/Q395
concepts[8].display_name	Mathematics
concepts[9].id	https://openalex.org/C104416048
concepts[9].level	2
concepts[9].score	0.4150095283985138
concepts[9].wikidata	https://www.wikidata.org/wiki/Q302518
concepts[9].display_name	Propagator
concepts[10].id	https://openalex.org/C202444582
concepts[10].level	1
concepts[10].score	0.373654842376709
concepts[10].wikidata	https://www.wikidata.org/wiki/Q837863
concepts[10].display_name	Pure mathematics
concepts[11].id	https://openalex.org/C121332964
concepts[11].level	0
concepts[11].score	0.34636250138282776
concepts[11].wikidata	https://www.wikidata.org/wiki/Q413
concepts[11].display_name	Physics
concepts[12].id	https://openalex.org/C37914503
concepts[12].level	1
concepts[12].score	0.2904273271560669
concepts[12].wikidata	https://www.wikidata.org/wiki/Q156495
concepts[12].display_name	Mathematical physics
concepts[13].id	https://openalex.org/C41008148
concepts[13].level	0
concepts[13].score	0.15545183420181274
concepts[13].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[13].display_name	Computer science
concepts[14].id	https://openalex.org/C109214941
concepts[14].level	1
concepts[14].score	0.1397242248058319
concepts[14].wikidata	https://www.wikidata.org/wiki/Q18334
concepts[14].display_name	Particle physics
concepts[15].id	https://openalex.org/C114614502
concepts[15].level	1
concepts[15].score	0.11377540230751038
concepts[15].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[15].display_name	Combinatorics
concepts[16].id	https://openalex.org/C199360897
concepts[16].level	1
concepts[16].score	0.0
concepts[16].wikidata	https://www.wikidata.org/wiki/Q9143
concepts[16].display_name	Programming language
concepts[17].id	https://openalex.org/C162324750
concepts[17].level	0
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q8134
concepts[17].display_name	Economics
concepts[18].id	https://openalex.org/C10138342
concepts[18].level	1
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q43015
concepts[18].display_name	Finance
keywords[0].id	https://openalex.org/keywords/extension
keywords[0].score	0.8175121545791626
keywords[0].display_name	Extension (predicate logic)
keywords[1].id	https://openalex.org/keywords/feynman-diagram
keywords[1].score	0.7599163055419922
keywords[1].display_name	Feynman diagram
keywords[2].id	https://openalex.org/keywords/loop
keywords[2].score	0.7191537022590637
keywords[2].display_name	Loop (graph theory)
keywords[3].id	https://openalex.org/keywords/rational-function
keywords[3].score	0.624076783657074
keywords[3].display_name	Rational function
keywords[4].id	https://openalex.org/keywords/set
keywords[4].score	0.552659273147583
keywords[4].display_name	Set (abstract data type)
keywords[5].id	https://openalex.org/keywords/rational-number
keywords[5].score	0.5434685945510864
keywords[5].display_name	Rational number
keywords[6].id	https://openalex.org/keywords/tadpole
keywords[6].score	0.49925756454467773
keywords[6].display_name	Tadpole (physics)
keywords[7].id	https://openalex.org/keywords/order
keywords[7].score	0.4608532786369324
keywords[7].display_name	Order (exchange)
keywords[8].id	https://openalex.org/keywords/mathematics
keywords[8].score	0.4281442165374756
keywords[8].display_name	Mathematics
keywords[9].id	https://openalex.org/keywords/propagator
keywords[9].score	0.4150095283985138
keywords[9].display_name	Propagator
keywords[10].id	https://openalex.org/keywords/pure-mathematics
keywords[10].score	0.373654842376709
keywords[10].display_name	Pure mathematics
keywords[11].id	https://openalex.org/keywords/physics
keywords[11].score	0.34636250138282776
keywords[11].display_name	Physics
keywords[12].id	https://openalex.org/keywords/mathematical-physics
keywords[12].score	0.2904273271560669
keywords[12].display_name	Mathematical physics
keywords[13].id	https://openalex.org/keywords/computer-science
keywords[13].score	0.15545183420181274
keywords[13].display_name	Computer science
keywords[14].id	https://openalex.org/keywords/particle-physics
keywords[14].score	0.1397242248058319
keywords[14].display_name	Particle physics
keywords[15].id	https://openalex.org/keywords/combinatorics
keywords[15].score	0.11377540230751038
keywords[15].display_name	Combinatorics
language	en
locations[0].id	doi:10.22323/1.375.0081
locations[0].is_oa	True
locations[0].source
locations[0].license	cc-by-nc-nd
locations[0].pdf_url	https://pos.sissa.it/375/081/pdf
locations[0].version	publishedVersion
locations[0].raw_type	proceedings-article
locations[0].license_id	https://openalex.org/licenses/cc-by-nc-nd
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)
locations[0].landing_page_url	https://doi.org/10.22323/1.375.0081
locations[1].id	pmh:oai:dora:psi_32806
locations[1].is_oa	False
locations[1].source.id	https://openalex.org/S4306400127
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	False
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	DORA Eawag (Swiss Federal Institute of Aquatic Science and Technology (Eawag))
locations[1].source.host_organization	https://openalex.org/I63664421
locations[1].source.host_organization_name	Swiss Federal Institute of Aquatic Science and Technology
locations[1].source.host_organization_lineage	https://openalex.org/I63664421
locations[1].license
locations[1].pdf_url
locations[1].version	submittedVersion
locations[1].raw_type	Text
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published	False
locations[1].raw_source_name
locations[1].landing_page_url	https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A32806
locations[2].id	pmh:oai:pos.sissa.it:RADCOR2019/081
locations[2].is_oa	True
locations[2].source.id	https://openalex.org/S4377196127
locations[2].source.issn
locations[2].source.type	repository
locations[2].source.is_oa	False
locations[2].source.issn_l
locations[2].source.is_core	False
locations[2].source.is_in_doaj	False
locations[2].source.display_name	Proceedings Of Science
locations[2].source.host_organization
locations[2].source.host_organization_name
locations[2].license	cc-by-nc-nd
locations[2].pdf_url
locations[2].version	submittedVersion
locations[2].raw_type	Text
locations[2].license_id	https://openalex.org/licenses/cc-by-nc-nd
locations[2].is_accepted	False
locations[2].is_published	False
locations[2].raw_source_name
locations[2].landing_page_url	https://pos.sissa.it/375/081/
indexed_in	crossref
authorships[0].author.id	https://openalex.org/A5024107038
authorships[0].author.orcid	https://orcid.org/0000-0001-9233-7951
authorships[0].author.display_name	Max F. Zoller
authorships[0].countries	CH
authorships[0].affiliations[0].institution_ids	https://openalex.org/I202697423
authorships[0].affiliations[0].raw_affiliation_string	Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland
authorships[0].affiliations[1].institution_ids	https://openalex.org/I2802229908
authorships[0].affiliations[1].raw_affiliation_string	Paul Scherrer Institut, Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland
authorships[0].institutions[0].id	https://openalex.org/I2802229908
authorships[0].institutions[0].ror	https://ror.org/03eh3y714
authorships[0].institutions[0].type	facility
authorships[0].institutions[0].lineage	https://openalex.org/I2799323385, https://openalex.org/I2802229908
authorships[0].institutions[0].country_code	CH
authorships[0].institutions[0].display_name	Paul Scherrer Institute
authorships[0].institutions[1].id	https://openalex.org/I202697423
authorships[0].institutions[1].ror	https://ror.org/02crff812
authorships[0].institutions[1].type	education
authorships[0].institutions[1].lineage	https://openalex.org/I202697423
authorships[0].institutions[1].country_code	CH
authorships[0].institutions[1].display_name	University of Zurich
authorships[0].author_position	first
authorships[0].raw_author_name	Max Zoller
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	Paul Scherrer Institut, Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland, Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland
authorships[1].author.id	https://openalex.org/A5040196836
authorships[1].author.orcid	https://orcid.org/0000-0002-5316-0759
authorships[1].author.display_name	Stefano Pozzorini
authorships[1].countries	CH
authorships[1].affiliations[0].institution_ids	https://openalex.org/I2802229908
authorships[1].affiliations[0].raw_affiliation_string	Paul Scherrer Institut, Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland
authorships[1].affiliations[1].institution_ids	https://openalex.org/I202697423
authorships[1].affiliations[1].raw_affiliation_string	Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland
authorships[1].institutions[0].id	https://openalex.org/I2802229908
authorships[1].institutions[0].ror	https://ror.org/03eh3y714
authorships[1].institutions[0].type	facility
authorships[1].institutions[0].lineage	https://openalex.org/I2799323385, https://openalex.org/I2802229908
authorships[1].institutions[0].country_code	CH
authorships[1].institutions[0].display_name	Paul Scherrer Institute
authorships[1].institutions[1].id	https://openalex.org/I202697423
authorships[1].institutions[1].ror	https://ror.org/02crff812
authorships[1].institutions[1].type	education
authorships[1].institutions[1].lineage	https://openalex.org/I202697423
authorships[1].institutions[1].country_code	CH
authorships[1].institutions[1].display_name	University of Zurich
authorships[1].author_position	middle
authorships[1].raw_author_name	Stefano Pozzorini
authorships[1].is_corresponding	False
authorships[1].raw_affiliation_strings	Paul Scherrer Institut, Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland, Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland
authorships[2].author.id	https://openalex.org/A5023969614
authorships[2].author.orcid	https://orcid.org/0000-0002-7472-6467
authorships[2].author.display_name	Hantian Zhang
authorships[2].countries	CH
authorships[2].affiliations[0].institution_ids	https://openalex.org/I2802229908
authorships[2].affiliations[0].raw_affiliation_string	Paul Scherrer Institut, Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland
authorships[2].affiliations[1].institution_ids	https://openalex.org/I202697423
authorships[2].affiliations[1].raw_affiliation_string	Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland
authorships[2].institutions[0].id	https://openalex.org/I2802229908
authorships[2].institutions[0].ror	https://ror.org/03eh3y714
authorships[2].institutions[0].type	facility
authorships[2].institutions[0].lineage	https://openalex.org/I2799323385, https://openalex.org/I2802229908
authorships[2].institutions[0].country_code	CH
authorships[2].institutions[0].display_name	Paul Scherrer Institute
authorships[2].institutions[1].id	https://openalex.org/I202697423
authorships[2].institutions[1].ror	https://ror.org/02crff812
authorships[2].institutions[1].type	education
authorships[2].institutions[1].lineage	https://openalex.org/I202697423
authorships[2].institutions[1].country_code	CH
authorships[2].institutions[1].display_name	University of Zurich
authorships[2].author_position	last
authorships[2].raw_author_name	Hantian Zhang
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	Paul Scherrer Institut, Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland, Physik-Institut, Universität Zürich, CH-8057 Zürich, Switzerland
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://pos.sissa.it/375/081/pdf
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Rational terms in two-loop calculations
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T10048
primary_topic.field.id	https://openalex.org/fields/31
primary_topic.field.display_name	Physics and Astronomy
primary_topic.score	0.9997000098228455
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/3106
primary_topic.subfield.display_name	Nuclear and High Energy Physics
primary_topic.display_name	Particle physics theoretical and experimental studies
related_works	https://openalex.org/W1854628891, https://openalex.org/W2264472900, https://openalex.org/W4297822032, https://openalex.org/W1556982829, https://openalex.org/W2606883940, https://openalex.org/W4206413553, https://openalex.org/W1531225664, https://openalex.org/W1522315692, https://openalex.org/W4307421620, https://openalex.org/W2013086216
cited_by_count	2
counts_by_year[0].year	2022
counts_by_year[0].cited_by_count	1
counts_by_year[1].year	2021
counts_by_year[1].cited_by_count	1
locations_count	3
best_oa_location.id	doi:10.22323/1.375.0081
best_oa_location.is_oa	True
best_oa_location.source
best_oa_location.license	cc-by-nc-nd
best_oa_location.pdf_url	https://pos.sissa.it/375/081/pdf
best_oa_location.version	publishedVersion
best_oa_location.raw_type	proceedings-article
best_oa_location.license_id	https://openalex.org/licenses/cc-by-nc-nd
best_oa_location.is_accepted	True
best_oa_location.is_published	True
best_oa_location.raw_source_name	Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)
best_oa_location.landing_page_url	https://doi.org/10.22323/1.375.0081
primary_location.id	doi:10.22323/1.375.0081
primary_location.is_oa	True
primary_location.source
primary_location.license	cc-by-nc-nd
primary_location.pdf_url	https://pos.sissa.it/375/081/pdf
primary_location.version	publishedVersion
primary_location.raw_type	proceedings-article
primary_location.license_id	https://openalex.org/licenses/cc-by-nc-nd
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)
primary_location.landing_page_url	https://doi.org/10.22323/1.375.0081
publication_date	2019-12-20
publication_year	2019
referenced_works	https://openalex.org/W2081198022, https://openalex.org/W2003899175, https://openalex.org/W1480048792, https://openalex.org/W3101054245, https://openalex.org/W2134657033, https://openalex.org/W3124861399, https://openalex.org/W2106643093, https://openalex.org/W2100840108, https://openalex.org/W2346324757, https://openalex.org/W3098839575, https://openalex.org/W2059036510, https://openalex.org/W2004393658
referenced_works_count	12
abstract_inverted_index.a	51, 75
abstract_inverted_index.UV	45, 100
abstract_inverted_index.We	0, 73
abstract_inverted_index.an	2, 59
abstract_inverted_index.at	15
abstract_inverted_index.be	27
abstract_inverted_index.in	12, 18, 29
abstract_inverted_index.of	4, 22, 40, 54, 61, 64, 67, 96, 99
abstract_inverted_index.on	9
abstract_inverted_index.to	70, 78, 105
abstract_inverted_index.up	104
abstract_inverted_index.we	91
abstract_inverted_index.$D$	13
abstract_inverted_index.QED	103
abstract_inverted_index.all	23
abstract_inverted_index.and	32, 44, 81
abstract_inverted_index.are	47
abstract_inverted_index.can	26
abstract_inverted_index.for	102
abstract_inverted_index.one	80
abstract_inverted_index.set	53, 95
abstract_inverted_index.the	5, 10, 20, 33, 38, 62, 93
abstract_inverted_index.two	71
abstract_inverted_index.four	30
abstract_inverted_index.from	37, 50, 85
abstract_inverted_index.full	94
abstract_inverted_index.type	68
abstract_inverted_index.$R_2$	69
abstract_inverted_index.based	8
abstract_inverted_index.fully	48
abstract_inverted_index.local	56
abstract_inverted_index.parts	43
abstract_inverted_index.poles	46
abstract_inverted_index.terms	35, 66
abstract_inverted_index.which	19
abstract_inverted_index.finite	52
abstract_inverted_index.level,	17
abstract_inverted_index.loops.	72
abstract_inverted_index.method	77
abstract_inverted_index.order.	107
abstract_inverted_index.origin	101
abstract_inverted_index.Feynman	24
abstract_inverted_index.compute	79
abstract_inverted_index.concept	63
abstract_inverted_index.general	76
abstract_inverted_index.massive	86
abstract_inverted_index.present	1, 92
abstract_inverted_index.provide	74
abstract_inverted_index.tadpole	88
abstract_inverted_index.diagrams	25
abstract_inverted_index.rational	34, 65, 83, 97
abstract_inverted_index.stemming	36
abstract_inverted_index.two-loop	16, 82, 106
abstract_inverted_index.extension	3, 60
abstract_inverted_index.interplay	39
abstract_inverted_index.numerator	42
abstract_inverted_index.one-scale	87
abstract_inverted_index.procedure	7
abstract_inverted_index.universal	55
abstract_inverted_index.\nFinally,	90
abstract_inverted_index.dimensions	14
abstract_inverted_index.integrals.	89
abstract_inverted_index.numerators	21
abstract_inverted_index.represents	58
abstract_inverted_index.R-operation	11
abstract_inverted_index.constructed	28
abstract_inverted_index.dimensions,	31
abstract_inverted_index.counterterms	84, 98
abstract_inverted_index.reconstructed	49
abstract_inverted_index.renormalisation	6
abstract_inverted_index.$(D-4)$-dimensional	41
abstract_inverted_index.counterterms.\nThis	57
cited_by_percentile_year.max	94
cited_by_percentile_year.min	89
countries_distinct_count	1
institutions_distinct_count	3
sustainable_development_goals[0].id	https://metadata.un.org/sdg/4
sustainable_development_goals[0].score	0.5799999833106995
sustainable_development_goals[0].display_name	Quality Education
citation_normalized_percentile.value	0.87661306
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False