UID:
edoccha_9961535646502883
Format:
1 online resource (90 pages)
Edition:
First edition.
ISBN:
3-031-53681-9
Series Statement:
SpringerBriefs in Physics Series
Content:
This book introduces readers to the fascinating world of quantum chromodynamics (QCD) and quarks and gluons, the elementary constituents of protons, neutrons, and all hadrons. Specifically, it focuses on the color of quarks and gluons, responsible for their mutual interactions via the strong force. The book provides an elementary introduction to the birdtrack technique, which is a powerful tool for addressing the color structure of QCD in a pictorial way. The technique shows how quark and gluon colors are combined and mixed in QCD. The author discusses color conservation, shows how to project on color states of systems of quarks, antiquarks, and gluons, how to derive their color charges. The book is enriched with many exercises integrated in the text to learn by doing. This book is primarily intended for particle physics students, graduates, and researchers working in the field of QCD. However, it requires no specific prerequisites in QCD, so it may also be of interest to students of mathematics, as an illustration of the use of the birdtrack pictorial technique in representation theory.
Note:
Intro -- Preface -- Contents -- 1 Pedestrian Introduction -- 1.1 The Basic Lego Bricks -- 1.2 First Trivial Rules -- 1.3 Fierz Identity -- 1.4 Lie Algebra -- 1.4.1 Lie Algebra in the Fundamental Representation -- 1.4.2 Lie Algebra in the Adjoint Representation -- 1.5 Sum Up -- 2 Color Conservation, Color Rotations, and normal upper S normal upper U left parenthesis upper N right parenthesisSU(N) Irreducible Representations -- 2.1 Color Conservation Pictorially -- 2.2 Color Rotations -- 2.2.1 normal upper S normal upper U left parenthesis upper N right parenthesisSU(N) Transformations -- 2.2.2 Color Rotations of Quark and Antiquark Coordinates -- 2.2.3 Color Rotations of Gluon Coordinates -- 2.2.4 Infinitesimal Color Rotations -- 2.3 normal upper S normal upper U left parenthesis upper N right parenthesisSU(N) Irreducible Representations -- 3 Diquark Color States, Schur's Lemma and Casimir Charges -- 3.1 Irreps of a Quark Pair -- 3.2 Schur's Lemma and Transition Operators -- 3.3 Casimir Charges -- 4 Color States of q q overbarq barq, q g and q q q Systems -- 4.1 Quark-Antiquark Pair -- 4.2 Quark-Gluon Pair -- 4.2.1 Derivation of qg Irreps -- 4.2.2 Why the Tensor Method Cannot Fail -- 4.3 System or Three Quarks -- 4.3.1 Decomposition of q q q into Irreps -- 4.3.2 Transition Operators -- 5 Color States of a Gluon Pair -- 5.1 The Star -- 5.2 Irreps of a Gluon Pair -- 5.2.1 Basis of Tensors -- 5.2.2 Multiplication Table -- 5.2.3 Projectors -- 5.2.4 Some normal upper S normal upper U left parenthesis 3 right parenthesisSU(3) Identities -- 5.3 Casimir Charges of g g Irreps -- 5.4 Color States of a Gluon Pair at a Glance -- 6 Interlude: Transverse Momentum Broadening in Proton-Nucleus Collisions -- 7 Irreps of q q q and q q q overbarq q barq States by Recursive Pairing -- 7.1 System q q q.
,
7.1.1 Product left parenthesis q q right parenthesis Subscript Sub Subscript dollar sign bold 6 dollar sign Baseline q(qq)6q -- 7.1.2 Product left parenthesis q q right parenthesis Subscript Sub Subscript dollar sign ModifyingAbove bold 3 With bold bar dollar sign Baseline q(qq)bar3q -- 7.1.3 Sum Up: Decomposition of q q q -- 7.2 System q q q overbarqqbarq -- 8 normal upper S normal upper U left parenthesis upper N right parenthesisSU(N) Irreps from the Index Method -- 8.1 The Index Method -- 8.2 Irreps of q q q overbarqqbarq from the Index Method -- 8.2.1 bold 6 circled times ModifyingAbove bold 3 With bold bar6 otimesbar3 -- 8.2.2 ModifyingAbove bold 3 With bold bar circled times ModifyingAbove bold 3 With bold barbar3 otimesbar3 -- 8.3 Some Training Exercises -- 8.4 q q q overbarqqbarq Irreps from a Different Pairing Order -- 8.5 Relating the Irreps Found with Different Pairings -- 9 Homework: bold 6 Subscript Baseline circled times bold 8 Subscript6 otimes8 and bold 15 Subscript Baseline circled times bold 8 Subscript15 otimes8 -- 9.1 bold 6 Subscript Baseline circled times bold 8 Subscript6 otimes8 -- 9.1.1 Tensor Method -- 9.1.2 Index Method -- 9.2 bold 15 Subscript Baseline circled times bold 8 Subscript15 otimes8 -- 9.2.1 Decomposition into backslash sunSU(N) Irreps -- 9.2.2 Projectors on Lower-Dimensional Irreps -- 9.2.3 Projectors on Higher-Dimensional Irreps -- References.
Additional Edition:
ISBN 3-031-53680-0
Language:
English
DOI:
10.1007/978-3-031-53681-6
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