Three-particle Physics And Dispersion Relation Theory
The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relati...
Saved in:
| Main Authors | , , , , , |
|---|---|
| Format | eBook |
| Language | English |
| Published |
Singapore
World Scientific Publishing Company
2013
WORLD SCIENTIFIC WSPC |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9814478806 9789814478809 |
| DOI | 10.1142/8779 |
Cover
| Abstract | The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book. |
|---|---|
| AbstractList | The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.Contents:IntroductionElements of Dispersion Relation Technique for Two-Body Scattering ReactionsSpectral Integral Equation for the Decay of a Spinless ParticleNon-relativistic Three-Body AmplitudePropagators of Spin Particles and Relativistic Spectral Integral EquationsIsobar Model and Partial Wave Analysis. D-Matrix MethodReggeon-Exchange TechniqueSearching for the Quark-Diquark Systematics of BaryonsConclusionReadership: Grudate students and researchers in high energy and particle physics. The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book. |
| Author | Anisovich, A V Nyiri, Julia Anisovich, Vladimir Vladislavovich Sarantsev, A V Nikonov, V A Matveev, M A |
| Author_xml | – sequence: 1 fullname: Anisovich, A V – sequence: 2 fullname: Anisovich, Vladimir Vladislavovich – sequence: 3 fullname: Matveev, M A – sequence: 4 fullname: Nikonov, V A – sequence: 5 fullname: Nyiri, Julia – sequence: 6 fullname: Sarantsev, A V |
| BookMark | eNpFkMlOwzAURY0YRKd_yA6xCNiOx2UpZZAqgVDF1nIcRzG14mIHqv49CUV08wbp3Kv37hictaG1AEwRvEGI4FvBuTwBYykQIVz09fS4QHYBRoJAIhmn-BLMUvqAEPYyyiAZAbpuorX5VsfOGW-z12afnEnZvK2ye5e2NiYX2uzNet0Nw7qxIe6n4LzWPtnZX5-A94flevGUr14enxfzVa4pR5jkBErDa4NLKDE0FDIsuES1KW1RClMZSgttiqoWmjBCKK4xx7I0jDNMdX9fMQHXB2OdNnaXmuC7pL69LUPYJCW5-H-aHdldiL5Kxtm2c7Uz6gAjqIa01JBWz14d2G0Mn182derX0vSSqL1a3i0QYgJJXPwAH6FmEA |
| ContentType | eBook |
| DEWEY | 539.721 |
| DOI | 10.1142/8779 |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISBN | 9814478814 9789814478816 9814478822 9789814478823 |
| Edition | 1 |
| ExternalDocumentID | 9789814478816 10.1142/8779 EBC1168192 |
| GroupedDBID | -VQ -VX 089 20A 38. 9WS A4J AABBV AATMT ABARN ABCYV ABIAV ABMRC ABQPQ ACLGV ACZWY ADVEM AERYV AFOJC AHWGJ AIXPE AJFER AKHYG ALMA_UNASSIGNED_HOLDINGS ALUEM AMYDA AZZ BBABE CZZ DUGUG EBSCA ECOWB EFU GEOUK IWG J-X JJU MYL PE5 PQQKQ PYZUL WMAQA XI1 IVK |
| ID | FETCH-LOGICAL-a57124-409c7fc2b0920c50628791fcbe3b8cdc553ac3df8a464452f2729bc67625a6043 |
| ISBN | 9814478806 9789814478809 |
| IngestDate | Fri Nov 08 00:03:05 EST 2024 Sat Mar 08 09:01:57 EST 2025 Wed Sep 10 04:42:25 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | false |
| Keywords | Hadrons Three-Body Systems Strong Interactions Diquarks Dispersion Relations Two-Particle Systems |
| LCCallNum_Ident | QC793.29 .T47 2013 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-a57124-409c7fc2b0920c50628791fcbe3b8cdc553ac3df8a464452f2729bc67625a6043 |
| OCLC | 840496752 |
| PQID | EBC1168192 |
| PageCount | 342 |
| ParticipantIDs | askewsholts_vlebooks_9789814478816 worldscientific_books_10_1142_8779 proquest_ebookcentral_EBC1168192 |
| PublicationCentury | 2000 |
| PublicationDate | 2013 20130500 2013-03-25 |
| PublicationDateYYYYMMDD | 2013-01-01 2013-05-01 2013-03-25 |
| PublicationDate_xml | – year: 2013 text: 2013 |
| PublicationDecade | 2010 |
| PublicationPlace | Singapore |
| PublicationPlace_xml | – name: Singapore |
| PublicationYear | 2013 |
| Publisher | World Scientific Publishing Company WORLD SCIENTIFIC WSPC |
| Publisher_xml | – name: World Scientific Publishing Company – name: WORLD SCIENTIFIC – name: WSPC |
| SSID | ssj0001425604 ssib045736286 |
| Score | 2.0294878 |
| Snippet | The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including... |
| SourceID | askewsholts worldscientific proquest |
| SourceType | Aggregation Database Publisher |
| SubjectTerms | Dispersion relations Particles (Nuclear physics) |
| TableOfContents | 3.1.2.1 Decay (JPin = 0−)-state → P1P2P3 -- 3.1.2.2 Miniconclusion -- 3.2 Non-relativistic approach and transition of two-particlespectral integral to the three-particle one -- 3.2.1 Non-relativistic approach -- 3.2.2 Threshold limit constraint -- 3.2.3 Transition of the two-particle spectral integral representation amplitude to the three-particle spectral integral -- 3.3 Consideration of amplitudes in terms of a three-particlespectral integral -- 3.3.1 Kinematics of the outgoing particles in the c.m. system -- 3.3.2 Calculation of the block B(0)13−12(s, s12) -- 3.4 Three-particle composite systems, their wave functions and form factors -- 3.4.1 Vertex and wave function -- 3.4.2 Three particle composite system form factor -- 3.5 Equation for an amplitude in the case of instantaneous interactions in the final state -- 3.6 Conclusion -- 3.7 Appendix A. Example: loop diagram with GL=GR=1 -- 3.8 Appendix B. Phase space for n-particle state -- 3.9 Appendix C. Feynman diagram technique and evolution of systems in the positive time-direction -- 3.9.1 The Feynman diagram technique and non relativistic three particle systems -- 3.9.1.1 Two particle c.m. system, k1 + k2 = 0 -- 3.9.1.2 Three particle c.m. system, k1 + k2 + k3 = 0 -- 3.10 Appendix D. Coordinate representation for non-relativistic three-particle wave function -- References -- 4. Non-relativistic Three-Body Amplitude -- 4.1 Introduction -- 4.1.1 Kinematics -- 4.1.2 Basic principles for selecting the diagrams -- 4.2 Non-resonance interaction of the produced particles -- 4.2.1 The structure of the amplitude with a total angular momentum J = 0 -- 4.2.1.1 Terms of the order of ∼ const and ∼ |kiℓ| -- 4.2.1.2 Double rescattering diagram, Fig. 4.2 -- 4.2.1.3 Setting of the relation between s′13 and z and calculation disc12A(13→12)n=2 (k212,E) -- 4.2.1.4 Calculation of A(13→12)n=2 (k212,E) 4.2.1.5 Amplitude and total cross section up to terms ∼ E -- 4.2.1.6 Miniconclusion -- 4.2.2 Production of three particles in a state with J = 1 -- 4.3 The production of three particles near the threshold when two particles interact strongly -- 4.3.1 The production of three spinless particles -- 4.4 Decay amplitude for K → 3 and pion interaction -- 4.4.1 The dispersion relation for the decay amplitude -- 4.4.2 Pion spectra and decay ratios in K → within taking into account mass differences of kaons and pions -- 4.4.2.1 Decay ratios in K → -- 4.4.2.2 Cusps in pion spectra at small relative momenta -- 4.4.3 Transformation of the dispersion relation for the K → amplitude to a single integral equation -- 4.5 Equation for the three-nucleon amplitude -- 4.5.1 Method of extraction of the leading singularities -- 4.5.1.1 Amplitude of production of three spinless particles -- 4.5.1.2 Separation of the threshold singularities and the cutoff procedure -- 4.5.1.3 Extraction of the leading singularities -- 4.5.2 Helium-3/tritium wave function -- 4.5.2.1 Miniconclusion -- 4.6 Appendix A. Landau rules for finding the singularities of the diagram -- 4.7 Appendix B. Anomalous thresholds and final state interaction -- 4.8 Appendix C. Homogeneous Skornyakov-Ter-Martirosyan equation -- 4.9 Appendix D. Coordinates and observables in the three body problem -- 4.9.1 Choice of coordinates and group theory properties -- 4.9.2 Parametrization of a complex sphere -- 4.9.3 The Laplace operator -- 4.9.4 Calculation of the generators Lik and Bik -- 4.9.5 The cubic operator Ω -- 4.9.6 Solution of the eigenvalue problem -- References -- 5. Propagators of Spin Particles and Relativistic Spectral Integral Equations -- 5.1 Boson propagators -- 5.1.1 Projection operators and denominators of the boson propagators -- 5.1.1.1 The photon projection operator 5.2 Propagators of fermions -- 5.2.1 The classification of the baryon states -- 5.2.2 Spin-1/2 wave functions -- 5.2.3 Spin-3/2 wave functions -- 5.2.3.1 Wave function for Δ -- 5.2.3.2 Wave function for Δ -- 5.2.3.3 Baryon projection operators -- 5.2.3.4 Projection operators for particles with J > -- 1/2 -- 5.3 Spectral integral equations for the coupled three-meson decaychannels in pp (JPC = 0−+) annihilation at rest -- 5.3.1 The S-P-D-wave meson rescatterings -- 5.3.1.1 P-wave interaction in the final state -- 5.3.1.2 D-wave interaction in the final state -- 5.3.2 Equations with inclusion of resonance production -- 5.3.2.1 Two-particle scattering amplitude -- 5.3.2.2 Three-particle production amplitude -- 5.3.3 The coupled decay channels pp(IJPC = 10−+) →π0π0π0, ηηπ0, KKπ0 -- 5.3.3.1 Reaction pp (10−+) → 0 0 0 -- 5.3.3.2 Reaction pp(0−+) → ηη 0 -- 5.3.3.3 Reaction pp(0−+) → K K 0 -- 5.4 Conclusion -- References -- 6. Isobar model and partial wave analysis. D-matrix method -- 6.1 The K-Matrix and D-Matrix Techniques -- 6.1.1 K-matrix approach -- 6.1.2 Spectral integral equation for the K-matrix amplitude -- 6.1.3 D-matrix approach -- 6.2 Meson-meson scattering -- 6.2.1 K-matrix fit -- 6.2.2 D-matrix fit -- 6.3 Partial wave analysis of baryon spectra in the frameworks of K-matrix and D-matrix methods -- 6.3.1 Pion and photo induced reactions -- References -- 7. Reggeon-Exchange Technique -- 7.1 Introduction -- 7.2 Meson-nucleon collisions at high energies: peripheral two meson production in terms of reggeon exchanges -- 7.2.1 K-matrix and D-matrix approaches -- 7.2.1.1 K-matrix approach -- 7.2.1.2 D-matrix approach -- 7.2.2 Reggeized pion-exchange trajectories for the waves JPC = 0++, 1−−, 2++, 3−−, 4++ -- 7.2.2.1 Kinematics for reggeon exchange amplitudes -- 7.2.2.2 Amplitude with leading and daughter pion trajectory exchanges Intro -- Contents -- Preface -- References -- 1. Introduction -- 1.1 Non-relativistic three-nucleon and three-quark systems -- 1.1.1 Description of three-nucleon systems -- 1.1.2 Three-quark systems -- 1.2 Dispersion relation technique for three particle systems -- 1.2.1 Elements of the dispersion relation technique for two-particle systems -- 1.2.2 Interconnection of three particle decay amplitudes and two-particle scattering ones in hadron physics -- 1.2.3 Quark-gluon language for processes in regions I, III and IV -- 1.2.4 Spectral integral equation for three particles -- 1.2.5 Isobar models -- 1.2.5.1 Amplitude poles -- 1.2.5.2 D-matrix propagator for an unstable particle and the K matrix amplitude -- 1.2.5.3 K-matrix and D-matrix masses and the amplitude pole -- 1.2.5.4 Accumulation of widths of overlapping resonances -- 1.2.5.5 Loop diagrams with resonances in the intermediate states -- 1.2.5.6 Isobar model for high energy peripheral production processes -- 1.2.6 Quark-diquark model for baryons and group theory approach -- 1.2.6.1 Quark-diquark model for baryons -- References -- 2. Elements of Dispersion Relation Technique for Two-Body Scattering Reactions -- 2.1 Analytical properties of four-point amplitudes -- 2.1.1 Mandelstam planes for four-point amplitudes -- 2.1.1.1 Dalitz plot for the 4 → 1 + 2 + 3 decay -- 2.1.2 Bethe-Salpeter equations in the momentum representation -- 2.1.2.1 Multiparticle intermediate states -- 2.1.2.2 Composite systems -- 2.1.2.3 Zoo-diagrams in the BS-equation -- 2.1.2.4 Miniconclusion: two-particle composite systemsin the BS-equation -- 2.2 Dispersion relation N/D-method and ansatz of separable interactions -- 2.2.1 N/D-method for the one-channel scattering amplitude of spinless particles -- 2.2.2 Scattering amplitude and energy non-conservation in the spectral integral representation 7.2.2.3 The t-channel 2 exchange 2.2.3 Composite system wave function and its form factors -- 2.2.4 Scattering amplitude with multivertex representation of separable interaction -- 2.2.4.1 Generalization for an arbitrary angular momentum state, L = J -- 2.3 Instantaneous interaction and spectral integral equation for two-body systems -- 2.3.1 Instantaneous interaction -- 2.3.1.1 Coordinate representation -- 2.3.1.2 Instantaneous interaction - transformation into a set of separable vertices -- 2.3.1.3 An example: expressions for q⊥ and t⊥ in the centre-of mass system -- 2.3.2 Spectral integral equation for a composite system -- 2.3.2.1 Spectral integral equation for vertex function with L = 0 -- 2.3.2.2 Spectral integral equation for the (L = 0)-wave function -- 2.3.2.3 The spectral integral equation for the states with angular momentum L -- 2.4 Appendix A. Angular momentum operators -- 2.4.1 Projection operators and denominators of the boson propagators -- 2.4.2 Useful relations for Z μ1...μn and X(n−1)ν2...νn -- 2.5 Appendix B: The ππ scattering amplitude near the two-pion thresholds, + − and 0 0 -- 2.6 Appendix C: Four-pole fit of the (00++) wave in the region M < -- 900 MeV -- References -- 3. Spectral Integral Equation for the Decay of a Spinless Particle -- 3.1 Three-body system in terms of separable interactions: analytic continuation of the four-point scattering amplitude to the decay region -- 3.1.1 Final state two-particle S-wave interactions -- 3.1.1.1 Calculation of A(0)12 (s12) in the c.m.s. of particles P1P2 -- 3.1.1.2 Analytic continuation of the integration contour over z -- 3.1.1.3 Threshold behavior of the three-particle amplitude A(Jin=0)P1P2P3(s12, s13, s23) -- 3.1.1.4 Spectral integral equations for S-wave interactions -- 3.1.2 General case: rescatterings of outgoing particles, PiPj → PiPj , with arbitrary angular momenta |
| Title | Three-particle Physics And Dispersion Relation Theory |
| URI | https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=1168192 https://www.worldscientific.com/doi/10.1142/8779 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9789814478816&uid=none |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFA66oThBvOK8UcQ3qa5p0rWvzskmbgqbY2-lTRsQZcJWffDX-6XpZRs-qC-l1wS-k56c0-b7DiEXLKZI_mVkchHGJpMC75zg0lTK4Bzph-RUkZN7fafzzO7HfFzWbkzZJUl4Jb5-5JX8x6o4B7sqluwfLFs0ihPYh32xhYWxXQp-i8PcuNM4RvSnzZ4WsMnVlm9flPa3-gZWLHQrCfjatg-pQ-h3B4-jbqsD1zC6bA_n039VisE2NVVYO5nBU679qFNCz0WKpDTinZ8dJFOCq25TV3BZkppeeHyVVClzKDxFFTNku1d-uWIqTNKiisX9DQ8pb3HgrJPNrLdr1VeN1ILZK7w2PHoyWwjmt1JlWM3-VIuj5mb34TapxorysUNW4skuWcvQ3CM8hdnIYTayCwZgNkqYjRxmQ8O8T0Z37WGrY2ZlJsyANxHeIIX2RBOjNGx4tCG4YpU2PUti8NqhKyLBuR0IO5JuwBA9ciopMpJQOJhHeAAk7ANSmbxP4kNiUEQC1JZWJDHti5CFLt5U25EsYjwKLFkn53NA-J9v6S_xmb-AfJ0YOT5-ej1bp-u3b1qW5SgJO7SzhJuvG9I8c-or1I9-09kx2SiH1QmpJNOP-BRxVhKeZYb_BoeMIXU |
| linkProvider | ProQuest Ebooks |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Three+Particle+Physics+and+Dispersion+Relation+Theory&rft.au=AL%2C+ANISOVICH+A+V+ET&rft.date=2013-03-25&rft.pub=WSPC&rft.isbn=9789814478816&rft_id=info:doi/10.1142%2F8779&rft.externalDocID=9789814478816 |
| thumbnail_m | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97898144%2F9789814478816.jpg |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.worldscientific.com%2Faction%2FshowCoverImage%3Fdoi%3D10.1142%2F8779 |