Cambridge University Press, 2003. – 310 pp. – (Series: Cambridge
Monographs on Mathematical Physics). – ISBN: 9780521818346.
Классическая работа (на англ. языке) по теории комплексных угловых
моментов в квантовой теории поля, которая была развита В.Н.
Грибовым для релятивистских частиц и сыграла выдающуюся роль в
физике элементарных частиц.
В теории Грибова фундаментальную роль играет реджеон с вакуумными квантовыми числами, положительной сигнатурой и интерсептом, равным (или большим) 1, названный Грибовым помероном в честь выдающегося советского физика И.Я. Померанчука. Этот реджеон определяет поведение полных сечений при больших энергиях.
Грибов дал последовательную полевую формулировку партонной модели, и в его работах, предшествовавших квантовой хромодинамике, были впервые получены уравнения эволюции для партонных распределений в жестких столкновениях, часто называемые уравнениями ДГЛАП (Докшицер – Грибов – Липатов – Альтарелли – Паризи).
Уже простой двухглюонный обмен в цвет-нейтральном состоянии служит некоторой моделью померона. Впрочем, эта модель довольно примитивна, так как не учитывает взаимодействие между глюонами. В более аккуратном варианте, померонное решение (но не в жестких столкновениях) появляется в уравнении БФКЛ (Балицкого – Фадина – Кураева – Липатова), учитывающем с логарифмической точностью взаимодействие (теперь уже реджезованных) глюонов.
В 1960-х – начале 1970-х гг. теория комплексных угловых моментов была основным и почти единственным инструментом теоретического анализа сильных взаимодействий. Из нее выросли модель Венециано и алгебра Вирасоро, струны и суперструны. Реджезация элементарных частиц создает мостик между квантовой теорией поля и теорией комплексных моментов и, по-видимому, указывает на связь реджезующихся частиц со струнами. Annotation This book provides a unique and rigorous introduction to the theory of complex angular momenta, based on the methods of field theory. It comprises an English translation of the series of lectures given by V.N. Gribov in 1969, when the physics of high energy hadron interactions was being created. Besides their historical significance, these lectures contain material which is highly relevant to research today. The basic physical results and the approaches Gribov developed are now being rediscovered in a new context: in the microscopic theory of hadrons provided by quantum chromodynamics. The ideas and calculation techniques presented in this book are useful for analysing high energy hadron scattering phenomena, deep inelastic lepton-hadron scattering, the physics of heavy ion collisions, and kinetic phenomena in phase transitions, and will be instrumental in the analysis of electroweak processes at the next generation particle accelerators, such as LHC and TESLA. VLADIMIR NAUMOVICH GRIBOV received his PhD in theoretical physics in 1957 from the Physico-Technical Institute in Leningrad where he had worked since 1954. From 1962 to 1980 he was the head of the Theory Division of the Particle Physics Department of that institute, which in 1971 became the Leningrad Institute for Nuclear Physics. In 1980 he moved to Moscow where he became head of the particle physics section of the Landau Institute for Theoretical Physics. From 1981 he regularly visited the Research Institute for Particle and Nuclear Physics in Budapest where he was a scientific adviser until his death in 1997. Vladimir Gribov was one of the leading theoretical physicists of his time, who made seminal contributions to many fields, including quantum electrodynamics, neutrino physics, non-Abelian field theory, and, in particular, the physics of hadron interactions at high energies. CONTENTS Foreword by Yuri Dokshitzer. Introduction by Yuri Dokshitzer and Leonid Frankfurt.
References. High energy hadron scattering.
Basic principles.
Invariant scattering amplitude and cross section.
Analyticity and causality.
Singularities.
Crossing symmetry.
The unitarity condition for the scattering matrix Mandelstam variables for two-particle scattering.
The Mandelstam plane.
Threshold singularities on the Mandelstam plane Partial wave expansion and unitarity.
Threshold behaviour of partial wave amplitudes.
Singularities of Im A on the Mandelstam plane (Karplus curve).
The Froissart theorem The Pomeranchuk theorem. Physics of the t-channel and complex angular momenta.
Analytical continuation of the t-channel unitarity condition.
The Mandelstam representation.
Inconsistency of the 'black disk' model of diffraction.
Complex angular momenta.
Partial wave expansion and Sommerfeld-Watson representation.
Continuation of partial wave amplitudes to complex l.
Non-relativistic quantum mechanics.
Relativistic theory.
Gribov-Froissart projection.
t-Channel partial waves and the black disk model. Singularities of partial waves and unitarity.
Continuation of partial waves with complex l to t < 0.
Threshold singularity and partial waves φl.
φl(t) At t < 0 and its discontinuity.
The unitarity condition for partial waves with complex l.
Singularities of the partial wave amplitude.
Left cut in non-relativistic theory.
Fixed singularities.
Moving singularities.
Moving poles and resonances. Properties of Regge poles.
Resonances.
Bound states.
Elementary particle or bound state?
Regge trajectories.
Regge pole exchange and particle exchange (t > 0).
Regge exchange and elementary particles (t < 0).
There is no elementary particle with J > 1.
Asymptotics of s-channel amplitudes and reggeization.
Factorization. Regge poles in high energy scattering.
t-Channel dominance.
Elastic scattering and the pomeron.
Quantum numbers of the pomeron.
Slope of the pomeron trajectory.
Shrinkage of the diffractive cone.
s-Channel partial waves in the impact parameter space.
Relation between total cross sections. Scattering of particles with spin.
Vector particle exchange.
Scattering of nucleons.
Reggeon quantum numbers and N-anti N —> reggeon vertices.
Vacuum pole in πN and NN scattering.
Conspiracy. Fermion Regge poles.
Backward scattering as a relativistic effect.
Pion-nucleon scattering.
Parity in the u-channel.
Fermion poles with definite parity and singularity at u = 0.
Oscillations in the fermion pole amplitude.
Reggeization of a neutron. Regge poles in perturbation theory.
Scattering of a particle in an exteal field.
Scalar field theory gφ3.
gφ3 Theory in the Duffin-Kemmer formalism.
Analytic properties of the amplitudes.
Order g4 ln s.
Order g6 ln s.
Ladder diagrams in all orders.
Non-ladder diagrams.
Interaction with vector mesons. Reggeization of an electron.
Electron exchange in O(g6) Compton scattering amplitude.
Electron Regge poles.
Conspiracy in perturbation theory.
Reggeization in QED (with massless photon).
Electron reggeization: nonsense states. Vector fleld theory.
Role of spin effects in reggeization.
Nonsense states in the unitarity condition.
Iteration of the unitarity condition.
Nonsense states from the s- and t-channel points of view.
The j = 1/2 pole in the perturbative nonsense-nonsense amplitude.
QED processes with photons in the t-channel.
The vacuum channel in QED.
The problem of the photon reggeization. Inconsistency of the Regge pole picture.
The pole l = –1 and restriction on the amplitude fall-off.
Contradiction with unitarity l = –1.
Poles condensing at l = –1.
Amplitude cannot fall faster than 1/s.
Particles with spin: failure of the Regge pole picture. Two-reggeon exchange and branch point singularities in the l plane.
Normalization of partial waves and the unitarity condition.
Redefinition of partial wave amplitudes.
Particles with spin in the unitarity condition.
Particle scattering via a two-particle intermediate state.
Two-reggeon exchange and production vertices.
Asymptotics of two-reggeon exchange amplitude.
Two-reggeon branching and l = –1.
Movement of the branching in the t and j planes.
Signature of the two-reggeon branching. Properties of Mandelstam branch singularities.
Branchings as a generalization of the l = –1 singularity.
Branchings in the j plane.
Branch singularity in the unitarity condition.
Branchings in the vacuum channel.
The patte of branch points in the j plane.
The Mandelstam representation in the presence of branchings.
Vacuum-non-vacuum pole branchings.
Experimental verification of branching singularities.
Branchings and conspiracy. Reggeon diagrams.
Two-particle-two-reggeon transition amplitude.
Structure of the vertex.
Analytic properties of the vertex.
Factorization.
Partial wave amplitude of the Mandelstam branching. Interacting reggeons. Reggeon field theory.
Enhanced reggeon diagrams.
Effective field theory of interacting reggeons.
Equation for the Green function G.
Equation for the vertex function Г2.
Weak and strong coupling regimes.
Pomeron Green function and reggeon unitarity condition. The structure of weak and strong coupling solutions.
Weak coupling regime.
The Green function.
P —> PP vertex.
Induced multi-reggeon vertices.
Vanishing of multi-reggeon couplings.
Problems of the strong coupling regime. Appendix A: Space-time description of the hadron interactions at high energies.
Wave function of the hadron. Orthogonality and normalization.
Distribution of the partons in space and momentum.
Deep inelastic scattering.
Strong interactions of hadrons.
Elastic and quasi-elastic processes.
References. Appendix B: Character of inclusive spectra and fluctuations produced in inelastic processes by multi-pomeron exchange.
The absorptive parts of reggeon diagrams in the s-channel. Classification of inelastic processes.
Relations among the absorptive parts of reggeon diagrams.
Inclusive cross sections.
Main corrections to the inclusive cross sections in the central region.
Fluctuations in the distribution of the density of produced particles.
References. Appendix C: Theory of the heavy pomeron.
Introduction.
Non-enhanced cuts at α’ = 0.
Estimation of enhanced cuts at α’ = 0.
Structure of the transition amplitude of one pomeron – to two.
The Green function and the vertex part at α’ = 0.
Properties of high energy processes in the theory with α’ = 0.
Two-particle processes, total cross sections.
Inclusive spectra, multiplicity.
Correlation, multiplicity distribution.
Probability of fluctuations in individual events: the inclusive spectrum in the three-pomeron limit. Multi-reggeon processes.
The case α’ =/= 0.
The contribution of cuts at small α’.
Conclusion.
References. Index.
В теории Грибова фундаментальную роль играет реджеон с вакуумными квантовыми числами, положительной сигнатурой и интерсептом, равным (или большим) 1, названный Грибовым помероном в честь выдающегося советского физика И.Я. Померанчука. Этот реджеон определяет поведение полных сечений при больших энергиях.
Грибов дал последовательную полевую формулировку партонной модели, и в его работах, предшествовавших квантовой хромодинамике, были впервые получены уравнения эволюции для партонных распределений в жестких столкновениях, часто называемые уравнениями ДГЛАП (Докшицер – Грибов – Липатов – Альтарелли – Паризи).
Уже простой двухглюонный обмен в цвет-нейтральном состоянии служит некоторой моделью померона. Впрочем, эта модель довольно примитивна, так как не учитывает взаимодействие между глюонами. В более аккуратном варианте, померонное решение (но не в жестких столкновениях) появляется в уравнении БФКЛ (Балицкого – Фадина – Кураева – Липатова), учитывающем с логарифмической точностью взаимодействие (теперь уже реджезованных) глюонов.
В 1960-х – начале 1970-х гг. теория комплексных угловых моментов была основным и почти единственным инструментом теоретического анализа сильных взаимодействий. Из нее выросли модель Венециано и алгебра Вирасоро, струны и суперструны. Реджезация элементарных частиц создает мостик между квантовой теорией поля и теорией комплексных моментов и, по-видимому, указывает на связь реджезующихся частиц со струнами. Annotation This book provides a unique and rigorous introduction to the theory of complex angular momenta, based on the methods of field theory. It comprises an English translation of the series of lectures given by V.N. Gribov in 1969, when the physics of high energy hadron interactions was being created. Besides their historical significance, these lectures contain material which is highly relevant to research today. The basic physical results and the approaches Gribov developed are now being rediscovered in a new context: in the microscopic theory of hadrons provided by quantum chromodynamics. The ideas and calculation techniques presented in this book are useful for analysing high energy hadron scattering phenomena, deep inelastic lepton-hadron scattering, the physics of heavy ion collisions, and kinetic phenomena in phase transitions, and will be instrumental in the analysis of electroweak processes at the next generation particle accelerators, such as LHC and TESLA. VLADIMIR NAUMOVICH GRIBOV received his PhD in theoretical physics in 1957 from the Physico-Technical Institute in Leningrad where he had worked since 1954. From 1962 to 1980 he was the head of the Theory Division of the Particle Physics Department of that institute, which in 1971 became the Leningrad Institute for Nuclear Physics. In 1980 he moved to Moscow where he became head of the particle physics section of the Landau Institute for Theoretical Physics. From 1981 he regularly visited the Research Institute for Particle and Nuclear Physics in Budapest where he was a scientific adviser until his death in 1997. Vladimir Gribov was one of the leading theoretical physicists of his time, who made seminal contributions to many fields, including quantum electrodynamics, neutrino physics, non-Abelian field theory, and, in particular, the physics of hadron interactions at high energies. CONTENTS Foreword by Yuri Dokshitzer. Introduction by Yuri Dokshitzer and Leonid Frankfurt.
References. High energy hadron scattering.
Basic principles.
Invariant scattering amplitude and cross section.
Analyticity and causality.
Singularities.
Crossing symmetry.
The unitarity condition for the scattering matrix Mandelstam variables for two-particle scattering.
The Mandelstam plane.
Threshold singularities on the Mandelstam plane Partial wave expansion and unitarity.
Threshold behaviour of partial wave amplitudes.
Singularities of Im A on the Mandelstam plane (Karplus curve).
The Froissart theorem The Pomeranchuk theorem. Physics of the t-channel and complex angular momenta.
Analytical continuation of the t-channel unitarity condition.
The Mandelstam representation.
Inconsistency of the 'black disk' model of diffraction.
Complex angular momenta.
Partial wave expansion and Sommerfeld-Watson representation.
Continuation of partial wave amplitudes to complex l.
Non-relativistic quantum mechanics.
Relativistic theory.
Gribov-Froissart projection.
t-Channel partial waves and the black disk model. Singularities of partial waves and unitarity.
Continuation of partial waves with complex l to t < 0.
Threshold singularity and partial waves φl.
φl(t) At t < 0 and its discontinuity.
The unitarity condition for partial waves with complex l.
Singularities of the partial wave amplitude.
Left cut in non-relativistic theory.
Fixed singularities.
Moving singularities.
Moving poles and resonances. Properties of Regge poles.
Resonances.
Bound states.
Elementary particle or bound state?
Regge trajectories.
Regge pole exchange and particle exchange (t > 0).
Regge exchange and elementary particles (t < 0).
There is no elementary particle with J > 1.
Asymptotics of s-channel amplitudes and reggeization.
Factorization. Regge poles in high energy scattering.
t-Channel dominance.
Elastic scattering and the pomeron.
Quantum numbers of the pomeron.
Slope of the pomeron trajectory.
Shrinkage of the diffractive cone.
s-Channel partial waves in the impact parameter space.
Relation between total cross sections. Scattering of particles with spin.
Vector particle exchange.
Scattering of nucleons.
Reggeon quantum numbers and N-anti N —> reggeon vertices.
Vacuum pole in πN and NN scattering.
Conspiracy. Fermion Regge poles.
Backward scattering as a relativistic effect.
Pion-nucleon scattering.
Parity in the u-channel.
Fermion poles with definite parity and singularity at u = 0.
Oscillations in the fermion pole amplitude.
Reggeization of a neutron. Regge poles in perturbation theory.
Scattering of a particle in an exteal field.
Scalar field theory gφ3.
gφ3 Theory in the Duffin-Kemmer formalism.
Analytic properties of the amplitudes.
Order g4 ln s.
Order g6 ln s.
Ladder diagrams in all orders.
Non-ladder diagrams.
Interaction with vector mesons. Reggeization of an electron.
Electron exchange in O(g6) Compton scattering amplitude.
Electron Regge poles.
Conspiracy in perturbation theory.
Reggeization in QED (with massless photon).
Electron reggeization: nonsense states. Vector fleld theory.
Role of spin effects in reggeization.
Nonsense states in the unitarity condition.
Iteration of the unitarity condition.
Nonsense states from the s- and t-channel points of view.
The j = 1/2 pole in the perturbative nonsense-nonsense amplitude.
QED processes with photons in the t-channel.
The vacuum channel in QED.
The problem of the photon reggeization. Inconsistency of the Regge pole picture.
The pole l = –1 and restriction on the amplitude fall-off.
Contradiction with unitarity l = –1.
Poles condensing at l = –1.
Amplitude cannot fall faster than 1/s.
Particles with spin: failure of the Regge pole picture. Two-reggeon exchange and branch point singularities in the l plane.
Normalization of partial waves and the unitarity condition.
Redefinition of partial wave amplitudes.
Particles with spin in the unitarity condition.
Particle scattering via a two-particle intermediate state.
Two-reggeon exchange and production vertices.
Asymptotics of two-reggeon exchange amplitude.
Two-reggeon branching and l = –1.
Movement of the branching in the t and j planes.
Signature of the two-reggeon branching. Properties of Mandelstam branch singularities.
Branchings as a generalization of the l = –1 singularity.
Branchings in the j plane.
Branch singularity in the unitarity condition.
Branchings in the vacuum channel.
The patte of branch points in the j plane.
The Mandelstam representation in the presence of branchings.
Vacuum-non-vacuum pole branchings.
Experimental verification of branching singularities.
Branchings and conspiracy. Reggeon diagrams.
Two-particle-two-reggeon transition amplitude.
Structure of the vertex.
Analytic properties of the vertex.
Factorization.
Partial wave amplitude of the Mandelstam branching. Interacting reggeons. Reggeon field theory.
Enhanced reggeon diagrams.
Effective field theory of interacting reggeons.
Equation for the Green function G.
Equation for the vertex function Г2.
Weak and strong coupling regimes.
Pomeron Green function and reggeon unitarity condition. The structure of weak and strong coupling solutions.
Weak coupling regime.
The Green function.
P —> PP vertex.
Induced multi-reggeon vertices.
Vanishing of multi-reggeon couplings.
Problems of the strong coupling regime. Appendix A: Space-time description of the hadron interactions at high energies.
Wave function of the hadron. Orthogonality and normalization.
Distribution of the partons in space and momentum.
Deep inelastic scattering.
Strong interactions of hadrons.
Elastic and quasi-elastic processes.
References. Appendix B: Character of inclusive spectra and fluctuations produced in inelastic processes by multi-pomeron exchange.
The absorptive parts of reggeon diagrams in the s-channel. Classification of inelastic processes.
Relations among the absorptive parts of reggeon diagrams.
Inclusive cross sections.
Main corrections to the inclusive cross sections in the central region.
Fluctuations in the distribution of the density of produced particles.
References. Appendix C: Theory of the heavy pomeron.
Introduction.
Non-enhanced cuts at α’ = 0.
Estimation of enhanced cuts at α’ = 0.
Structure of the transition amplitude of one pomeron – to two.
The Green function and the vertex part at α’ = 0.
Properties of high energy processes in the theory with α’ = 0.
Two-particle processes, total cross sections.
Inclusive spectra, multiplicity.
Correlation, multiplicity distribution.
Probability of fluctuations in individual events: the inclusive spectrum in the three-pomeron limit. Multi-reggeon processes.
The case α’ =/= 0.
The contribution of cuts at small α’.
Conclusion.
References. Index.