Series: London Mathematical Society Lecture Note Series (No.
332)
Paperback (ISBN-13: 9780521680455 | ISBN-10: 052168045X)
Tilting theory originates in the representation theory of finite
dimensional algebras. Today the subject is of much interest in
various areas of mathematics, such as finite and algebraic group
theory, commutative and non-commutative algebraic geometry, and
algebraic topology. The aim of this book is to present the basic
concepts of tilting theory as well as the variety of applications.
It contains a collection of key articles, which together form a
handbook of the subject, and provide both an introduction and
reference for newcomers and experts alike.
* Comprehensive treatment of the subject, from basic results
through to applications
* Contributors of the highest calibre cover up-to-date results
* Ideal for self-teaching and as a reference or handbook
Contents
1. Introduction; 2. Basic results of classic tilting theory L.
Angeleri Hugel, D. Happel and H. Krause; 3. Classification of
representation-finite algebras and their modules T. Brustle; 4. A
spectral sequence analysis of classical tilting functors S.
Brenner and M. C. R. Butler; 5. Derived categories and tilting B.
Keller; 6. Fourier-Mukai transforms L. Hille and M. Van den
Bergh; 7. Tilting theory and homologically finite subcategories
with applications to quasihereditary algebras I. Reiten; 8.
Tilting modules for algebraic groups and finite dimensional
algebras S. Donkin; 9. Combinatorial aspects of the set of
tilting modules L. Unger; 10. Cotilting dualities R. Colpi and K.
R. Fuller; 11. Infinite dimensional tilting modules and cotorsion
pairs J. Trlifaj; 12. Infinite dimensional tilting modules over
finite dimensional algebras O. Solberg; 13. Representations of
finite groups and tilting J. Chuang and J. Rickard; 14. Morita
theory in stable homotopy theory B. Shipley.
Lecture Notes - Monograph Series,vol.48
This volume contains 29 contributions by Mike's closest
colleagues covering a broad range of topics in Dynamics and
Stochastics.
View Table of Contents
Series: Cambridge Tracts in Mathematics (No. 169)
Hardback (ISBN-13: 9780521834506 | ISBN-10: 0521834503)
The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
* This book is the first to describe how the mathematical constructions of noncommutative geometry and quantum stochastic structures are related
* Contains many unique features, e.g. discussion of calculus with unbounded operator coefficients
* Accessible to a wide range of graduate students and researchers
Contents
1. Introduction; 2. Preliminaries; 3. Quantum dynamical semigroups; 4. Hilbert modules; 5. Quantum stochastic calculus with bounded coefficients; 6. Dilation of quantum dynamical semigroups with bounded generator; 7. Quantum stochastic calculus with unbounded coefficients; 8. Dilation of quantum dynamical semigroups with unbounded generator; 9. Noncommutative geometry and quantum stochastic processes; Bibliography; Index.
Hardback (ISBN-13: 9780521864497 | ISBN-10: 0521864496)
Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.
* A complete treatment of elementary particle theory from basics to advanced topics
* Contains 250 excercises with solutions available to lecturers at www.cambridge.org/9780521864497
* Presented in a logical sequence
* Written in a flexible, modular format with fully self-contained chapters
Contents
Preface for students; Preface for instructors; Acknowledgements; Part I. Spin Zero: 1. Attempts at relativistic quantum mechanics; 2. Lorentz invariance; 3. Canonical quantization of scalar fields; 4. The spin-statistics theorem; 5. The LSZ reduction formula; 6. Path integrals in quantum mechanics; 7. The path integral for the harmonic oscillator; 8. The path integral for free field theory; 9. The path integral for interacting field theory; 10. Scattering amplitudes and the Feynman rules; 11. Cross sections and decay rates; 12. Dimensional analysis with ?=c=1; 13. The Lehmann-Kallen form; 14. Loop corrections to the propagator; 15. The one-loop correction in Lehmann-Kallen form; 16. Loop corrections to the vertex; 17. Other 1PI vertices; 18. Higher-order corrections and renormalizability; 19. Perturbation theory to all orders; 20. Two-particle elastic scattering at one loop; 21. The quantum action; 22. Continuous symmetries and conserved currents; 23. Discrete symmetries: P, T, C, and Z; 24. Nonabelian symmetries; 25. Unstable particles and resonances; 26. Infrared divergences; 27. Other renormalization schemes; 28. The renormalization group; 29. Effective field theory; 30. Spontaneous symmetry breaking; 31. Broken symmetry and loop corrections; 32. Spontaneous breaking of continuous symmetries; Part II. Spin One Half: 33. Representations of the Lorentz Group; 34. Left- and right-handed spinor fields; 35. Manipulating spinor indices; 36. Lagrangians for spinor fields; 37. Canonical quantization of spinor fields I; 38. Spinor technology; 39. Canonical quantization of spinor fields II; 40. Parity, time reversal, and charge conjugation; 41. LSZ reduction for spin-one-half particles; 42. The free fermion propagator; 43. The path integral for fermion fields; 44. Formal development of fermionic path integrals; 45. The Feynman rules for Dirac fields; 46. Spin sums; 47. Gamma matrix technology; 48. Spin-averaged cross sections; 49. The Feynman rules for majorana fields; 50. Massless particles and spinor helicity; 51. Loop corrections in Yukawa theory; 52. Beta functions in Yukawa theory; 53. Functional determinants; Part III. Spin One: 54. Maxwell's equations; 55. Electrodynamics in coulomb gauge; 56. LSZ reduction for photons; 57. The path integral for photons; 58. Spinor electrodynamics; 59. Scattering in spinor electrodynamics; 60. Spinor helicity for spinor electrodynamics; 61. Scalar electrodynamics; 62. Loop corrections in spinor electrodynamics; 63. The vertex function in spinor electrodynamics; 64. The magnetic moment of the electron; 65. Loop corrections in scalar electrodynamics; 66. Beta functions in quantum electrodynamics; 67. Ward identities in quantum electrodynamics I; 68. Ward identities in quantum electrodynamics II; 69. Nonabelian gauge theory; 70. Group representations; 71. The path integral for nonabelian gauge theory; 72. The Feynman rules for nonabelian gauge theory; 73. The beta function for nonabelian gauge theory; 74. BRST symmetry; 75. Chiral gauge theories and anomalies; 76. Anomalies in global symmetries; 77. Anomalies and the path integral for fermions; 78. Background field gauge; 79. Gervais-Neveu gauge; 80. The Feynman rules for N x N matrix fields; 81. Scattering in quantum chromodynamics; 82. Wilson loops, lattice theory, and confinement; 83. Chiral symmetry breaking; 84. Spontaneous breaking of gauge symmetries; 85. Spontaneously broken abelian gauge theory; 86. Spontaneously broken nonabelian gauge theory; 87. The standard model: Gauge and Higgs sector; 88. The standard model: Lepton sector; 89. The standard model: Quark sector; 90. Electroweak interactions of hadrons; 91. Neutrino masses; 92. Solitons and monopoles; 93. Instantons and theta vacua; 94. Quarks and theta vacua; 95. Supersymmetry; 96. The minimal supersymmetric standard model; 97. Grand unification; Bibliography.
Reviews
'This accessible and conceptually structured introduction to quantum field theory will be of value not only to beginning students but also to practicing physicists interested in learning or reviewing specific topics. The book is organized in a modular fashion, which makes it easy to extract the basic information relevant to the reader's area(s) of interest. The material is presented in an intuitively clear and informal style. Foundational topics such as path integrals and Lorentz representations are included early in the exposition, as appropriate for a modern course; later material includes a detailed description of the Standard Model and other advanced topics such as instantons, supersymmetry, and unification, which are essential knowledge for working particle physicists, but which are not treated in most other field theory texts.' Washington Taylor, Massachusetts Institute of Technology
'Over the years I have used parts of Srednicki's book to teach field theory to physics graduate students not specializing in particle physics. This is a vast subject, with many outstanding textbooks. Among these, Srednicki's stands out for its pedagogy. The subject is built logically, rather than historically. The exposition walks the line between getting the idea across and not shying away from a serious calculation. Path integrals enter early, and renormalization theory is pursued from the very start.... By the end of the course the student should understand both beta functions and the Standard Model, and be able to carry through a calculation when a perturbative calculation is called for.' Predrag Cvitanovi, Georgia Institute of Technology
'This book should become a favorite of quantum field theory students and instructors. The approach is systematic and comprehensive, but the friendly and encouraging voice of the author comes through loud and clear to make the subject feel accessible. Many interesting examples are worked out in pedagogical detail.' Ann Nelson, University of Washington
'I expect that this will be the textbook of choice for many quantum field theory courses. The presentation is straightforward and readable, with the author's easy-going 'voice' coming through in his writing. The organization into a large number of short chapters, with the prerequisites for each chapter clearly marked, makes the book flexible and easy to teach from or to read independently. A large and varied collection of special topics is available, depending on the interests of the instructor and the student.' Joseph Polchinski, University of California, Santa Barbara