Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521769143)
Page extent: 280 pages
Size: 247 x 174 mm
As the structures in our Universe are mapped out on ever larger scales, and with increasing detail, the use of inhomogeneous models is becoming an essential tool for analyzing and understanding them. This book reviews a number of important developments in the application of inhomogeneous solutions of Einstein’s field equations to cosmology. It shows how inhomogeneous models can be employed to study the evolution of structures such as galaxy clusters and galaxies with central black holes, and to account for cosmological observations like supernovae dimming, the cosmic microwave background, baryon acoustic oscillations or the dependence of the Hubble parameter on redshift within classical general relativity. Whatever `dark matter’ and `dark energy’ turn out to be, inhomogeneities exist on many scales and need to be investigated with all appropriate methods. This book is of great value to all astrophysicists and researchers working in cosmology, from graduate students to academic researchers.
Presents inhomogeneous cosmological models, allowing readers to familiarise
themselves with basic properties of these models Shows how inhomogeneous
models can be used to analyse cosmological observations such as supernovae,
cosmic microwave background, and baryon acoustic oscillations Reviews
important developments in the application of inhomogeneous solutions of
Einstein’s field equations to cosmology
1. The purpose of this book; Part I. Theoretical Background: 2. Exact solutions of Einstein's equations that are used in cosmology; 3. Light propagation; Part II. Applications of the Models in Cosmology: 4. Structure formation; 5. The cosmological constant and coincidence problems; 6. The horizon problem; 7. CMB temperature fluctuations; 8. Conclusions; References; Index.
Hardback (ISBN-13: 9780521877602)
230 exercises
Page extent: 750 pages
Size: 246 x 189 mm
Students and instructors alike will find this organized and detailed approach to quantum mechanics ideal for a two-semester graduate course on the subject. This textbook covers, step-by-step, important topics in quantum mechanics, from traditional subjects like bound states, perturbation theory and scattering, to more current topics such as coherent states, quantum Hall effect, spontaneous symmetry breaking, superconductivity, and basic quantum electrodynamics with radiative corrections. The large number of diverse topics are covered in concise, highly focused chapters, and are explained in simple but mathematically rigorous ways. Derivations of results and formulae are carried out from beginning to end, without leaving students to complete them. With over 200 exercises to aid understanding of the subject, this textbook provides a thorough grounding for students planning to enter research in physics. Several exercises are solved in the text, and password-protected solutions for remaining exercises are available to instructors at www.cambridge.org/9780521877602.
Diverse topics are covered in logical order through concise, highly focused
chapters Topics are explained in simple but mathematically rigorous ways
Derivations of results and formulae are carried out from beginning to end,
without leaving students to complete them
Preface; 1. Basic formalism; 2. Fundamental commutator and time evolution of state vectors and operators; 3. Dynamical equations; 4. Free particles; 5. Particles with spin 1/2; 6. Gauge invariance, angular momentum and spin; 7. Stern-Gerlach experiments; 8. Some exactly solvable bound state problems; 9. Harmonic oscillator; 10. Coherent states; 11. Two-dimensional isotropic harmonic oscillator; 12. Landau levels and quantum Hall effect; 13. Two-level problems; 14. Spin 1/2 systems in the presence of magnetic field; 15. Oscillation and regeneration in neutrino and neutral K-mesons as two-level systems; 16. Time-independent perturbation for bound states; 17. Time-dependent perturbation; 18. Interaction of charged particles and radiation in perturbation theory; 19. Scattering in one dimension; 20. Scattering in three dimensions - a formal theory; 21. Partial wave amplitudes and phase shifts; 22. Analytic structure of the S-matrix; 23. Poles of the Green's function and composite systems; 24. Approximation methods for bound states and scattering; 25. Lagrangian method and Feynman path integrals; 26. Rotations and angular momentum; 27. Symmetry in quantum mechanics and symmetry groups; 28. Addition of angular momenta; 29. Irreducible tensors and Wigner-Eckart theorem; 30. Entangled states; 31. Special theory of relativity: Klein Gordon and Maxwell's equation; 32. Klein Gordon and Maxwell's equation; 33. Dirac equation; 34. Dirac equation in the presence of spherically symmetric potentials; 35. Dirac equation in a relativistically invariant form; 36. Interaction of Dirac particle with electromagnetic field; 37. Multiparticle systems and second quantization; 38. Interactions of electrons and phonons in condensed matter; 39. Superconductivity; 40. Bose Einstein condensation and superfluidity; 41. Lagrangian formulation of classical fields; 42. Spontaneous symmetry breaking; 43. Basic quantum electrodynamics and Feynman diagrams; 44. Radiative corrections; 45. Anomalous magnetic moment and Lamb shift; Appendix; References; Index.
Series: Dolciani Mathematical Expositions (No. 37)
Hardback (ISBN-13: 9780883853436)
Page extent: 110 pages
Size: 247 x 174 mm
This concise guide to real analysis covers the core material of a graduate level real analysis course. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form. The prerequisite is a familiarity with classical real-variable theory.
Covers the core material found on a graduate course on real analysis
Gives an overview of the subject so that it can be used as a guide for
a beginner or as a refresher for those who have previously studied the
subject To remain concise, essential definitions, major theorems, and
key ideas of proofs are included and technical details are not
Preface; Prologue: notation, terminology, and set theory; Numbers; sets and mappings; Zorn's lemma; 1. Topology; 2. Measure and integration: general theory; 3. Measure and integration; 4. Rudiments of functional analysis; 5. Function spaces; 6. Topics in analysis on Euclidean space; Bibliography; Index
Series: London Mathematical Society Lecture Note Series (No. 368)
Paperback (ISBN-13: 9780521733076)
Page extent: 415 pages
Size: 228 x 152 mm
Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation theory, coding, thermodynamic formalism, and topology of three-dimensional manifolds. This collection of articles, authored by leading authorities in the field, comprises 16 expository essays presenting original research and up-to-date surveys of important topics related to Riemann surfaces and their geometry. It complements the body of recorded research presented in the primary literature by broadening, re-working and extending it in a more focused and less formal framework, and provides a valuable commentary on contemporary work in the subject. An introductory section sets the scene and provides sufficient background to allow graduate students and research workers from other related areas access to the field.
An up-to-date survey of a rapidly expanding area of mathematics Authored
by well-known authorities in the field Contains an introductory section
that opens up the field to graduate students and researchers from a variety
of related fields
Preface; Foreword W. J. Harvey; Semisimple actions of mapping class groups
on CAT(0) spaces M. R. Bridson; A survey of research inspired by Harvey's
theorem on cyclic groups of automorphisms E. Bujalance, F. J. Cirre and
G. Gromadzki; Algorithms for simple closed geodesics P. Buser; Matings
in holomorphic dynamics S. Bullett; Equisymmetric strata of the singular
locus of the moduli space of Riemann surfaces of genus 4 A. F. Costa and
M. Izquierdo; Diffeomorphisms and automorphisms of compact hyperbolic 2-orbifolds
C. J. Earle; Holomorphic motions and related topics F. P. Gardiner, Y.
Jiang and Z. Wang; Cutting sequences and palindromes J. Gilman and L. Keen;
On a Schottky problem for the singular locus of A5 V. Gonzalez-Aguilera;
Non-special divisors supported on the branch set of a p-gonal Riemann surface
G. Gonzalez-Diez; A note on the lifting of automorphisms R. Hidalgo and
B. Maskit; Simple closed geodesics of equal length on a torus G. McShane
and H. Parlier; On extensions of holomorphic motions a survey S. Mitra;
Complex hyperbolic quasi-Fuchsian groups J. R. Parker and I. D. Platis;
Geometry of optimal trajectories M. Pontani and P. Teofilatto; Actions
of fractional Dehn twists on moduli spaces R. Silhol.
Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521662659)
Page extent: 456 pages
Size: 247 x 174 mm
Providing a new perspective on quantum field theory, this book gives a pedagogical and up-to-date exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research work in theoretical physics. It describes in detail non-perturbative methods in quantum field theory, and explores two- dimensional and four- dimensional gauge dynamics using those methods. The book concludes with a summary emphasizing the interplay between two- and four- dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics (QCD) in particular, are thoroughly described.
Presents a new perspective on relativistic quantum field theory Features
detailed studies of major subjects, including conformal symmetry, bosonization
and large N Explains applications to gauge theories in general and QCD
in particular, including spectrum and scattering
Preface; Acknowledgements; Part I. Non-Perturbative Methods in Two Dimensional Field Theory: 1. From massless free scalar field to conformal field theories; 2. Conformal field theory; 3. Theories invariant under affine current algebras; 4. Wess-Zumino-Witten model and Coset models; 5. Solitons and two dimensional integrable models; 6. Bosonization; 7. The large N limit of two dimensional models; Part II. Two Dimensional Non-Perturbative Gauge Dynamics: 8. Gauge theories in two dimensions - basics; 9. Bosonized gauge theories; 10. The t'Hooft solution of 2d QCD; 11. Mesonic spectrum from current algebra; 12. DLCQ and the spectra of QC with fundamental and adjoint fermions; 13. The baryonic spectrum of multiflavour QCD2 in the strong coupling limit; 14. Confinement versus screening; 15. QCD2, Coset models and BRST quantization; 16. Generalized Yang Mills theory on Riemann surface; Part III. From Two to Four Dimensions: 17. Conformal invariance in four dimensional field theories and in QCD; 18. Integrability in four dimensional gauge dynamics; 19. Large N methods in QCD4; 20. From 2d bosonized baryons to 4d skyrmions; 21. From two dimensional solitons to four dimensional magnetic monopoles; 22. Instantons of QCD; 23. Summary, conclusions and outlook; References; Index.