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Introduction to Quantum Effects in Gravity
Publisher description
Linear Algebra Via Exterior Products
This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.
Eternal Inflation
In this book, I discuss the long-standing technical and conceptual problems arising within the statistical framework describing models of cosmological inflation, known collectively as the "measure problem" in multiverse cosmology. After reviewing various existing approaches and mathematical techniques developed in the past two decades for studying these issues, I describe a new proposal for a measure in the multiverse, called the reheating-volume (RV) measure. The RV measure is based on approximating an infinite multiverse by a family of progressively larger but finite multiverses. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type and to landscape scenarios. The RV prescription is formulated differently for scenarios with eternal inflation of the random walk type and for landscape scenarios. I derive analytic formulas for RV-regulated probability distributions that is suitable for numerical computations.
Gauge/Gravity Duality
The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.
Inflationary Cosmology
Some 25 years after the birth of inflationary cosmology, this volume sets out to provide both an authoritative and pedagogical introduction and review of the current state of the field. Readers learn about the arguments supporting the many different scenarios of cosmic inflation. Articles are written by eminent scientists, many of whom have made pioneering contributions to the field of inflationary cosmology.
A First Course in General Relativity
Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
Tensor Spaces and Exterior Algebra
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. to facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. in particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
Algorithms, Part II
This book is Part II of the fourth edition of Robert Sedgewick and Kevin Wayne’s Algorithms, the leading textbook on algorithms today, widely used in colleges and universities worldwide. Part II contains Chapters 4 through 6 of the book. The fourth edition of Algorithms surveys the most important computer algorithms currently in use and provides a full treatment of data structures and algorithms for sorting, searching, graph processing, and string processing -- including fifty algorithms every programmer should know. In this edition, new Java implementations are written in an accessible modular programming style, where all of the code is exposed to the reader and ready to use. The algorith...
Physical Foundations of Cosmology
Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. This textbook, first published in 2005, explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.
