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This book offers a concise introduction to quantum field theory and functional integration for students of physics and mathematics. Its aim is to explain mathematical methods developed in the 1970s and 1980s and apply these methods to standard models of quantum field theory. In contrast to other textbooks on quantum field theory, this book treats functional integration as a rigorous mathematical tool. More emphasis is placed on the mathematical framework as opposed to applications to particle physics. It is stressed that the functional integral approach, unlike the operator framework, is suitable for numerical simulations. The book arose from the author's teaching in Wroclaw and preserves the form of his lectures. So some topics are treated as an introduction to the problem rather than a complete solution with all details. Some of the mathematical methods described in the book resulted from the author's own research.

Is everything Information? This is a tantalizing question which emerges in modern physics, life sciences, astronomy and in today's information and technology-driven society. In Powers of Two expert authors undertake a unique expedition - in words and images - throughout the world (and scales) of information. The story resembles, in a way, the classic Powers of Ten journeys through space: from us to the macro and the micro worlds. However, by following Powers of Two through the world of information, a completely different and timely paradigm unfolds. Every power of two, 1, 2, 4, 8…. tells us a different story: starting from the creation of the very first bit at the Big Bang and the evolution of life, through 50 years of computational science, and finally into deep space, describing the information in black holes and even in the entire universe and beyond…. All this to address one question: Is our universe made of information? In this book, we experience the Information Universe in nature and in our society and how information lies at the very foundation of our understanding of the Universe.From the Foreword by Robbert Dijkgraaf: This book is in many ways a vastly extended version of Shannon's one-page blueprint. It carries us all the way to the total information content of the Universe. And it bears testimony of how widespread the use of data has become in all aspects of life. Information is the connective tissue of the modern sciences. […] Undoubtedly, future generations will look back at this time, so much enthralled by Big Data and quantum computers, as beholden to the information metaphor. But that is exactly the value of this book. With its crisp descriptions and evocative illustrations, it brings the reader into the here and now, at the very frontier of scientific research, including the excitement and promise of all the outstanding questions and future discoveries.Message for the e-reader of the book Powers of Two The book has been designed to be read in two-page spreads in full screen mode. For optimal reader experience in a downloaded.pdf file we strongly recommend you use the following settings in Adobe Acrobat Reader: - Taskbar: View > Page Display > two page view - Taskbar: View > Page Display > Show Cover Page in Two Page View - Taskbar: ^ Preferences > Full Screen > deselect'Fill screen with one page at a time'- Taskbar: View > Full screen mode or ctrl L (cmd L on a Mac) ••••• Note: for reading the previews on Spinger link (and on-line reading in a browser), the full screen two-page view only works with these browsers: Firefox - Taskbar: on top of the text, at the uppermost right you will see then >> (which is a drop-down menu) >> even double pages - Fullscreen: F11 or Control+Cmd+F with Mac Edge - Taskbar middle: Two-page view and select show cover page separately

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert's works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, butsheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Intended as a companion book to The Created Cosmos: What the Bible Reveals About Astronomy, the new book, The Expanse of Heaven: Where Creation and Astronomy Intersect, is a comprehensive treatment of astronomy, interpreted within the biblical model of creation. It begins with a chapter on ancient cosmologies, and concludes with a chapter on modern cosmology. In between are chapters on the appearance of astronomical bodies in the sky, discussions of the moon, the earth and other planets in the solar system, the sun, the stars, our Milky Way Galaxy and other galaxies. Evolutionary theories are described and critiqued, while creationary theories are explained. Evidence for design and recent origin is presented. This unique book is intended for general reading by lay audiences, but it can be adapted as a textbook on astronomy. You will learn how unique the earth is in the universe You will see incredible design in the moon, the sun, and other astronomical bodies You will better understand the role of evolutionary and creationary theories in astronomy today

The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for both perturbative as well as non-perturbative studies, and is known to already provide a framework of choice for the theoretical investigation of non-abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman's formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. Later the lattice formulation of gravity is presented as an essential tool towards an understanding of key features of the non-perturbative vacuum. The book ends with a discussion of contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.

This book is a new edition of'Tensors and Manifolds: With Applications to Mechanics and Relativity'which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, as well as additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.