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This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West. Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work...
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
A lively, varied and topical presentation of this branch of theoretical physics.
The Adriatic Meetings have traditionally been conferences on the most - vanced status of science. They are one of the very few conferences in physics aiming at a very broad participation of young and experienced researchers with di?erent backgrounds in particle physics. Particle physics has grown into a highly multi-faceted discipline over the sixty years of its existence, mainly because of two reasons: Particle physics as an experimental science is in need of large-scale laboratory set-ups, involving typically collaborations of several hundreds or even thousands of researchers and technicians with the most diverse expertise. This forces particle physics, being one of the most fundamental di...
This volume contains the proceedings of a meeting held at Imperial College which is devoted to recent developments in string theory, supersymmetry and quantum gravity. The volume comprises two different sections. The first consists of five pedagogical reviews by prominent physicists, covering the currently important subjects of supermembranes, duality, D-branes, new non-perturbative methods and string phenomenology. The second section consists of research reports in these areas and also on other currently important topics such as supersymmetric gauge theories, two-dimensional quantum gravity and black holes.
A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.
This collection of invited lectures (at the Conference on Secondary Calculus and Cohomological Physics, Moscow, 1997) reflects the state-of-the-art in a new branch of mathematics and mathematical physics arising at the intersection of geometry of nonlinear differential equations, quantum field theory, and cohomological algebra. This is the first comprehensive and self-contained book on modern quantum field theory in the context of cohomological methods and the geometry of nonlinear PDEs.
Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.
In 1561, a Eucharistic controversy erupted in Danzig of the sixteenth century, sparked by disagreements on the real presence and the practical treatment of the Eucharistic elements. It was one of many inner-Lutheran struggles over the Lord's Supper in the years following the Reformation and therefore Björn Ole Hovda supplements the scientific studies on that topic. Different understandings of the presence of Christ during the Lord's Supper formed different religious norms of practice. On the one hand, the controversy is here analyzed as a discussion on doctrine between opposing ecclesiastical factions, set in the context of reformatory theology and liturgical practice. The theological discu...