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One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts.   This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison.   The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Field theory (Physics). --- Global analysis. --- Mathematics. --- Quantum field theory. --- Quantum theory. --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Geometry --- Atomic Physics --- Quantum gravity. --- Gravity, Quantum --- Relativistic quantum field theory --- Algebra. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Global Analysis and Analysis on Manifolds. --- Field Theory and Polynomials. --- General relativity (Physics) --- Gravitation --- Quantum theory --- Field theory (Physics) --- Relativity (Physics) --- Classical field theory --- Continuum physics --- Continuum mechanics --- Mathematical analysis --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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Geometry, Differential. --- Differential topology. --- Géométrie différentielle. --- Topologie différentielle. --- Fermions. --- Quantum theory. --- Geometry, Differential --- Fermions --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Fermi-Dirac particles --- Particles (Nuclear physics) --- Quantum statistics --- Interacting boson-fermion models --- Leptons (Nuclear physics) --- Differential geometry

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This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Gravitation. --- Mathematical physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Mathematical Physics. --- Physical mathematics --- Physics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Mathematics --- Properties --- Quantum gravity --- Gravitation --- Gravity, Quantum --- General relativity (Physics) --- Quantum theory --- Research. --- Mathematical models.