In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes'' approach to the standard model.

In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes' approach to the standard model.

The contributions presented in this volume address graduatestudents as wellas researchers. They are intelligible andpedagogically well-written reviewsof the most recentdevelopments in quantum field theory and both quantumgravity and quantum supergravity. Alongside technicalproblems of field quantization the reader will also findcareful discussions of the conceptual framework and ofapplications to quantum cosmology.

This is a review written by leading specialists on the stateof the art of computational methods in lattice field theory.They cover a wide range: computer-assisted proofs,algorithms for computer simulation of field theories,effective field theories, computer studies of finite sizeeffects, simulation with fast algorithms, and computerapplicationsin experimental particle physics. The bookaddresses researchers, engineers,and graduate students inparticle physics.

In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes'' approach to the standard model.

In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes' approach to the standard model.

The contributions presented in this volume address graduatestudents as wellas researchers. They are intelligible andpedagogically well-written reviewsof the most recentdevelopments in quantum field theory and both quantumgravity and quantum supergravity. Alongside technicalproblems of field quantization the reader will also findcareful discussions of the conceptual framework and ofapplications to quantum cosmology.

This is a review written by leading specialists on the stateof the art of computational methods in lattice field theory.They cover a wide range: computer-assisted proofs,algorithms for computer simulation of field theories,effective field theories, computer studies of finite sizeeffects, simulation with fast algorithms, and computerapplicationsin experimental particle physics. The bookaddresses researchers, engineers,and graduate students inparticle physics.