Geometry, Topology and Quantum Field Theory

This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed t...

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Main Author: Bandyopadhyay, P.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 2003, 2003
Edition:1st ed. 2003
Series:Fundamental Theories of Physics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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300 |a XI, 220 p. 1 illus  |b online resource 
505 0 |a 1 Theory of Spinors -- 2 Fermions and Topology -- 3 Electroweak Theory -- 4 Skyrme Model -- 5 Geometrical Aspects of a Skyrmion -- 6 Noncommutative Geometry -- References 
653 |a Global Analysis and Analysis on Manifolds 
653 |a Nuclear Physics, Heavy Ions, Hadrons 
653 |a Differential geometry 
653 |a Nuclear physics 
653 |a Quantum field theory 
653 |a Elementary particles (Physics) 
653 |a Quantum Physics 
653 |a Heavy ions 
653 |a Differential Geometry 
653 |a Quantum physics 
653 |a Manifolds (Mathematics) 
653 |a Elementary Particles, Quantum Field Theory 
653 |a Global analysis (Mathematics) 
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520 |a This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. The geometrical feature of a skyrmion also helps us to realize the internal symmetry of hadrons from reflection group. Finally it has been shown that noncommutative geometry where the space time manifold is taken to be X = M x Zz has its relevance in the description of a massive 4 fermion as a skyrmion when the discrete space is considered as the internal space and the symmetry breaking leads to chiral anomaly. In chap. l preliminary mathematical formulations related to the spinor structure have been discussed. In chap