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Quantum Field Theory of Many-Body SystemsFrom the Origin of Sound to an Origin of Light and Electrons$
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Xiao-Gang Wen

Print publication date: 2007

Print ISBN-13: 9780199227259

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199227259.001.0001

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Quantum Gauge Theories

Quantum Gauge Theories

Quantum Field Theory of Many-Body Systems

Xiao-Gang Wen

Oxford University Press

The last few chapters have discussed many-boson theory and many-fermion theory because nature has many-boson systems and many-fermion systems. Do many-boson/many-fermion theories describe all the systems in nature? The answer is no. Nature also has photons. Although photons are bosons, they cannot be described by the local bosonic theory discussed in Chapter 3. Photons are described by a non-local quantum theory which is called U(1) gauge theory. This chapter discusses U(1) gauge theory as well as Z_2 gauge theory on lattice. It stresses the non-localness in their Hilbert space. The gapless photonic, as well as the ‘electric’ and the ‘magnetic’ excitations are studied. The chapter also discusses the confinement phase transition in those gauge theories, and a duality between U(1) gauge theory and XY model in 1+2 dimensions.

Keywords:   gauge theory, gauge symmetry, photon, flux, vortex, topological degeneracy

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