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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Geometric Analysis and Applications to Quantum Field Theory (Hardcover, 2002 ed.)
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Geometric Analysis and Applications to Quantum Field Theory (Hardcover, 2002 ed.)
Series: Progress in Mathematics, 205
Expected to ship within 10 - 15 working days
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In recent years, there has been tremendous progress on the
interface of geometry and mathematical physics. This book reflects
the expanded articles of several lectures in these areas delivered
at the University of Adelaide, with an audience of primarily
graduate students. The aim of this volume is to provide surveys of
recent progress without assuming too much prerequisite knowledge
and with a comprehensive bibliography, so that researchers and
graduate students in geometry and mathematical physics will
benefit. The contributors cover a number of areas in mathematical
physics. Chapter 1 offers a self-contained derivation of the
partition function of Chern-Simons gauge theory in the
semiclassical approximation. Chapter 2 considers the algebraic and
geometric aspects of the Knizhnik-Zamolodchikov equations in
conformal field theory, including their relation to the braid
group, quantum groups and infinite dimensional Lie algebras.
Chapter 3 surveys the application of the representation theory of
loop groups to simple models in quantum field theory and to certain
integrable systems. Chapter 4 examines the variational methods in
Hermitian geometry from the viewpoint of the critical points of
action functionals together with physical backgrounds. Chapter 5 is
a review of monopoles in non-Abelian gauge theories and the various
approaches to understanding them. Chapter 6 covers much of the
exciting recent developments in quantum cohomology, including
relative Gromov-Witten invariant, birational geometry, naturality
and mirror symmetry. Chapter 7 explains the physics origin of the
Seiberg-Witten equations in four-manifold theory and a number of
important concepts in quantum field theory, such asvacuum, mass
gap, (super)symmetry, anomalies and duality. Contributors: D.H.
Adam, P. Bouwknegt, A.L. Carey, A. Harris, E. Langmann, M.K.
Murray, Y. Ruan, S. Wu D. H. Adams: Semiclassical Approximation in
Chern-Simons Gauge Theory P. Bouwknegt: The Knizhnik-Zamolodchikov
Equations A. L. Carey and E. Langmann: Loop Groups and Quantum
Fields A. Harris: Some Applications of Variational Calculus in
Hermitian Geometry M. K. Murray: Monopoles Y. Ruan: On
Gromov-Witten Invariants and Quantum Cohomology S. Wu The Geometry
and Physics of the Seiberg-Witten Equations
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