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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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BRST Symmetry and de Rham Cohomology (Hardcover, 2015 ed.)
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BRST Symmetry and de Rham Cohomology (Hardcover, 2015 ed.)
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This book provides an advanced introduction to extended theories of
quantum field theory and algebraic topology, including Hamiltonian
quantization associated with some geometrical constraints,
symplectic embedding and Hamilton-Jacobi quantization and
Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham
cohomology. It offers a critical overview of the research in this
area and unifies the existing literature, employing a consistent
notation. Although the results presented apply in principle to all
alternative quantization schemes, special emphasis is placed on the
BRST quantization for constrained physical systems and its
corresponding de Rham cohomology group structure. These were
studied by theoretical physicists from the early 1960s and appeared
in attempts to quantize rigorously some physical theories such as
solitons and other models subject to geometrical constraints. In
particular, phenomenological soliton theories such as Skyrmion and
chiral bag models have seen a revival following experimental data
from the SAMPLE and HAPPEX Collaborations and these are discussed.
The book describes how these model predictions were shown to
include rigorous treatments of geometrical constraints because
these constraints affect the predictions themselves. The
application of the BRST symmetry to the de Rham cohomology
contributes to a deep understanding of Hilbert space of constrained
physical theories. Aimed at graduate-level students in quantum
field theory, the book will also serve as a useful reference for
those working in the field. An extensive bibliography guides the
reader towards the source literature on particular topics.
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