Research into the stability of matter has been one of the most
successful chapters in mathematical physics, and is a prime example
of how modern mathematics can be applied to problems in physics. A
unique account of the subject, this book provides a complete,
self-contained description of research on the stability of matter
problem. It introduces the necessary quantum mechanics to
mathematicians, and aspects of functional analysis to physicists.
The topics covered include electrodynamics of classical and
quantized fields, Lieb-Thirring and other inequalities in spectral
theory, inequalities in electrostatics, stability of large Coulomb
systems, gravitational stability of stars, basics of equilibrium
statistical mechanics, and the existence of the thermodynamic
limit. The book is an up-to-date account for researchers, and its
pedagogical style makes it suitable for advanced undergraduate and
graduate courses in mathematical physics.
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