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In recent years the subject of relativistic fluid dynamics has
found substantial applications in astrophysics and cosmology
(theories of gravitational collapse, models of neutron stars,
galaxy formation), as well as in plasma physics (relativistic
fluids have been considered as models for relativistic particle
beams) and nuclear physics (relativistic fluids are currently used
in the analysis of the heavy ion reactions). Modern methods of
analysis and differential geometry have now also been introduced.
The International C.I.M.E. Course brought together expertise and
interest from several areas (astrophysics, plasma physics, nuclear
physics, mathematical methods) to create an appropriate arena for
discussion and exchange of ideas. The main lecture courses
introduced the most significant aspects of the subject and were
delivered by leading specialists. The notes of these have been
written up for this volume and constitute an up-to-date and
thorough treatment of these topics. Several contributions from the
seminars on specialized topics of complementary interest to the
courses are also included.
This reference book, which has found wide use as a text, provides
an answer to the needs of graduate physical mathematics students
and their teachers. The present edition is a thorough revision of
the first, including a new chapter entitled Connections on
Principle Fibre Bundles'' which includes sections on holonomy,
characteristic classes, invariant curvature integrals and problems
on the geometry of gauge fields, monopoles, instantons, spin
structure and spin connections. Many paragraphs have been
rewritten, and examples and exercises added to ease the study of
several chapters. The index includes over 130 entries.
Twelve problems have been added to the first edition; four of them
are supplements to problems in the first edition. The others deal
with issues that have become important, since the first edition of
Volume II, in recent developments of various areas of physics. All
the problems have their foundations in volume 1 of the 2-Volume set
"Analysis, Manifolds and Physics". It would have been prohibitively
expensive to insert the new problems at their respective places.
They are grouped together at the end of this volume, their logical
place is indicated by a number of parenthesis following the title.
In A Lady Mathematician, the distinguished mathematician and
physicist, Yvonne Choquet-Bruhat, at the urging of her children,
recounts and reflects upon various key events and people from her
life - first childhood memories of France, then schooling, followed
by graduate studies, and finally her continuous research in the
mathematics of General Relativity and other fundamental physical
fields. She recalls conversations, collaborations and even
arguments shared with many great scientists, including her
experiences with Albert Einstein. She also describes some of her
numerous trips around the world, spurred by a passion for travel,
beauty and mathematics. At once reflective, enlightening and
bittersweet, this book allows readers a look into the life and
thought processes of an esteemed female academic.
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