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The Geometry of Minkowski Spacetime - An Introduction to the Mathematics of the Special Theory of Relativity (Paperback, Softcover reprint of hardcover 2nd ed. 2011)
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The Geometry of Minkowski Spacetime - An Introduction to the Mathematics of the Special Theory of Relativity (Paperback, Softcover reprint of hardcover 2nd ed. 2011)
Series: Applied Mathematical Sciences, 92
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This book offers a presentation of the special theory of relativity
that is mathematically rigorous and yet spells out in considerable
detail the physical significance of the mathematics. It treats, in
addition to the usual menu of topics one is accustomed to finding
in introductions to special relativity, a wide variety of results
of more contemporary origin. These include Zeeman's
characterization of the causal automorphisms of Minkowski
spacetime, the Penrose theorem on the apparent shape of a
relativistically moving sphere, a detailed introduction to the
theory of spinors, a Petrov-type classification of electromagnetic
fields in both tensor and spinor form, a topology for Minkowski
spacetime whose homeomorphism group is essentially the Lorentz
group, and a careful discussion of Dirac's famous Scissors Problem
and its relation to the notion of a two-valued representation of
the Lorentz group. This second edition includes a new chapter on
the de Sitter universe which is intended to serve two purposes. The
first is to provide a gentle prologue to the steps one must take to
move beyond special relativity and adapt to the presence of
gravitational fields that cannot be considered negligible. The
second is to understand some of the basic features of a model of
the empty universe that differs markedly from Minkowski spacetime,
but may be recommended by recent astronomical observations
suggesting that the expansion of our own universe is accelerating
rather than slowing down. The treatment presumes only a knowledge
of linear algebra in the first three chapters, a bit of real
analysis in the fourth and, in two appendices, some elementary
point-set topology. The first edition of the book received the 1993
CHOICE award for Outstanding Academic Title. Reviews of first
edition: ..". a valuable contribution to the pedagogical literature
which will be enjoyed by all who delight in precise mathematics and
physics." (American Mathematical Society, 1993) "Where many physics
texts explain physical phenomena by means of mathematical models,
here a rigorous and detailed mathematical development is
accompanied by precise physical interpretations." (CHOICE, 1993)
..". his talent in choosing the most significant results and
ordering them within the book can't be denied. The reading of the
book is, really, a pleasure." (Dutch Mathematical Society, 1993)
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