Explorations in Mathematical Physics

The concepts behind an elegant language

Don Koks

560 pages, parution le 02/11/2006

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Résumé

"With enjoyable and sometimes surprising excursions along the way, the journey provides a fresh look at many familiar topics, as it takes us from basic linear mathematics to general relativity ... look forward to having your geometric intuition nourished and expanded by the author's intelligent commentaries." Eugen Merzbacher, University of North Carolina, Chapel Hill

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature?

This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory,-along with Green functions and the art of complex integration, and finally general relativity and cosmology.

The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods.

Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

Sommaire

The language of physics
A trip down linear lane
The natural langage of random processes
A roundabout route to geometric algebra
Special relativity and the Lorentz transform
Four-vectors and the road to tensors
Accelerated frames: onward to the principle of covariance
The elegance and power of tensor notation
Curvature and differential geometry
Variational calculus and field theory
The green function approach to solving field equations
Airlines, black holes, and cosmology: the ABC of general relativity

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Don Koks
Parution	02/11/2006
Nb. de pages	560
Format	16 x 24
Couverture	Relié
Poids	920g
Intérieur	Noir et Blanc
EAN13	9780387309439
ISBN13	978-0-387-30943-9