TY - BOOK ID - 210081 TI - Explorations in Mathematical Physics : The Concepts Behind an Elegant Language PY - 2006 SN - 0387327932 9780387309439 0387309438 9780387327938 1441921680 PB - New York, NY : Springer New York : Imprint: Springer, DB - UniCat KW - Mathematical physics. KW - Physics. KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Physical mathematics KW - Physics KW - Mathematics KW - Quantum theory. KW - Theoretical, Mathematical and Computational Physics. KW - Mathematical Methods in Physics. KW - Physics, general. KW - Quantum Physics. KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Mechanics KW - Thermodynamics KW - Quantum physics. UR - https://www.unicat.be/uniCat?func=search&query=sysid:210081 AB - 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'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll 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. ER -