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Metric and Topological Spaces 
Posted on 20150510
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The syllabus for the course is defined by the Faculty Board Schedules
(which are minimal for lecturing and maximal for examining). What is presented here
contains some results which it would not, in my opinion, be fair to set as bookwork
although they could well appear as problems. In addition, I have included a small amount
of material which appears in other 1B courses. I should very much appreciate being told
of any corrections or possible improvements and might even part with a small reward to
the first finder of particular errors. . . . . 






Manybody physics with ultracold gases 
Posted on 20150509
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This paper reviews recent experimental and theoretical progress concerning manybody phenomena
in dilute, ultracold gases. It focuses on effects beyond standard weakcoupling descriptions, such as the
MottHubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or
lowestLandaulevel physics in quasitwodimensional gases in fast rotation. Strong correlations in
fermionic gases are discussed in optical lattices or nearFeshbach resonances in the BCSBEC
crossover. . . . . 






Introduction to Quantum Field Theory 
Posted on 20150508
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Contents: The Microscopic Theory of Radiation; Lorentz Invariance and Conventions; Second Quantization; Classical Field Theory; Old Fashioned Perturbation Theory; Cross Sections and Decay Rates; The LSZ reduction formula
and the Feynman propagator; Feynman Rules; Gauge Invariance; Scalar QED; Spinors and the Dirac Equation; Quantum Electrodynamics; Treelevel QED; Path Integrals; The Casimir Effect; Vacuum Polarization; g2; Systematic Renormalization; Infrared Divergences; The Lamb Shift; Renormalizability of QED; NonRenormalizable and
Supe . . . . 






Combinatorics and algebra of tensor calculus 
Posted on 20150507
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In this paper, motivated by the theory of operads and PROPs we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarsegraining of graphs and characterizes the algebraic nature of tensor calculus. . . . . 






Spacetime algebra as a powerful tool for electromagnetism 
Posted on 20150506
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We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a . . . . 






Software Innovation 
Posted on 20150505
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This short book was originally written as course notes for a part of
a new Software Innovation course at the Department of
Computer Science, Aalborg University in Denmark. The students
have primarily engineering backgrounds and a primarily
technical education.
The book was intended to provide
counterpoint – that is to provide a scientific, but nontechnical
account of an emerging systems development topic, written in a
nonnormative style, where the intention is to further the students’
understanding of their own and other system devel . . . . 






