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  Metric and Topological Spaces
Posted on 2015-05-10 (Send to a Friend Send to a Friend )
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 book-work 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. . . . .
 
 
  Many-body physics with ultracold gases
Posted on 2015-05-09 (Send to a Friend Send to a Friend )
This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover. . . . .
 
 
  Introduction to Quantum Field Theory
Posted on 2015-05-08 (Send to a Friend Send to a Friend )
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; Tree-level QED; Path Integrals; The Casimir Effect; Vacuum Polarization; g-2; Systematic Renormalization; Infrared Divergences; The Lamb Shift; Renormalizability of QED; Non-Renormalizable and Supe . . . .
 
 
   Combinatorics and algebra of tensor calculus
Posted on 2015-05-07 (Send to a Friend Send to a Friend )
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 coarse-graining of graphs and characterizes the algebraic nature of tensor calculus. . . . .
 
 
   Spacetime algebra as a powerful tool for electromagnetism
Posted on 2015-05-06 (Send to a Friend Send to a Friend )
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 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a . . . .
 
 
  Software Innovation
Posted on 2015-05-05 (Send to a Friend Send to a Friend )
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 non-technical account of an emerging systems development topic, written in a non-normative style, where the intention is to further the students’ understanding of their own and other system devel . . . .
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