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9 The Goldstone Theorem
The mechanism of SSB does not only provide a general strategy for unifying the description of apparently different systems, but it also provide...
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Introduction to Part II
These notes arose from courses given at the International School for Advanced Studies (Trieste) and at the Scuola Normale Superiore (Pisa) in various...
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6 Sectors with Energy-Momentum Density
We shall now discuss the requirement III of finite energy-momentum, briefly mentioned in the previous section. Clearly, the possibility of using...
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Noncommutative Line Bundles and Gerbes
We introduce noncommutative line bundles and gerbes within the framework of deformation quantization. The Seiberg-Witten map is used to construct the...
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Secondary Characteristic Classes of Lie Algebroids
We show how the intrinsic characteristic classes of Lie algebroids can be seen as characteristic classes of representations. We present two...
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Local Models for Manifolds with Symplectic Connections of Ricci Type*
We show that any symplectic manifold (Mω) of dimension 2n(n≥ 2) admitting a symplectic connection of Ricci type can locally be constructed by a...
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13 Fermi and Bose Gas at Non-zero Temperature
As an example of symmmetry breaking at non-zero temperature we discuss the free Fermi and Bose gas, starting from finite volume and then discussing...
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1 Symmetries of a Classical System
The realization of symmetries in physical systems has proven to be of help in the description of physical phenomena: it makes it possible to relate...
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14 Quantum Fields at Non-zero Temperature
The general structure discussed above provides a neat and unique prescription for the quantization of relativistic fields at non-zero temperature...
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8 Examples
The model describes the simplest non-linear field theory and it can be regarded as a prototype of field theories in one space dimension (s=1). The...
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Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces
I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on...
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An Infinite Family of Isospectral Pairs Topological Aspects
We give some basic properties of the isospectral pairs (Γ,Γ) of two bipartite graphs Γ and Γ. Then we present a systematic method of constructing an...
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Some Noncommutative Spheres
Noncommutative geometry provides us various means to deal with noncommutative phenomena in mathematics, and C*-algebras (and von Neumann algebras)...
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From Quantum Tori to Quantum Homogeneous Spaces
We construct dual objects for quantum complex projective spaces as quantum homogeneous spaces of quantum unitary groups, in which the deformation...
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Index Theorems and Noncommutative Topology
These lecture notes are mainly devoted to a K-theory proof of the Atiyah-Singer index theorem. Some applications of the K-theory to noncommutative...
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10-Neon
This document is part of Subvolume C 'Tables of Neutron Resonance Parameters (Supplement to Subvolume B)' of Volume 16 'Low Energy Neutron Physics'....
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B Physics and CP Violation
After an introduction to the Standard-Model description of CP violation, we turn to the main focus of these lectures, the B-meson system. Since...
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Unifying Aspects of Light- and Heavy-Systems
Dyson-Schwinger equations furnish a Poincaré covariant framework within which to study hadrons. A particular feature is the existence of a...
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Heavy Flavor Production off Protons and in a Nuclear Environment
These lectures present an overview of the current status of the QCD based phenomenology for open and hidden heavy flavor production at high energies....
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4 Abelian Gauge Fixing
The formation of monopoles and their condensation in the QCD ground state is a feature which is related to abelian gauge fixing, discussed in this...