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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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Spin-Based Quantum Dot Quantum Computing
This chapter is an overview of the research on spin-based quantum dot quantum computation, which covers two most prominent architectures, one based...
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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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Semiconductor Few-Electron Quantum Dots as Spin Qubits
The spin of an electron placed in a magnetic field provides a natural two-level system suitable as a qubit in a quantum computer[1]. In this work, we...
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Method of Invariant Grids
The method of invariant grids is developed for a grid-based computation of invariant manifolds.
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Invariance Equation in Differential Form
Definition of invariance in terms of motions and trajectories assumes, at least, existence and uniqueness theorems for solutions of the original...
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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...
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Appendix D. Color Charges of Quarks and Gluons
In $SU\left( 2\right) $ , the charge operator is:...
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Introduction
The state of a physical system is the mathematical description of our knowledge of it, and provides information on its future and past. A state...
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2 Quantum Tomographic Methods
The state of a physical system is the mathematical object that provides a complete information on the system. The knowledge of the state is...
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6 Galilei Invariant Wave Equations
According to the results of the previous sections, a free elementary quantum object that is invariant under the Galilei group is described by an...
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13 Pressure
Technically one could introduce pressure within classical statistical mechanics as an observable, i.e., as a function of the micro state. The...
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5 The Program for the Foundation of Thermodynamics
For a foundation of thermodynamics it is tempting to give an abstract but, nevertheless, intuitively appealing definition of entropy, such as:...
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3 Basics of Thermodynamics and Statistics
After having introduced some central concepts, results, and equations from quantum mechanics, we will now present the main definitions and laws of...