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Chiral Anomalies and Topology
When a field theory has a symmetry, global or local like in gauge theories, in the tree or classical approximation formal manipulations lead to...
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Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method
We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e....
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Index
Abstract not available
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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...
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7 System and Environment
In a typical thermodynamic situation we consider a bipartite system with the larger part being called “environment” or “container”, c, whereas the...
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9 Quantum Operations on Qubitsand Their Characterization
Information encoded in quantum system has to obey rules of quantum physics which impose strict bounds on state estimation and on possible...
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1 A Synopsis of Quantum Mechanics
This chapter collects the basic elements of quantum mechanics in the form that is appropriate for an analysis of space-time symmetries. The reader...
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5 Galilei Invariant Elementary Particles
In this chapter we apply the general theory of symmetry actions as developed in Chaps. 2 and 3 to the Galilei groups of Chap. 4 splitting the...
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A Appendix
This dictionary gives the definitions and the basic properties of most of the mathematical concepts that are freely used in the book. No references...
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3 The Symmetry Actions and Their Representations
This chapter is devoted to the study of the homomorphisms $G \ni...
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21 Summary and Conclusion
This book essentially had two intentions: to define what precisely thermodynamic behavior should be and to show that a certain class of bipartite...