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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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Mathematical Notation and Some Terminology
– The operator L from space W to space E: L : W → E
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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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Entropy, Quasiequilibrium, and Projectors Field
Projection operators Py contribute both to the invariance equation (3.2), and to the film extension of the dynamics (4.5). Limiting results, exact...
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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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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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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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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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4 The Galilei Groups
In this chapter we describe the Galilei group and its universal central extension both in 3 + 1 and in 2 + 1 dimensions.
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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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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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3 The Symmetry Actions and Their Representations
This chapter is devoted to the study of the homomorphisms $G \ni...
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B Hilbert Space Average under Microcanonical Conditions
We consider a space with the Cartesian coordinates {η AB ab ,ξ AB...
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6 Outline of the Present Approach
As already indicated we want to derive the properties of thermodynamic quantities from non-relativistic quantum mechanics, i.e., from starting with a...
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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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Appendix B: The Relation between Minkowski and Euclidean Actions
The Minkowski action leads to canonical quantization and it is used to calculate matrix elements of the evolution operator e...
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5 The Confinement of SU(3) Color Charges
If we wish to describe color confinement in terms of the Meissner effect of a dual superconductor, we need to adapt the Landau-Ginzburg model to the...
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Appendix D. Color Charges of Quarks and Gluons
In $SU\left( 2\right) $ , the charge operator is:...