Problems with calculations of Berry properties in real and reciprocal spaces and physical characteristics involving manifestations of Berry properties are included.

Problems considering identical particles in the context of addition of angular momenta, perturbation theory, chemistry, and many-body physics are included.

Problems on properties of the Dirac equation and emphasis on nontrivial topology and specific materials (such as graphene) are included.

Problems involving calculations of various properties associated with the density operator and entropies and their relations to more general situations in physics are included.

This chapter begins the final section of the book, which presents both review and new results of original research on decoherence and measurement theory. In this chapter, it is shown that normal quantum mechanics can lead to irreversible behavior in an open system, in contrast to the expectation of the Poincaré theorem that predicts repeating, cyclical behavior for all closed systems. The quantum Boltzmann equation, which implies the famous H-theorem that underlies all statistical mechanics, is derived.

This chapter presents the surprising mathematical result that classical systems can indeed have entanglement. However, the degree to which they can be entangled is strictly limited, while quantum systems have no limit to their amount of entanglement.

This chapter surveys some of the ways in which the Copenhagen interpretation of quantum mechanics has led to a various views of the world with spiritual and moral implications; the perspective of this chapter is that most of these views are not demanded by the actual theory and experiments of quantum mechanics.

This chapter discusses some of the “super” properties of lasers, superfluids, and superconductors in the context of quantum field theory, including their innate property of spontaneous coherence, which can be seen as the opposite of decoherence.

As the final part of the nonmathematical discussion in this book, this chapter surveys how quantum mechanics plays an important role in existing technology such as the transistors used in computers and nuclear energy, as well as more cutting-edge technologies such as quantum computing, and the strange properties of lasers and superconductors.

This chapter introduces the formal second quantization method for fermions in quantum field theory, and the connection to second quantization of bosons is shown. The picture of fermions as rotations between two states is presented, which helps the reader to see where the Pauli exclusion rule comes from. Finally, Dirac’s original derivation of his equation for relativistic motion of fermions is given.

This chapter gives a brief but quantitative introduction to the method of Feynman diagrams in quantum field theory, sufficient for the reader to understand what these diagrams mean. The concept of “vacuum energy” is discussed in this context.

This chapter gives a quantitative introduction to decoherence theory, including density matrix formalism in the context of quantum field theory, and a survey of the quantum trajectories method. Finally, the mathematical structure for a new proposal for spontaneous collapse, introduced nonmathematically in Chapter 6, is given.