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

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 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.

This chapter shows how particles arise naturally as an effect of waves, known as “resonance,” and that the particle concept, properly understood, is not somehow incompatible with the existence of waves. The definitions of “fermion” and “boson” fields, often associated with “matter” and “energy” particles, are introduced. The solidness of objects in our experience is a direct consequence of fermion wave properties.

This chapter surveys modern progress in physics on the topic of “decoherence,” the physical process by which irreversible behavior can occur in wave systems. A substantial part of the chapter discusses a proposal by the author of this book for a spontaneous collapse theory that is connected to decoherence.

This chapter starts out a short, two-chapter section on very basic mathematics of quantum mechanics, appropriate for those who have taken undergraduate science or engineering courses. The method of “unit analysis” is used as a way of getting at when quantum mechanics will play a role in the behavior of things.

For a proper quantum mechanical description of multiple-particle systems, we must account for the indistinguishability of fundamental particles. The symmetrization postulate requires that the quantum state vector of a system of identical particles be either symmetric or antisymmetric with respect to exchange of any pair of identical particles within the system. Nature dictates that integer spin particles – bosons – have symmetric states, while half-integer spin particles – fermions – have antisymmetric states. The best-known manifestation of this is the Pauli exclusion principle, which limits the number of electrons in given atomic levels and leads to the structure of the periodic table.

Fermi--Dirac statistics lead to specific thermodynamic consequences at low temperatures.A key quantity is the Fermi energy, which is equal to the chemical potential at zero temperature, and can be used to define a temperature scale, the Fermi temperature.At temperatures that are small compared to the Fermi temperature, thermodynamic quantities may be calculated using the Sommerfeld expansion.The properties of metals and the existence of compact stars such as white dwarfs and neutron stars are a direct consequence of Fermi--Dirac statistics.

Unlike classical particles, quantum particles are indistinguishable.Fermions and bosons differ in their quantum statistics, and the consequences of this for their statistical mechanics are explored in the grand canonical ensemble.The Fermi--Dirac and Bose--Einstein distribution functions are derived, and utilized to write thermal averages using the density of states.