Abstract:
We review generalizations of quantum statistics, including parabose, parafermi, and quon statistics, but not including anyon statistics, which is special to two dimensions.

Abstract:
I review the discovery of the color degree of freedom in hadronic physics, and the developments which led from that discovery to the local gauge theory of color, quantum chromodynamics.

Abstract:
After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the statistics of ``quons'' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the $q$-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter $q$ for electrons due to the Ramberg-Snow experiment.

Abstract:
I survey the use of the Haag expansion as a technique to solve quantum field theories. After an exposition of the asymptotic condition and the Haag expansion, I report the results of applying the Haag expansion to several quantum field theories, including galilean-invariant theories, matter at finite temperature (using the BCS model of superconductivity as an illustrative example), the Nambu--Jona-Lasinio model and the Schwinger model. I conclude with the outlook for further development of this method.

Abstract:
I calculate the structure function for scattering from the two-body bound state in its lowest level in a non-relativistic model of confined scalar ``quarks'' of masses $m_A$ and $m_B$. The scaling limit in $x={\bf q}^2/2(m_A+m_B)q^0$ exists and is non-vanishing only for the values $x=m_A/(m_A+m_B)$ and $x=m_B/(m_A+m_B)$ which correspond to the fractions of the momentum of the two-body system carried by each of the ``quarks.'' In the scaling limit, the interference from scattering off of the two ``quarks'' vanishes. Thus the scaling limit of this model agrees with the parton picture.

Abstract:
I review the main features of the color charge degree of freedom in particle physics, sketch the paradox in the early quark model that led to color, give a personal perspective on the discovery of color and describe the introduction of the gauge theory of color.

Abstract:
Conservation of statistics requires that fermions be coupled to Grassmann external sources. Correspondingly, conservation of statistics requires that parabosons, parafermions and quons be coupled to external sources that are the appropriate generalizations of Grassmann numbers.

Abstract:
An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.

Abstract:
The breadth of Eugene Wigner's interests and contributions is amazing and humbling. At different times in his life he did seminal work in areas as diverse as pure mathematics and chemical engineering. His seminal research in physics is, of course, the best known. In this talk I first describe Wigner's supermultiplet theory of 1936 using the approximate symmetry of the nuclear Hamiltonian under a combined spin-isospin symmetry to describe the spectroscopy of stable nuclei up to about the nucleus molybdenum. I then show how Wigner's ideas of 1936 have had far reaching and unexpected implications: his ideas led to the discovery of the color degree of freedom for quarks and to the symmetric quark model of baryons which is the basis of baryon spectroscopy. I conclude by pointing out that the color degree of freedom, made into a local symmetry using Yang-Mills theory, leads to the gauge theory of color, quantum chromodynamics, which is our present theory of the strong interactions.