We investigate properties of the color space of $SU(N_c)$ gauge theories in the limit of small number of colors $(N_c \to 0)$ and large number of flavors. More generally, we introduce a rescaling of $\alpha_s$ and $n_f$ which assigns a finite limit to colored quantities as $N_c \to 0$, which reproduces their known large-$N_c$ limit, and which expresses them as an analytic function of $N_c^2$ for arbitrary value of $N_c$. The vanishing-$N_c$ limit has an Abelian character and is also the small-$N_c$ limit of $[U(1)]^{N_c-1}$. This limit does not have an obvious quantum field theory interpretation; however, it provides practical consistency checks on QCD perturbative quantities by comparing them to their QED counterparts. Our analysis also describes the two-dimensional topological structure involved in the interpretation of the small $N_c$-limit in color space.

We derive a set of equations describing the real time dynamics of modes with spatial momentum of order g2T in a high temperature gauge theory, where g is the coupling constant and T is the temperature. This dynamics is stochastic in nature. Important implications for baryon number violation at high temperature and for the physics at the electroweak phase transition, are discussed.

I address the phenomenology of CPT violation in the neutral kaon system under the assumption that it originates from Planck scale physics. This assumption opens the door to a new set of CPT violating parameters whose phenomenology is distinct from the $\Delta$ parameter usually considered in the Hamiltonian. The origin of these parameters reflects a possible departure from a $S$-matrix evolution. Existing bounds on CPT violation are near the expected range based on naive dimensional analysis. This provides a strong incentive to pursue the quest of CPT violation in near-future kaon experiments. (Talk given at the Workshop on K Physics, Orsay, France, May 30 - June 4, 1996.)

An overlap method for regularizing Majorana-Weyl fermions interacting with gauge fields is presented. A mod(2) index is introduced in relation to the anomalous violation of a discrete global chiral symmetry. Most of the paper is restricted to 2 dimensions but generalizations to 2 + 8k dimensions should be straightforward.

We develop a new and general method to calculate the effects of CP violation from extensions of the standard model on the mechanism of electroweak baryogenesis. We illustrate its applicability in the framework of two-higgs doublet models.

We reconsider the model of quantum mechanics violation in the K0−K0 system, due to Ellis, Hagelin, Nanopoulos, and Srednicki, in which CP- and CPT-violating signatures arise from the evolution of pure states into mixed states. We present a formalism for computing time-dependent asymmetries in this model and show that present data constrains its parameters significantly. In the future, this model will be put to very stringent tests at a ø-factory. We present the theory of these tests and show the relation between particular ø-decay correlations and the parameters of quantum mechanics violation.