Negative Specific Heat in a Quasi-2D Generalized Vorticity Model

Negative specific heat is a dramatic phenomenon where processes decrease in temperature when adding energy. It has been observed in gravo-thermal collapse of globular clusters. We now report finding this phenomenon in bundles of nearly parallel, periodic, single-sign generalized vortex filaments in the electron magnetohydrodynamic (EMH) model for the unbounded plane under strong magnetic confinement. We derive the specific heat using a steepest descent method and a mean field property. Our derivations show that as temperature increases, the overall size of the system increases exponentially and the energy drops. The implication of negative specific heat is a runaway reaction, resulting in a collapsing inner core surrounded by an expanding halo of filaments.Comment: 12 pages, 3 figures; updated with revision

Quaternionic Mass Matrices and CP Symmetry

A viable formulation of gauge theory with extra generations in terms of quaternionic fields is presented. For the theory to be acceptable, the number of generations should be equal to or greater than 4. The quark-lepton mass matrices are generalized into quaternionic matrices.It is concluded that explicit CP violation automatically disappears in both strong- and weak-interaction sectors.Comment: 10 pages, LaTe

Mean field theory and coherent structures for vortex dynamics on the plane

We present a new derivation of the Onsager-Joyce-Montgomery (OJM) equilibrium statistical theory for point vortices on the plane, using the Bogoliubov-Feynman inequality for the free energy, Gibbs entropy function and Landau's approximation. This formulation links the heuristic OJM theory to the modern variational mean field theories. Landau's approximation is the physical counterpart of a large deviation result, which states that the maximum entropy state does not only have maximal probability measure but overwhelmingly large measure relative to other macrostates.Comment: PACS: 47.15.Ki, 67.40.Vs, 68.35.Rh 16 page

Abstract Wiener measure using abelian Yang-Mills action on R4\mathbb{R}^4

Let $\mathfrak{g}$ be the Lie algebra of a compact Lie group. For a $\mathfrak{g}$-valued 1-form $A$, consider the Yang-Mills action \begin{equation} S_{{\rm YM}}(A) = \int_{\mathbb{R}^4} \left|dA + A \wedge A \right|^2 \nonumber \end{equation} using the standard metric on $T\mathbb{R}^4$. When we consider the Lie group $U(1)$, the Lie algebra $\mathfrak{g}$ is isomorphic to $\mathbb{R} \otimes i$, thus $A \wedge A = 0$. For some simple closed loop $C$, we want to make sense of the following path integral, \begin{equation} \frac{1}{Z}\ \int_{A \in \mathcal{A} /\mathcal{G}} \exp \left[ \int_{C} A\right] e^{-\frac{1}{2}\int_{\mathbb{R}^4}|dA|^2}\ DA, \nonumber \end{equation} whereby $DA$ is some Lebesgue type of measure on the space of $\mathfrak{g}$-valued 1-forms, modulo gauge transformations, $\mathcal{A} /\mathcal{G}$, and $Z$ is some partition function. We will construct an Abstract Wiener space for which we can define the above Yang-Mills path integral rigorously, using renormalization techniques found in lattice gauge theory. We will further show that the Area Law formula do not hold in the abelian Yang-Mills theory