Thermal Abundances of Heavy Particles

Matsumoto and Yoshimura [hep-ph/9910393] have argued that there are loop corrections to the number density of heavy particles (in thermal equilibrium with a gas of light particles) that are not Boltzmann suppressed by a factor of e^(-M/T) at temperatures T well below the mass M of the heavy particle. We argue, however, that their definition of the number density does not correspond to a quantity that could be measured in a realistic experiment. We consider a model where the heavy particles carry a conserved U(1) charge, and the light particles do not. The fluctuations of the net charge in a given volume then provide a measure of the total number of heavy particles in that same volume. We show that these charge fluctuations are Boltzmann suppressed (to all orders in perturbation theory). Therefore, we argue, the number density of heavy particles is also Boltzmann suppressed.Comment: 9 pages, 1 figure; minor improvements in revised versio

The Taiwan Strait Crisis of 1954-55 and U.S.-R.O.C Relations

On September 3, 1954, Chinese artillery began shelling Quemoy (Jinmen), one of the Kuomintang-held offshore islands, setting off the first Taiwan Strait Crisis. This paper focuses on the crisis and analyzes the following three questions: (1) What was the policy the U.S. took towards the Republic of China (R.O.C), especially towards the offshore islands, to try to end the Taiwan Strait Crisis? (2) What were the intentions of the U.S. government in trying to end the Taiwan Strait Crisis? And (3) how should U.S. policy towards the R.O.C. which led to solving the Taiwan Strait Crisis be positioned in the history of Sino-American relations? Through analysis of these questions, this study concludes that the position the U.S. took to bring an end to crisis, one which prevented China from “liberating Taiwan†and the Kuomintang from “attacking the mainland,†brought about the existence of a de facto “two-China†situation.Taiwan Strait Crisis, Quemoy, Jinmen, U.S.-R.O.C. Relations, Two-China, Taiwan, China, United States, International Relations, Foreign Policy

Temperature Power Law of Equilibrium Heavy Particle Density

A standard calculation of the energy density of heavy stable particles that may pair-annihilate into light particles making up thermal medium is performed to second order of coupling, using the technique of thermal field theory. At very low temperatures a power law of temperature is derived for the energy density of the heavy particle. This is in sharp contrast to the exponentially suppressed contribution estimated from the ideal gas distribution function. The result supports a previous dynamical calculation based on the Hartree approximation, and implies that the relic abundance of dark matter particles is enhanced compared to that based on the Boltzmann equation.Comment: 12 pages, LATEX file with 6 PS figure

New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.Comment: 19 pages, LATEX file with 2 PS figure

Generalized β\beta-conformal change and special Finsler spaces

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized $\beta$-conformal change, which we call the b-condition, and investigate the geometric consequences of such condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.Comment: References added, some modifications are performed, LateX file, 24 page

The Taiwan Strait Crisis of 1954-55 and U.S.-R.O.C Relations

On September 3, 1954, Chinese artillery began shelling Quemoy (Jinmen), one of theKuomintang-held offshore islands, setting off the first Taiwan Strait Crisis. This paper focuses on the crisis and analyzes the following three questions: (1) What was the policy the U.S. took towards the Republic of China (R.O.C), especially towards the offshore islands, to try to end the Taiwan Strait Crisis? (2) What were the intentions of the U.S. government in trying to end the Taiwan Strait Crisis? And (3) how should U.S. policy towards the R.O.C. which led to solving the Taiwan Strait Crisis be positioned in the history of Sino-American relations? Through analysis of these questions, this study concludes that the position the U.S. took to bring an end to crisis,one which prevented China from “liberating Taiwan” and the Kuomintang from“attacking the mainland,” brought about the existence of a de facto “two-China”situation

The Evolution of the "One China" Concept in the Process of Taiwan\u27s Democratization

This paper investigates how Taiwan\u27s "one China" concept evolved during the democratization process that occurred under the leadership of former President Lee Teng-hui. The author argues that there was a crucial evolution of the "one China" concept and that the transformation of the concept resulted from changes in Taiwan\u27s internal political circumstances. The evolution of the concept creates a real possibility that the "status quo" sought by the ROC in the Taiwan Strait both during and after the Cold War might be destroyed. In addition, any further evolution of the "one China" concept will surely make the "status quo" of Taiwan untenable, in that it would induce Taiwan to seek de jure instead of de facto independence, possibly initiating a conflict between the PRC and the ROC. To prevent such a conflict in the Taiwan Strait, the international community must persuade the ROC not to go beyond the "status quo" and to stay within the framework of de facto independence. At the same time, both the PRC and the ROC should be urged to maintain an open conduit of communication for productive talks on the reunification of China

Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.Comment: Completely rewritten. Discussions on coexistence of is- or id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave superconductors are added; 4 pages, 3 figure

Boltzmann Suppression of Interacting Heavy Particles

Matsumoto and Yoshimura have recently argued that the number density of heavy particles in a thermal bath is not necessarily Boltzmann-suppressed for T << M, as power law corrections may emerge at higher orders in perturbation theory. This fact might have important implications on the determination of WIMP relic densities. On the other hand, the definition of number densities in a interacting theory is not a straightforward procedure. It usually requires renormalization of composite operators and operator mixing, which obscure the physical interpretation of the computed thermal average. We propose a new definition for the thermal average of a composite operator, which does not require any new renormalization counterterm and is thus free from such ambiguities. Applying this definition to the model of Matsumoto and Yoshimura we find that it gives number densities which are Boltzmann-suppressed at any order in perturbation theory. We discuss also heavy particles which are unstable already at T=0, showing that power law corrections do in general emerge in this case.Comment: 7 pages, 5 figures. New section added, with the discussion of the case of an unstable heavy particle. Version to appear on Phys. Rev.