Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain

Recently a new integral equation describing the thermodynamics of the 1D Heisenberg model was discovered by Takahashi. Using the integral equation we have succeeded in obtaining the high temperature expansion of the specific heat and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than those obtained so far by the standard methods such as the linked-cluster algorithm. Our results will be useful to examine various approximation methods to extrapolate the high temperature expansion to the low temperature region.Comment: 5 pages, 4 figures, 2 table

A New Current Regularization of Thirring Model

We study an ambiguity of the current regularization in the Thirring model. We find a new current definition which enables to make a comprehensive treatment of the current. Our formulation is simpler than Klaiber's formulation. We compare our result with other formulations and find a very good agreement with their result. We also obtain the Schwinger term and the general formula for any current regularization.Comment: 7 pages, some comments and references added, to appear in Prog. Theor. Phy

Chiral Primordial Gravitational Waves from a Lifshitz Point

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho${\rm\check{r}}$ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.Comment: 4 pages,2 figures;v2:reference added; v3:reference adde