Curvature Induced Phase Transition in a Four-Fermion Theory Using the Weak Curvature Expansion

Curvature induced phase transition is thoroughly investigated in a four- fermion theory with $N$ components of fermions for arbitrary space-time dimensions $(2 \leq D < 4)$. We adopt the $1/N$ expansion method and calculate the effective potential for a composite operator $\bar{\psi}\psi$. The resulting effective potential is expanded asymptotically in terms of the space-time curvature $R$ by using the Riemann normal coordinate. We assume that the space-time curves slowly and keep only terms independent of $R$ and terms linear in $R$. Evaluating the effective potential it is found that the first-order phase transition is caused and the broken chiral symmetry is restored for a large positive curvature. In the space-time with a negative curvature the chiral symmetry is broken down even if the coupling constant of the four-fermion interaction is sufficiently small. We present the behavior of the dynamically generated fermion mass. The critical curvature, $R_{cr}$, which divides the symmetric and asymmetric phases is obtained analytically as a function of the space-time dimension $D$. At the four-dimensional limit our result $R_{cr}$ agrees with the exact results known in de Sitter space and Einstein universe.Comment: 19 pages, uses LaTeX, eepic.st

Color Superconductivity and Radius of Quark Star in Extended NJL Model by Using the Dimensional Regularization

A radius of a dense star on the color superconducting phase is investigated in an extended NJL type model with two flavors of quarks. Since the model is non-renormalizable, the results depend on the regularization procedure. Here we apply the dimensional regularization and evaluate the radius of a dense star. Evaluating the TOV equation, we show the relationship between mass and radius of the dense star in the dimensional regularization.Comment: 4 pages.To appear in the proceedings of 7th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT 05), Barcelona, Catalonia, Spain, 5-9 Sep 2005. References are ad

Boltzmann Equation for Relativistic Neutral Scalar Field in Non-equilibrium Thermo Field Dynamics

A relativistic neutral scalar field is investigated on the basis of the Schwinger-Dyson equation in the non-equilibrium thermo field dynamics. A time evolution equation for a distribution function is obtained from a diagonalization condition for the Schwinger-Dyson equation. An explicit expression of the time evolution equation is calculated in the $\lambda\phi^4$ interaction model at the 2-loop level. The Boltzmann equation is derived for the relativistic scalar field. We set a simple initial condition and numerically solve the Boltzmann equation and show the time evolution of the distribution function and the relaxation time.Comment: 23 pages, 9 figure

Influence of QED Corrections on the Orientation of Chiral Symmetry Breaking in the NJL model

We study QED corrections to chiral symmetry breaking in the Nambu--Jona-Lasinio (NJL) model with two flavors of quarks. In this model, the isospin symmetry is broken by the differences between the current quark masses and the electromagnetic charges of the up and down quarks. To leading order in the 1/N expansion, we calculate the effective potential of the model with one-loop QED corrections at finite temperature. Evaluating the effective potential, we study the influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass plays an essential role in maintaining the orientation of the chiral symmetry breaking. If the average of the up and down quark masses is small enough, we find a phase in which the pion field has non-vanishing expectation value and dynamical CP violation takes place.Comment: 22 pages, 13 figures; added discussion about pion mass differenc

Lock-in transition of charge density waves in quasi-one-dimensional conductors: reinterpretation of McMillan's theory

We investigated the lock-in transition of charge density waves (CDWs) in quasi-one-dimensional conductors, based on McMillan's free energy. The higher-order umklapp terms play an essential role in this study. McMillan's theory was extended by Nakanishi and Shiba in order to treat multiple CDW vectors. Although their theories were aimed at understanding CDWs in quasi-two-dimensional conductors, we applied them to the quasi-one-dimensional conductors, including K$_{0.3}$MoO$_3$, NbSe$_3$, and $m$-TaS$_3$, and confirmed its validity for these cases. Then we discussed our previous experimental result of $o$-TaS$_3$, which revealed the coexistence of commensurate and incommensurate states. We found that the coexistence of multiple CDW vectors is essential for the lock-in transition to occur in $o$-TaS$_3$. The even- and odd-order terms in the free energy play roles for amplitude development and phase modulation, respectively. Moreover, consideration of the condition of being commensurate CDWs allowed us to relate it with that of the weak localization in random media.Comment: 12 pages, 3 figure