37,726 research outputs found

    Finite-Temperature and -Density QED: Schwinger-Dyson Equation in the Real-Time Formalism

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    Based on the real-time formalism, especially, on Thermo Field Dynamics, we derive the Schwinger-Dyson gap equation for the fermion propagator in QED and Four-Fermion model at finite-temperature and -density. We discuss some advantage of the real-time formalism in solving the self-consistent gap equation, in comparison with the ordinary imaginary-time formalism. Once we specify the vertex function, we can write down the SD equation with only continuous variables without performing the discrete sum over Matsubara frequencies which cannot be performed in advance without further approximation in the imaginary-time formalism. By solving the SD equation obtained in this way, we find the chiral-symmetry restoring transition at finite-temperature and present the associated phase diagram of strong coupling QED. In solving the SD equation, we consider two approximations: instantaneous-exchange and p0p_0-independent ones. The former has a direct correspondence in the imaginary time formalism, while the latter is a new approximation beyond the former, since the latter is able to incorporate new thermal effects which has been overlooked in the ordinary imaginary-time solution. However both approximations are shown to give qualitatively the same results on the finite-temperature phase transition.Comment: 28 pages+15 figures (figures: not included, available upon request

    (D+1)-Dimensional Formulation for D-Dimensional Constrained Systems

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    D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in (D+1)-dimensional canonical formulation. The Langevin equations for the constrained system are obtained as Hamilton's equations of motion where conjugate momenta play a part of noise fields.Comment: 10 pages (Plain TeX), CHIBA-EP-58-Re

    Asymptotics for penalized additive B-spline regression

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    This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the algorithm as well as the uniqueness of its solution are shown. The asymptotic bias and variance of penalized spline estimator are derived by an efficient use of the asymptotic results for the penalized spline estimator in marginal univariate model. Asymptotic normality of estimator is also developed, by which an approximate confidence interval can be obtained. Some numerical experiments confirming theoretical results are provided.Comment: 24 pages, 6 figure

    Dynamical Symmetry Breaking on Langevin Equation : Nambu \cdot Jona-Lasinio Model

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    In order to investigate dynamical symmetry breaking, we study Nambu\cdotJona-Lasinio model in the large-N limit in the stochastic quantization method. Here in order to solve Langevin equation, we impose specified initial conditions and construct ``effective Langevin equation'' in the large-N limit and give the same non-perturbative results as path-integral approach gives. Moreover we discuss stability of vacuum by means of ``effective potential''.Comment: 12 pages (Plain TeX), 7 figures(not included, sorry!), CHIBA-EP-6

    Symplectic structure and monopole strength in 12C

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    The relation between the monopole transition strength and existence of cluster structure in the excited states is discussed based on an algebraic cluster model. The structure of 12^{12}C is studied with a 3α\alpha model, and the wave function for the relative motions between α\alpha clusters are described by the symplectic algebra Sp(2,R)zSp(2,R)_z, which corresponds to the linear combinations of SU(3)SU(3) states with different multiplicities. Introducing Sp(2,R)zSp(2,R)_z algebra works well for reducing the number of the basis states, and it is also shown that states connected by the strong monopole transition are classified by a quantum number Λ\Lambda of the Sp(2,R)zSp(2,R)_z algebra.Comment: Phys. Rev. C in pres