Time-Evolution of Collective Meson Fields and Amplification of Quantum Meson Modes in Chiral Phase Transition

The time evolution of quantum meson fields in the O(4) linear sigma model is investigated in a context of the dynamical chiral phase transition. It is shown that amplitudes of quantum pion modes are amplified due to both mechanisms of a parametric resonance and a resonance by the forced oscillation according to the small oscillation of the chiral condensate in the late time of chiral phase transition.Comment: 4 pages; Talk presented at the XVIth International Conference on Particles and Nuclei (PANIC02), Sep. 30 - Oct. 4, 2002, Osaka, Japan, to appear in Nuclear Physics

Nonequilibrium chiral dynamics by the time dependent variational approach with squeezed states

We investigate the inhomogeneous chiral dynamics of the O(4) linear sigma model in 1+1 dimensions using the time dependent variational approach in the space spanned by the squeezed states. We compare two cases, with and without the Gaussian approximation for the Green's functions. We show that mode-mode correlation plays a decisive role in the out-of-equilibrium quantum dynamics of domain formation and squeezing of states.Comment: 5 pages, 4 figures. RevTex, version to appear in Phys. Rev. C. Rapid Communicatio

Parametric Resonance versus Forced Oscillation in Time-Evolution of Quantum Meson Fields

The time-evolution of quantum meson fields in O(4)-linear sigma model is treated approximately. It is shown that the amplification of the amplitudes of pion modes with low momenta occurs by means of both the parametric resonance and the forced oscillation.Comment: 8 pages, no figure, using PTPTeX styl

Scalar and Pseudoscalar Glueball Masses within a Gaussian Wavefunctional Approximation

The lowest scalar and pseudoscalar glueball masses are evaluated by means of the time-dependent variational approach to the Yang-Mills gauge theory without fermions in the Hamiltonian formalism within a Gaussian wavefunctional approximation. The glueball mass is calculated as a pole of the propagator for a composite glueball field which consists of two massless gluons. The glueball propagator is here evaluated by using the linear response theory for the composite external glueball field. As a result, a finite glueball mass is obtained through the interaction between two massless gluons, in which the glueball mass depends on the QCD coupling constant g in the nonperturbative form.Comment: 24 pages, 3 figure

A Possible Extension of a Trial State in the TDHF Theory with Canonical Form in the Lipkin Model

With the aim of the extension of the TDHF theory in the canonical form in the Lipkin model, the trial state for the variation is constructed, which is an extension of the Slater determinant. The canonicity condition is imposed to formulate the variational approach in the canonical form. A possible solution of the canonicity condition is given and the zero-point fluctuation induced by the uncertainty principle is investigated. As an application, the ground state energy is evaluated.Comment: 15 pages, 1 figure, using PTPTeX styl

Variational Approach to the Chiral Phase Transition in the Linear Sigma Model

The chiral phase transition at finite temperature is investigated in the linear sigma model, which is regarded as a low energy effective theory of QCD with three momentum cutoff, in the variational method with the Gaussian approximation in the functional Schroedinger picture. It is shown that the Goldstone theorem is retained and the meson pair excitations are automatically included by taking into account the linear response to the external fields. It is pointed out that the behavior of chiral phase transition depends on the three-momentum cutoff, which leads to the careful treatment of the problem.Comment: 14 pages, 5 figures, using PTPTeX cl

Time-Evolution of a Collective Meson Field by the Use of a Squeezed State

A time-evolution of quantum meson fields is investigated in a linear sigma model by means of the time-dependent variational approach with a squeezed state. The chiral condensate, which is a mean field of the quantum meson fields, and quantum fluctuations around it are treated self-consistently in this approach. The attention is payed to the description of the relaxation process of the chiral condensate, where the energy stored in the mean field configuration flows to the fluctuation modes. It is shown that the quantum fluctuations play an important role to describe this relaxation process.Comment: 18 pages, 22 postscript figures, uses PTPTeX.st