Gaussian Wave Functional Approximation Research Articles

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.

Time-Dependent Variational Approach to the Non-Abelian Pure Gauge Theory: Its Application to Evaluation of the Shear Viscosity of Quantum Gluonic Matter

The time-dependent variational approach to the pure Yang-Mills gauge theory, especially a color su(3) gauge theory, is formulated in the functional Schroedinger picture with a Gaussian wave functional approximation. The equations of motion for the quantum gauge fields are formulated in the Liouville-von Neumann form. This variational approach is applied in order to derive the transport coefficients, such as the shear viscosity, for the pure gluonic matter by using the linear response theory. As a result, the contribution to the shear viscosity from the quantum gluons is zero up to the lowest order of the coupling g in the quantum gluonic matter.

Amplification of Quantum Meson Modes in the Late Time of the Chiral Phase Transition

It is shown that there exists a possibility of amplification of amplitudes of quantum pion modes with low momenta in the late time of chiral phase transition by using the Gaussian wave functional approximation in the O(4) linear sigma model. It is also shown that the amplification occurs in the mechanism of the resonance by forced oscillation as well as the parametric resonance induced by the small oscillation of the chiral condensate. These mechanisms are investigated in both the case of spatially homogeneous system and the spatially expanded system described by the Bjorken coordinate.

Dynamical symmetry breaking and the Nambu–Goldstone theorem in the Gaussian wave functional approximation

We analyze the group-theoretical ramifications of the Nambu–Goldstone (NG) theorem in the self-consistent relativistic variational Gaussian wave functional approximation to spinless field theories. In an illustrative example we show how the Nambu–Goldstone theorem would work in the O(N) symmetric φ4 scalar field theory, if the residual symmetry of the vacuum were lesser than O(N−1), e.g., if the vacuum were O(N−2), or O(N−3),… symmetric. (This does not imply that any of the “lesser” vacua is actually the absolute energy minimum: stability analysis has not been done.) The requisite number of NG bosons would be (2N−3), or (3N−6),…, respectively, which may exceed N, the number of elementary fields in the Lagrangian. We show how the requisite new NG bosons would appear even in channels that do not carry the same quantum numbers as one of N “elementary particles” [scalar field quanta, or Castillejo–Dalitz–Dyson (CDD) poles] in the Lagrangian, i.e., in those “flavor” channels that have no CDD poles. The corresponding Nambu–Goldstone bosons are composites (bound states) of pairs of massive elementary (CDD) scalar fields excitations. As a nontrivial example of this method we apply it to the physically more interesting ’t Hooft σ model (an extended Nf=2 bosonic linear σ model with four scalar and four pseudoscalar fields), with spontaneously and explicitly broken chiral O(4)×O(2)≃SUR(2)×SUL(2)×UA(1) symmetry.

Linear [formula omitted] model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action

We show an explicit connection between the solution to the equations of motion in the Gaussian functional approximation [I. Nakamura, V. Dmitrašinović, Prog. Theor. Phys. 106 (2001) 1195] and the minimum of the (Gaussian) effective potential/action of the linear Σ model, as well as with the N/D method in dispersion theory. The resulting equations contain analytic functions with branch cuts in the complex mass squared plane. Therefore the minimum of the effective action may lie in the complex mass squared plane. Many solutions to these equations can be found on the second, third, etc. Riemann sheets of the equation, though their physical interpretation is not clear. Our results and the established properties of the S-matrix in general, and of the N/D solutions in particular, guide us to the correct choice of the Riemann sheet. We count the number of states and find only one in each spin-parity and isospin channel with quantum numbers corresponding to the fields in the Lagrangian, i.e., to Castillejo–Dalitz–Dyson (CDD) poles. We examine the numerical solutions in both the strong and weak coupling regimes and calculate the Källén–Lehmann spectral densities and then use them for physical interpretation.