The Auxiliary Field Method in Quantum Mechanical Four-Fermi Models -- A Study Toward Chiral Condensation in QED

A study for checking validity of the auxiliary field method (AFM) is made in quantum mechanical four-fermi models which act as a prototype of models for chiral symmetry breaking in Quantum Electrodynamics. It has been shown that AFM, defined by an insertion of Gaussian identity to path integral formulas and by the loop expansion, becomes more accurate when taking higher order terms into account under the bosonic model with a quartic coupling in 0- and 1-dimensions as well as the model with a four-fermi interaction in 0-dimension. The case is also confirmed in terms of two models with the four-fermi interaction among $N$ species in 1-dimension (the quantum mechanical four-fermi models): higher order corrections lead us toward the exact energy of the ground state. It is found that the second model belongs to a WKB-exact class that has no higher order corrections other than the lowest correction. Discussions are also made for unreliability on the continuous time representation of path integration and for a new model of QED as a suitable probe for chiral symmetry breaking.Comment: 30 pages, 12 figure

Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations

The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics", IEEE Transactions on Antennas and Propagation, vol. 42, no. 1, pp. 62--69, 1994), where numerical evidence for specific media have been used. We use von Neumann analysis to give necessary and sufficient stability conditions for these schemes for any medium, in accordance with the partial results of [1]

Nambu-Jona-Lasinio Model Coupled to Constant Electromagnetic Fields in D-Dimension

Critical dynamics of the Nambu-Jona-Lasinio model, coupled to a constant electromagnetic field in D=2, 3, and 4, is reconsidered from a viewpoint of infrared behavior and vacuum instability. The latter is associated with constant electric fields and cannot be avoidable in the nonperturbative framework obtained through the proper time method. As for magnetic fields, an infrared cut-off is essential to investigate the critical phenomena. The result reconfirms the fact that the critical coupling in D=3 and 4 goes to zero even under an infinitesimal magnetic field. There also shows that a non-vanishing $F_{\mu\nu}\widetilde F^{\mu\nu}$ causes instability. A perturbation with respect to external fields is adopted to investigate critical quantities, but the resultant asymptotic expansion excellently matches with the exact value.Comment: 27 pages, 17 figure files, LaTe

Coherent states, Path integral, and Semiclassical approximation

Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by a linear combination of generators. In our case,WKB approximation is achieved by taking a large ``spin'' limit: $J,K\rightarrow \infty$. The result is obtained directly by knowing that the each coefficient vanishes under the $J^{-1}$($K^{-1}$) expansion and is examined by another method to be legitimated. We also point out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression leads us to a wrong result. Therefore a great care must be taken when some geometrical action would be adopted, even if it is so beautiful, as the starting ingredient of path integral.Comment: latex 33 pages and 2 figures(uuencoded postscript file), KYUSHU-HET-19 We have corrected the proof of the WKB-exactness in the section

Extensions and further applications of the nonlocal Polyakov--Nambu--Jona-Lasinio model

The nonlocal Polyakov-loop-extended Nambu--Jona-Lasinio (PNJL) model is further improved by including momentum-dependent wave-function renormalization in the quark quasiparticle propagator. Both two- and three-flavor versions of this improved PNJL model are discussed, the latter with inclusion of the (nonlocal) 't Hooft-Kobayashi-Maskawa determinant interaction in order to account for the axial U(1) anomaly. Thermodynamics and phases are investigated and compared with recent lattice-QCD results.Comment: 28 pages, 11 figures, 4 tables; minor changes compared to v1; extended conclusion