264 research outputs found
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 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
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 and (in the discrete series) are WKB exact,if
the starting point is expressed as the trace of with
being given by a linear combination of generators. In our case,WKB
approximation is achieved by taking a large ``spin'' limit: . The result is obtained directly by knowing that the each coefficient
vanishes under the () 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
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