214 research outputs found
A New Symmetric Expression of Weyl Ordering
For the creation operator \adag and the annihilation operator of a
harmonic oscillator, we consider Weyl ordering expression of (\adag a)^n and
obtain a new symmetric expression of Weyl ordering w.r.t. \adag a \equiv N
and a\adag =N+1 where is the number operator. Moreover, we interpret
intertwining formulas of various orderings in view of the difference theory.
Then we find that the noncommutative parameter corresponds to the increment of
the difference operator w.r.t. variable . Therefore, quantum
(noncommutative) calculations of harmonic oscillators are done by classical
(commutative) ones of the number operator by using the difference theory. As a
by-product, nontrivial relations including the Stirling number of the first
kind are also obtained.Comment: 15 pages, Latex2e, the title before replacement is "Orderings of
Operators in Quantum Physics", new proofs by using a difference operator
added, some references added, to appear in Modern Physics Letters
Determination of QCD phase diagram from the imaginary chemical potential region
We test the reliability of the the Polyakov-loop extended Nambu-Jona-Lasinio
(PNJL) model, comparing the model result with the lattice data at nonzero
imaginary chemical potential. The PNJL model with the vector-type four-quark
and scalar-type eight-quark interactions reproduces the lattice data on the
pseudocritical temperatures of the deconfinement and chiral phase transitions.
The QCD phase diagram in the real chemical potential region is predicted by the
PNJL model. The critical endpoint survives, even if the vector-type four-quark
interaction is taken into account.Comment: 8 pages, 12 figure
Effect of Dynamical SU(2) Gluons to the Gap Equation of Nambu--Jona-Lasinio Model in Constant Background Magnetic Field
In order to estimate the effect of dynamical gluons to chiral condensate, the
gap equation of SU(2) gauged Nambu--Jona-Lasinio model, under a constant
background magnetic field, is investigated up to the two-loop order in 2+1 and
3+1 dimensions. We set up a general formulation allowing both cases of electric
as well as magnetic background field. We rely on the proper time method to
maintain gauge invariance. In 3+1 dimensions chiral symmetry breaking
(SB) is enhanced by gluons even in zero background magnetic field and
becomes much striking as the background field grows larger. In 2+1 dimensions
gluons also enhance SB but whose dependence on the background field is
not simple: dynamical mass is not a monotone function of background field for a
fixed four-fermi coupling.Comment: 20 pages, 5 figure
Chiral Bosons Through Linear Constraints
We study in detail the quantization of a model which apparently describes
chiral bosons. The model is based on the idea that the chiral condition could
be implemented through a linear constraint. We show that the space of states is
of indefinite metric. We cure this disease by introducing ghost fields in such
a way that a BRST symmetry is generated. A quartet algebra is seen to emerge.
The quartet mechanism, then, forces all physical states, but the vacuum, to
have zero norm.Comment: 9 page
Eight-quark interactions as a chiral thermometer
A NJL Lagrangian extended to six and eight quark interactions is applied to
study temperature effects (SU(3) flavor limit, massless case), and (realistic
massive case). The transition temperature can be considerably reduced as
compared to the standard approach, in accordance with recent lattice
calculations. The mesonic spectra built on the spontaneously broken vacuum
induced by the 't Hooft interaction strength, as opposed to the commonly
considered case driven by the four-quark coupling, undergoes a rapid crossover
to the unbroken phase, with a slope and at a temperature which is regulated by
the strength of the OZI violating eight-quark interactions. This strength can
be adjusted in consonance with the four-quark coupling and leaves the spectra
unchanged, except for the sigma meson mass, which decreases. A first order
transition behavior is also a possible solution within the present approach.Comment: 4 pages, 4 figures, prepared for the proceedings of Quark Matter 2008
- 20th International Conference on Ultra-Relativistic Nucleus Nucleus
Collisions, February 4-10, Jaipur (India
- …