241 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
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
Phase diagram in the imaginary chemical potential region and extended Z3 symmetry
Phase transitions in the imaginary chemical potential region are studied by
the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model that possesses the
extended Z3 symmetry. The extended Z3 invariant quantities such as the
partition function, the chiral condensate and the modifed Polyakov loop have
the Roberge-Weiss (RW) periodicity. There appear four types of phase
transitions; deconfinement, chiral, Polykov-loop RW and chiral RW transitions.
The orders of the chiral and deconfinement transitions depend on the presence
or absence of current quark mass, but those of the Polykov-loop RW and chiral
RW transitions do not. The scalar-type eightquark interaction newly added in
the model makes the chiral transition line shift to the vicinity of the
deconfiment transition line.Comment: 22 pages,17 figure
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
Critical endpoint for deconfinement in matrix and other effective models
We consider the position of the deconfining critical endpoint, where the
first order transition for deconfinement is washed out by the presence of
massive, dynamical quarks. We use an effective matrix model, employed
previously to analyze the transition in the pure glue theory. If the param-
eters of the pure glue theory are unaffected by the presence of dynamical
quarks, and if the quarks only contribute perturbatively, then for three colors
and three degenerate quark flavors this quark mass is very heavy, m_de \sim 2.5
GeV, while the critical temperature, T_de, barely changes, \sim 1% below that
in the pure glue theory. The location of the deconfining critical endpoint is a
sensitive test to differentiate between effective models. For example, models
with a logarithmic potential for the Polyakov loop give much smaller values of
the quark mass, m_de \sim 1 GeV, and a large shift in T_de \sim 10% lower than
that in the pure glue theory.Comment: 16 pages; 3 figure
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