1,055 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
A General Form of the Constraints in the Path Integral Formula
A form of the constraints, specifying a -dimensional manifold embedded in
dimensional Euclidean space, is discussed in the path integral formula
given by a time discretization. Although the mid-point prescription is
privileged in the sphere case, it is more involved in generic cases. An
interpretation on the validity of the formula is put in terms of the operator
formalism. Operators from this path integral formula are also discussed.Comment: 13 pages, LaTe
Topological feature and phase structure of QCD at complex chemical potential
The pseudo-critical temperature of the confinement-deconfinement transition
and the phase transition surface are investigated by using the complex chemical
potential. We can interpret the imaginary chemical potential as the
Aharonov-Bohm phase, then the analogy of the topological order suggests that
the Roberge-Weiss endpoint would define the pseudo-critical temperature. The
behavior of the Roberge-Weiss endpoint at small real quark chemical potential
is investigated with the perturbative expansion. The expected QCD phase diagram
at complex chemical potential is presented.Comment: 6 pages, 2 figure
Chiral Invariance and Species Doublers in Generic Fermion Models on the Lattice
Discussions are made on the structures of chirally invariant lattice actions
without any restriction of hermiticity. With the help of the Ward-Takahashi
identity a general conclusion can be derived that there must be species
doublers in any chirally invariant model provided that the model is chosen as
well-regularized, that is, there is no singularity in the propagator after
introducing fermion mass on the lattice. Various examples are discussed to pick
up better models defined in the sense that the number of species doubler is
smaller than that of the naive Dirac action.Comment: 23 pages, 1 figure ( included
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