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

A General Form of the Constraints in the Path Integral Formula

A form of the constraints, specifying a $D$-dimensional manifold embedded in $D+1$ 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 $S^D$ 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