Chiral Anomaly for a New Class of Lattice Dirac Operators

A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands for a non-negative integer and $k=0$ corresponds to the ordinary Ginsparg-Wilson relation. We analyze the chiral anomaly and index theorem for all these Dirac operators in an explicit elementary manner. We show that the coefficient of anomaly is independent of a small variation in the parameters $r$ and $m_{0}$, which characterize these Dirac operators, and the correct chiral anomaly is obtained in the (naive) continuum limit $a\to 0$.Comment: 23 pages. Corrected typos and misprints. Made several sentences more precise, and references up-dated. (To appear in Nucl. Phys. B

CP breaking in lattice chiral gauge theory

The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear.Comment: 3 pages, Lattice2002(chiral

Characterizing Reaction Route Map of Realistic Molecular Reactions based on Weight Rank Clique Filtration of Persistent Homology

A reaction route map (RRM) constructed using GRRM program is a collection of elementary reaction pathways, each of which consists of two equilibrium (EQ) geometries and one transition-state (TS) geometry, connected by the intrinsic reaction coordinate (IRC). An RRM can be mathematically represented by a graph with weights assigned to both vertices, corresponding to EQs, and edges, corresponding to TSs, representing the corresponding energies. In this study, we propose a method to extract topological descriptors of a weighted graph representing an RRM based on persistent homology (PH). The work of Mirth et al. [J. Chem. Phys. 2021, 154, 114114], in which PH analysis was applied to the (3N-6)-dimensional potential energy surface of an N atomic system, is related to the present method, but the latter is practically applicable to realistic molecular reactions. The results of this study suggest that the descriptors obtained using the proposed method reflect the characteristics of the chemical reactions and/or physicochemical properties of the system accurately.Comment: 38 pages, 19 figure

Ginsparg-Wilson operators and a no-go theorem

If one uses a general class of Ginsparg-Wilson operators, it is known that CP symmetry is spoiled in chiral gauge theory for a finite lattice spacing and the Majorana fermion is not defined in the presence of chiral symmetric Yukawa couplings. We summarize these properties in the form of a theorem for the general Ginsparg-Wilson relation.Comment: 8 pages, Latex, references updated, version to appear in Phys. Lett.

One-loop analyses of lattice QCD with the overlap Dirac operator

We discuss the weak coupling expansion of lattice QCD with the overlap Dirac operator. The Feynman rules for lattice QCD with the overlap Dirac operator are derived and the quark self-energy and vacuum polarization are studied at the one-loop level. We confirm that their divergent parts agree with those in the continuum theory.Comment: 19pages, 7figures, latex; added references :final version for publicatio

Enlargement of accessory spleen subsequent to splenectomy associated with gastrectomy can mimic a solitary tumor : report of a case

We report a case of a 65-year-old woman with an incidental about 20-mm solitary mass between the lateralsegment of the left lobe of the liver and left kidney 5 years after splenectomy associated with total gastrectomy. The mass wassurgically resected, and histological examination revealed it to be an accessory spleen. Small accessory spleens mostly locatednear the splenic hilus, but large accessory spleens are unusual after total gastrectomy with regional lymph nodes resection. Theremaining accessory splenic tissue would undergo compensatory hypertrophy. Hence, the possibility of accessory spleens mustbe considered when an intra-abdominal mass is identified in a patient with splenectomy associated with gastrectomy

Locality Properties of a New Class of Lattice Dirac Operators

A new class of lattice Dirac operators $D$ which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands for a non-negative integer and $k=0$ corresponds to the ordinary Ginsparg-Wilson relation. We analyze the locality properties of Dirac operators which solve the above algebraic relation. We first show that the free fermion operator is analytic in the entire Brillouin zone for a suitable choice of parameters $m_{0}$ and $r$, and there exists a well-defined ``mass gap'' in momentum space, which in turn leads to the exponential decay of the operator in coordinate space for any finite $k$. This mass gap in the free fermion operator suggests that the operator is local for sufficiently weak background gauge fields. We in fact establish a finite locality domain of gauge field strength for $\Gamma_{5}=\gamma_{5}-(a\gamma_{5}D)^{2k+1}$ for any finite $k$, which is sufficient for the cohomological analyses of chiral gauge theory. We also present a crude estimate of the localization length defined by an exponential decay of the Dirac operator, which turns out to be much shorter than the one given by the general Legendre expansion.Comment: Some clarifying comments are added, and a misprint was corrected. Nuclear Physics B(in press

A Perturbative Study of a General Class of Lattice Dirac Operators

A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. We study one-loop fermion contributions to the self-energy of the gauge field, which are related to the fermion contributions to the one-loop $\beta$ function and to the Weyl anomaly. We first explicitly demonstrate that the Ward identity is satisfied by the self-energy tensor. By performing careful analyses, we then obtain the correct self-energy tensor free of infra-red divergences, as a general consideration of the Weyl anomaly indicates. This demonstrates that our general operators give correct chiral and Weyl anomalies. In general, however, the Wilsonian effective action, which is supposed to be free of infra-red complications, is expected to be essential in the analyses of our general class of Dirac operators for dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in press