A generalized Ginsparg-Wilson relation

We show that, under certain general assumptions, any sensible lattice Dirac operator satisfies a generalized form of the Ginsparg-Wilson relation (GWR). Those assumptions, on the other hand, are mostly dictated by large momentum behaviour considerations. We also show that all the desirable properties often deduced from the standard GWR hold true of the general case as well; hence one has, in fact, more freedom to modify the form of the lattice Dirac operator, without spoiling its nice properties. Our construction, a generalized Ginsparg-Wilson relation (GGWR), is satisfied by some known proposals for the lattice Dirac operator. We discuss some of these examples, and also present a derivation of the GGWR in terms of a renormalization group transformation with a blocking which is not diagonal in momentum space, but nevertheless commutes with the Dirac operator.Comment: 16 pages, Latex, no figure

Anomalous Chiral Action from the Path-Integral

By generalizing the Fujikawa approach, we show in the path-integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern-Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. Our method uses Schwinger's ``proper-time'' representation of the Green's function and the gauge invariant point-splitting technique. We find that the consistency requirement and the point-splitting technique allow both an anomalous and a non-anomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory, or, a non-anomalous theoryComment: 28 page

Hawking Radiation in the Dilaton Gravity with a Non-Minimally Coupled Scalar Field

We discuss the two-dimensional dilaton gravity with a scalar field as the source matter where the coupling with the gravity is given, besides the minimal one, through an external field. This coupling generalizes the conformal anomaly in the same way as those found in recent literature, but with a diferent motivation. The modification to the Hawking radiation is calculated explicity and shows an additional term that introduces a dependence on the (effective) mass of the black-hole.Comment: 13 pages, latex file, no figures, to be published in IJM

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

Lorentz-invariant CPT violation

A Lorentz-invariant CPT violation, which may be termed as long-distance CPT violation in contrast to the familiar short-distance CPT violation, has been recently proposed. This scheme is based on a non-local interaction vertex and characterized by an infrared divergent form factor. We show that the Lorentz covariant $T^{\star}$-product is consistently defined and the energy-momentum conservation is preserved in perturbation theory if the path integral is suitably defined for this non-local theory, although unitarity is generally lost. It is illustrated that T violation is realized in the decay and formation processes. It is also argued that the equality of masses and decay widths of the particle and anti-particle is preserved if the non-local CPT violation is incorporated either directly or as perturbation by starting with the conventional CPT-even local Lagrangian. However, we also explicitly show that the present non-local scheme can induce the splitting of particle and anti-particle mass eigenvalues if one considers a more general class of Lagrangians.Comment: 28 pages; note added in proof; version published in Eur. Phys. J. C (2013) 73: 234

Processing ceramics

A method of hot hydrostatic pressing of ceramics is described. A detailed description of the invention is given. The invention is explained through an example, and a figure illustrates the temperature and pressure during the hot hydrostatic pressing treatment

Sealing ceramic material in low melting point glass

A structured device placed in an aerated crucible to pack ceramics molding substance that is to be processed was designed. The structure is wrapped by sealing material made of pyrex glass and graphite foil or sheet with a weight attached on top of it. The crucible is made of carbon; the ceramics material to be treated through heat intervenient press process is molding substance consisting mainly of silicon nitride

Domain wall fermion and CP symmetry breaking

We examine the CP properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables $q$ and $\bar q$ together with Pauli-Villars fields $Q$ and $\bar Q$ are utilized. It is shown that this domain wall representation in the infinite flavor limit $N=\infty$ is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and CP symmetry still persists for finite lattice spacing $a$. The CP transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice CP transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of CP symmetry at least in the topologically trivial sector. We note that the conflict with CP symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.Comment: 33 pages. Note added and a new reference were added. Phys. Rev.D (in press

Asynchronous vibration problem of centrifugal compressor

An unstable asynchronous vibration problem in a high pressure centrifugal compressor and the remedial actions against it are described. Asynchronous vibration of the compressor took place when the discharge pressure (Pd) was increased, after the rotor was already at full speed. The typical spectral data of the shaft vibration indicate that as the pressure Pd increases, pre-unstable vibration appears and becomes larger, and large unstable asynchronous vibration occurs suddenly (Pd = 5.49MPa). A computer program was used which calculated the logarithmic decrement and the damped natural frequency of the rotor bearing systems. The analysis of the log-decrement is concluded to be effective in preventing unstable vibration in both the design stage and remedial actions

Geometric phases, gauge symmetries and ray representation

The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood as defining generalized rays in the Hilbert space is not generally consistent with the superposition principle in interference and polarization phenomena. The hidden local gauge symmetry, which arises from the arbitrariness of the choice of coordinates in the functional space, is then proposed as a basic gauge symmetry in the non-adiabatic phase. This re-formulation reproduces all the successful aspects of the non-adiabatic phase in a manner manifestly consistent with the conventional notion of rays and the superposition principle. The hidden local symmetry is thus identified as the natural origin of the gauge symmetry in both of the adiabatic and non-adiabatic phases in the absence of gauge fields, and it allows a unified treatment of all the geometric phases. The non-adiabatic phase may well be regarded as a special case of the adiabatic phase in this re-formulation, contrary to the customary understanding of the adiabatic phase as a special case of the non-adiabatic phase. Some explicit examples of geometric phases are discussed to illustrate this re-formulation.Comment: 30 pages. Some clarifying sentences have been added in abstract and in the body of the paper. A new additional reference and some typos have been corrected. To appear in Int. J. Mod. Phys.