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

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

Generalized Ginsparg-Wilson algebra and index theorem on the lattice

Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific 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. It is shown that local chiral anomaly and the instanton-related index of all these operators are identical. The locality of all these Dirac operators for vanishing gauge fields is proved on the basis of explicit construction, but the locality with dynamical gauge fields has not been established yet. We suggest that the Wilsonian effective action is essential to avoid infrared singularities encountered in general perturbative analyses.Comment: 11 pages. Talk given at APCTP-Nankai Joint Symposium on Lattice Statistics and Mathematical Physics, Tianjin, China, 8-11 October, 2001. To be published in the Proceedings and in Int. Jour. Mod. Phys.

Phase Operator for the Photon Field and an Index Theorem

An index relation $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 1$ is satisfied by the creation and annihilation operators $a^{\dagger}$ and $a$ of a harmonic oscillator. A hermitian phase operator, which inevitably leads to $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 0$, cannot be consistently defined. If one considers an $s+1$ dimensional truncated theory, a hermitian phase operator of Pegg and Barnett which carries a vanishing index can be defined. However, for arbitrarily large $s$, we show that the vanishing index of the hermitian phase operator of Pegg and Barnett causes a substantial deviation from minimum uncertainty in a characteristically quantum domain with small average photon numbers. We also mention an interesting analogy between the present problem and the chiral anomaly in gauge theory which is related to the Atiyah-Singer index theorem. It is suggested that the phase operator problem related to the above analytic index may be regarded as a new class of quantum anomaly. From an anomaly view point ,it is not surprising that the phase operator of Susskind and Glogower, which carries a unit index, leads to an anomalous identity and an anomalous commutator.Comment: 32 pages, Late

Temperature in Fermion Systems and the Chiral Fermion Determinant

We give an interpretation to the issue of the chiral determinant in the heat-kernel approach. The extra dimension (5-th dimension) is interpreted as (inverse) temperature. The 1+4 dim Dirac equation is naturally derived by the Wick rotation for the temperature. In order to define a ``good'' temperature, we choose those solutions of the Dirac equation which propagate in a fixed direction in the extra coordinate. This choice fixes the regularization of the fermion determinant. The 1+4 dimensional Dirac mass ($M$) is naturally introduced and the relation: $|$4 dim electron momentum$|$ $\ll$ $|M|$ $\ll$ ultraviolet cut-off, naturally appears. The chiral anomaly is explicitly derived for the 2 dim Abelian model. Typically two different regularizations appear depending on the choice of propagators. One corresponds to the chiral theory, the other to the non-chiral (hermitian) theory.Comment: 24 pages, some figures, to be published in Phys.Rev.

Inelastic Scattering from Core-electrons: a Multiple Scattering Approach

The real-space multiple-scattering (RSMS) approach is applied to model non-resonant inelastic scattering from deep core electron levels over a broad energy spectrum. This approach is applicable to aperiodic or periodic systems alike and incorporates ab initio, self-consistent electronic structure and final state effects. The approach generalizes to finite momentum transfer a method used extensively to model x-ray absorption spectra (XAS), and includes both near edge spectra and extended fine structure. The calculations can be used to analyze experimental results of inelastic scattering from core-electrons using either x-ray photons (NRIXS) or electrons (EELS). In the low momentum transfer region (the dipole limit), these inelastic loss spectra are proportional to those from XAS. Thus their analysis can provide similar information about the electronic and structural properties of a system. Results for finite momentum transfer yield additional information concerning monopole, quadrupole, and higher couplings. Our results are compared both with experiment and with other theoretical calculations.Comment: 11 pages, 8 figures. Submitted to Phys. Rev.

Development of a Large-Area Aerogel Cherenkov Counter Onboard BESS

This paper describes the development of a threshold type aerogel Cherenkov counter with a large sensitive area of 0.6 m$^2$ to be carried onboard the BESS rigidity spectrometer to detect cosmic-ray antiprotons. The design incorporates a large diffusion box containing 46 finemesh photomultipliers, with special attention being paid to achieving good performance under a magnetic field and providing sufficient endurance while minimizing material usage. The refractive index of the aerogel was chosen to be 1.03. By utilizing the muons and protons accumulated during the cosmic-ray measurements at sea level, a rejection factor of 10$^4$ was obtained against muons with $\beta \approx 1$, while keeping 97% efficiency for protons below the threshold.Comment: 13 pages, LaTex, 9 eps figures included, submitted to NIM

Fluctuation-dissipation theorem and quantum tunneling with dissipation

We suggest to take the fluctuation-dissipation theorem of Callen and Welton as a basis to study quantum dissipative phenomena (such as macroscopic quantum tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous symmetry breakdown. It is shown that the essential physical contents of the Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic dissipation are derived from general principles only, namely, the fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion relations), without referring to an explicit form of the Lagrangian. An interesting connection between quantum tunneling with Ohmic dissipation and the Anderson's orthogonality theorem is also noted.Comment: To appear in Phys. Rev.

General bounds on the Wilson-Dirac operator

Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived for 2p-2<m<2p for general p=1,2,...,d where d is the spacetime dimension. The bounds can alternatively be viewed as localisation bounds on the real spectrum of the usual Wilson-Dirac operator. They are needed for the rigorous evaluation of the classical continuum limit of the axial anomaly and index of the overlap Dirac operator at general values of m, and provide information on the topological phase structure of overlap fermions. They are also useful for understanding the instanton size-dependence of the real spectrum of the Wilson-Dirac operator in an instanton background.Comment: 26 pages, 2 figures. v3: Completely rewritten with new material and new title; to appear in Phys.Rev.