2,289 research outputs found
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 and
together with Pauli-Villars fields and are utilized. It is shown
that this domain wall representation in the infinite flavor limit 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 . 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
where stands for a non-negative integer.
The choice 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 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
where stands for a non-negative integer.
The choice 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 is
satisfied by the creation and annihilation operators and of a
harmonic oscillator. A hermitian phase operator, which inevitably leads to
, cannot be consistently
defined. If one considers an dimensional truncated theory, a hermitian
phase operator of Pegg and Barnett which carries a vanishing index can be
defined. However, for arbitrarily large , 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 () is naturally
introduced and the relation: 4 dim electron momentum
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 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 was obtained against muons with , 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.
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