2,362 research outputs found
Second quantized formulation of geometric phases
The level crossing problem and associated geometric terms are neatly
formulated by the second quantized formulation. This formulation exhibits a
hidden local gauge symmetry related to the arbitrariness of the phase choice of
the complete orthonormal basis set. By using this second quantized formulation,
which does not assume adiabatic approximation, a convenient exact formula for
the geometric terms including off-diagonal geometric terms is derived. The
analysis of geometric phases is then reduced to a simple diagonalization of the
Hamiltonian, and it is analyzed both in the operator and path integral
formulations. If one diagonalizes the geometric terms in the infinitesimal
neighborhood of level crossing, the geometric phases become trivial (and thus
no monopole singularity) for arbitrarily large but finite time interval .
The integrability of Schr\"{o}dinger equation and the appearance of the
seemingly non-integrable phases are thus consistent. The topological proof of
the Longuet-Higgins' phase-change rule, for example, fails in the practical
Born-Oppenheimer approximation where a large but finite ratio of two time
scales is involved and is identified with the period of the slower system.
The difference and similarity between the geometric phases associated with
level crossing and the exact topological object such as the Aharonov-Bohm phase
become clear in the present formulation. A crucial difference between the
quantum anomaly and the geometric phases is also noted.Comment: 22 pages, 3 figures. The analysis in the manuscript has been made
more precise by including a brief account of the hidden local gauge symmetry
and by adding several new equations. This revised version is to be published
in Phys. Rev.
Conformal Anomaly in 4D Gravity-Matter Theories Non-minimally Coupled with Dilaton
The conformal anomaly for 4D gravity-matter theories, which are non-minimally
coupled with the dilaton, is systematically studied. Special care is taken for:
rescaling of fields, treatment of total derivatives, hermiticity of the system
operator and choice of measure. Scalar, spinor and vector fields are taken as
the matter quantum fields and their explicit conformal anomalies in the
gravity-dilaton background are found. The cohomology analysis is done and some
new conformal invariants and trivial terms, involving the dilaton, are
obtained. The symmetry of the constant shift of the dilaton field plays an
important role. The general structure of the conformal anomaly is examined. It
is shown that the dilaton affects the conformal anomaly characteristically for
each case: 1)[Scalar] The dilaton changes the conformal anomaly only by a new
conformal invariant, ; 2)[Spinor] The dilaton does {\it not} change the
conformal anomaly; 3)[Vector] The dilaton changes the conformal anomaly by
three new (generalized) conformal invariants, . We present some
new anomaly formulae which are useful for practical calculations. Finally, the
anomaly induced action is calculated for the dilatonic Wess-Zumino model. We
point out that the coefficient of the total derivative term in the conformal
anomaly for the 2D scalar coupled to a dilaton is ambiguous. This resolves the
disagreement between calculations in refs.\cite{ENO,NO,SI97,KLV} and the result
of Hawking-Bousso\cite{BH}.Comment: 37 pages, Latex, No figur
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
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
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.
Anomaly Matching in Gauge Theories at Finite Matter Density
We investigate the application of 't Hooft's anomaly matching conditions to
gauge theories at finite matter density. We show that the matching conditions
constrain the low-energy quasiparticle spectrum associated with possible
realizations of global symmetries.Comment: 11 pages, 1 figure, LaTeX. Section C is corrected and added
reference
Is there still a strong CP problem?
The role of a chiral U(1) phase in the quark mass in QCD is analysed from
first principles. In operator formulation, there is a parity symmetry and the
phase can be removed by a change in the representation of the Dirac gamma
matrices. Moreover, these properties are also realized in a Pauli-Villars
regularized version of the theory. In the functional integral scenario,
attempts to remove the chiral phase by a chiral transformation are thought to
be obstructed by a nontrivial Jacobian arising from the fermion measure and the
chiral phase may therefore seem to break parity. But if one starts from the
regularized action with the chiral phase also present in the regulator mass
term, the Jacobian for a combined chiral rotation of quarks and regulators is
seen to be trivial and the phase can be removed by a combined chiral rotation.
This amounts to a taming of the strong CP problem.Comment: 6 pages, REVTeX; brief discussion available at
http://theory.saha.ernet.in/~mitra/scp.htm
A gauge invariant and string independent fermion correlator in the Schwinger model
We introduce a gauge invariant and string independent two-point fermion
correlator which is analyzed in the context of the Schwinger model (QED_2). We
also derive an effective infrared worldline action for this correlator, thus
enabling the computation of its infrared behavior. Finally, we briefly discuss
possible perspectives for the string independent correlator in the QED_3
effective models for the normal state of HTc superconductors.Comment: 14 pages, LaTe
A CubeSat for Calibrating Ground-Based and Sub-Orbital Millimeter-Wave Polarimeters (CalSat)
We describe a low-cost, open-access, CubeSat-based calibration instrument
that is designed to support ground-based and sub-orbital experiments searching
for various polarization signals in the cosmic microwave background (CMB). All
modern CMB polarization experiments require a robust calibration program that
will allow the effects of instrument-induced signals to be mitigated during
data analysis. A bright, compact, and linearly polarized astrophysical source
with polarization properties known to adequate precision does not exist.
Therefore, we designed a space-based millimeter-wave calibration instrument,
called CalSat, to serve as an open-access calibrator, and this paper describes
the results of our design study. The calibration source on board CalSat is
composed of five "tones" with one each at 47.1, 80.0, 140, 249 and 309 GHz. The
five tones we chose are well matched to (i) the observation windows in the
atmospheric transmittance spectra, (ii) the spectral bands commonly used in
polarimeters by the CMB community, and (iii) The Amateur Satellite Service
bands in the Table of Frequency Allocations used by the Federal Communications
Commission. CalSat would be placed in a polar orbit allowing visibility from
observatories in the Northern Hemisphere, such as Mauna Kea in Hawaii and
Summit Station in Greenland, and the Southern Hemisphere, such as the Atacama
Desert in Chile and the South Pole. CalSat also would be observable by
balloon-borne instruments launched from a range of locations around the world.
This global visibility makes CalSat the only source that can be observed by all
terrestrial and sub-orbital observatories, thereby providing a universal
standard that permits comparison between experiments using appreciably
different measurement approaches
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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