3,013 research outputs found
Quantum and Classical Gauge Symmetries in a Modified Quantization Scheme
The use of the mass term as a gauge fixing term has been studied by
Zwanziger, Parrinello and Jona-Lasinio, which is related to the non-linear
gauge of Dirac and Nambu in the large mass limit. We have
recently shown that this modified quantization scheme is in fact identical to
the conventional {\em local} Faddeev-Popov formula {\em without} taking the
large mass limit, if one takes into account the variation of the gauge field
along the entire gauge orbit and if the Gribov complications can be ignored.
This suggests that the classical massive vector theory, for example, is
interpreted in a more flexible manner either as a gauge invariant theory with a
gauge fixing term added, or as a conventional massive non-gauge theory. As for
massive gauge particles, the Higgs mechanics, where the mass term is gauge
invariant, has a more intrinsic meaning.
It is suggested to extend the notion of quantum gauge symmetry (BRST
symmetry) not only to classical gauge theory but also to a wider class of
theories whose gauge symmetry is broken by some extra terms in the classical
action. We comment on the implications of this extended notion of quantum gauge
symmetry.Comment: 14 pages. Substantially revised and enlarged including the change of
the title. To appear in International Journal of Modern Physics
Cancellation of quantum mechanical higher loop contributions to the gravitational chiral anomaly
We give an explicit demonstration, using the rigorous Feynman rules developed
in~\0^{1}, that the regularized trace \tr \gamma_5 e^{-\beta \Dslash^2} for
the gravitational chiral anomaly expressed as an appropriate quantum mechanical
path integral is -independent up to two-loop level. Identities and
diagrammatic notations are developed to facilitate rapid evaluation of graphs
given by these rules.Comment: 10 pages, LaTeX and psfig (many figures
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
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
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
D=26 and Exact Solution to the Conformal-Gauge Two-Dimensional Quantum Gravity
The conformal-gauge two-dimensional quantum gravity is formulated in the
framework of the BRS quantization and solved completely in the Heisenberg
picture: All n-point Wightman functions are explicitly obtained. The
field-equation anomaly is shown to exist as in other gauges, but there is no
other subtlety. At the critical dimension D=26 of the bosonic string, the
field-equation anomaly is shown to be absent. However, this result is not
equivalent to the statement that the conformal anomaly is proportional to D-26.
The existence of the FP-ghost number current anomaly is seen to be an illusion.Comment: 18 pages, LaTe
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 -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
Axial Anomaly in Noncommutative QED on R^4
The axial anomaly of the noncommutative U(1) gauge theory is calculated by a
number of methods and compared with the commutative one. It is found to be
given by the corresponding Chern class.Comment: LaTeX, axodraw.sty; v2: typos are fixed; v3: version to appear in
Int. J. Mod. Phys. A. (2001
Hawking Radiation, Covariant Boundary Conditions and Vacuum States
The basic characteristics of the covariant chiral current are obtained from a
chiral effective action. These results are used to justify the covariant
boundary condition used in recent approaches
\cite{Isowilczek,Isoumtwilczek,shailesh,shailesh2,Banerjee} of computing the
Hawking flux from chiral gauge and gravitational anomalies. We also discuss a
connection of our results with the conventional calculation of nonchiral
currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware)
states.Comment: 18 pages, no figures, minor changes, to appear in Phys. Rev.
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