1,938 research outputs found
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
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
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
Remark on Pauli-Villars Lagrangian on the Lattice
It is interesting to superimpose the Pauli-Villars regularization on the
lattice regularization. We illustrate how this scheme works by evaluating the
axial anomaly in a simple lattice fermion model, the Pauli-Villars Lagrangian
with a gauge non-invariant Wilson term. The gauge non-invariance of the axial
anomaly, caused by the Wilson term, is remedied by a compensation among
Pauli-Villars regulators in the continuum limit. A subtlety in Frolov-Slavnov's
scheme for an odd number of chiral fermions in an anomaly free complex gauge
representation, which requires an infinite number of regulators, is briefly
mentioned.Comment: 14 pages, Phyzzx. The final version to appear in Phys. Rev.
Chiral and axial anomalies in the framework of generalized Hamiltonian BFV-quantization
The regularization scheme is proposed for the constrained Hamiltonian
formulation of the gauge fields coupled to the chiral or axial fermions. The
Schwinger terms in the regularized operator first-class constraint algebra are
shown to be consistent with the covariant divergence anomaly of the
corresponding current. Regularized quantum master equations are studied, and
the Schwinger terms are found out to break down both nilpotency of the
BRST-charge and its conservation law. Wess-Zumino consistency conditions are
studied for the BRST anomaly and they are shown to contradict to the covariant
Schwinger terms in the BRST algebra.Comment: LaTeX, 24p
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
Fluctuation-dissipation theorem and quantum tunneling with dissipation at finite temperature
A reformulation of the fluctuation-dissipation theorem of Callen and Welton
is presented in such a manner that the basic idea of Feynman-Vernon and
Caldeira -Leggett of using an infinite number of oscillators to simulate the
dissipative medium is realized manifestly without actually introducing
oscillators. If one assumes the existence of a well defined dissipative
coefficient which little depends on the temperature in the energy
region we are interested in, the spontanous and induced emissions as well as
induced absorption of these effective oscillators with correct Bose
distribution automatically appears.
Combined with a dispersion relation, we reproduce the tunneling formula in
the presence of dissipation at finite temperature without referring to an
explicit model Lagrangian. The fluctuation-dissipation theorem of Callen-Welton
is also generalized to the fermionic dissipation (or fluctuation) which allows
a transparent physical interpretation in terms of second quantized fermionic
oscillators. This fermionic version of fluctuation-dissipation theorem may
become relevant in the analyses of, for example, fermion radiation from a black
hole and also supersymmetry at the early universe.Comment: 19 pages. Phys. Rev. E (in press
Continuous non-perturbative regularization of QED
We regularize in a continuous manner the path integral of QED by construction
of a non-local version of its action by means of a regularized form of Dirac's
functions. Since the action and the measure are both invariant under
the gauge group, this regularization scheme is intrinsically non-perturbative.
Despite the fact that the non-local action converges formally to the local one
as the cutoff goes to infinity, the regularized theory keeps trace of the
non-locality through the appearance of a quadratic divergence in the transverse
part of the polarization operator. This term which is uniquely defined by the
choice of the cutoff functions can be removed by a redefinition of the
regularized action. We notice that as for chiral fermions on the lattice, there
is an obstruction to construct a continuous and non ambiguous regularization in
four dimensions. With the help of the regularized equations of motion, we
calculate the one particle irreducible functions which are known to be
divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and
revised version, to appear in Phys. Rev.
Invariant Regularization of Anomaly-Free Chiral Theories
We present a generalization of the Frolov-Slavnov invariant regularization
scheme for chiral fermion theories in curved spacetimes. local gauge symmetries
of the theory, including local Lorentz invariance. The perturbative scheme
works for arbitrary representations which satisfy the chiral gauge anomaly and
the mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on
the other hand manifest themselves by having divergent fermion loops which
remain unregularized by the scheme. Since the invariant scheme is promoted to
also include local Lorentz invariance, spectator fields which do not couple to
gravity cannot be, and are not, introduced. Furthermore, the scheme is truly
chiral (Weyl) in that all fields, including the regulators, are left-handed;
and only the left-handed spin connection is needed. The scheme is, therefore,
well suited for the study of the interaction of matter with all four known
forces in a completely chiral fashion. In contrast with the vectorlike
formulation, the degeneracy between the Adler-Bell-Jackiw current and the
fermion number current in the bare action is preserved by the chiral
regularization scheme.Comment: 28pgs, LaTeX. Typos corrected. Further remarks on singlet current
Quantum anomaly and geometric phase; their basic differences
It is sometimes stated in the literature that the quantum anomaly is regarded
as an example of the geometric phase. Though there is some superficial
similarity between these two notions, we here show that the differences bewteen
these two notions are more profound and fundamental. As an explicit example, we
analyze in detail a quantum mechanical model proposed by M. Stone, which is
supposed to show the above connection. We show that the geometric term in the
model, which is topologically trivial for any finite time interval ,
corresponds to the so-called ``normal naive term'' in field theory and has
nothing to do with the anomaly-induced Wess-Zumino term. In the fundamental
level, the difference between the two notions is stated as follows: The
topology of gauge fields leads to level crossing in the fermionic sector in the
case of chiral anomaly and the {\em failure} of the adiabatic approximation is
essential in the analysis, whereas the (potential) level crossing in the matter
sector leads to the topology of the Berry phase only when the precise adiabatic
approximation holds.Comment: 28 pages. The last sentence in Abstract has been changed, the last
paragraph in Section 1 has been re-written, and the latter half of Discussion
has been replaced by new materials. New Conclusion to summarize the analysis
has been added. This new version is to be published in Phys. Rev.
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