1,961 research outputs found
Geometric phases, gauge symmetries and ray representation
The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is
based on the equivalence class which is not
a symmetry of the Schr\"{o}dinger equation. This equivalence class when
understood as defining generalized rays in the Hilbert space is not generally
consistent with the superposition principle in interference and polarization
phenomena. The hidden local gauge symmetry, which arises from the arbitrariness
of the choice of coordinates in the functional space, is then proposed as a
basic gauge symmetry in the non-adiabatic phase. This re-formulation reproduces
all the successful aspects of the non-adiabatic phase in a manner manifestly
consistent with the conventional notion of rays and the superposition
principle. The hidden local symmetry is thus identified as the natural origin
of the gauge symmetry in both of the adiabatic and non-adiabatic phases in the
absence of gauge fields, and it allows a unified treatment of all the geometric
phases. The non-adiabatic phase may well be regarded as a special case of the
adiabatic phase in this re-formulation, contrary to the customary understanding
of the adiabatic phase as a special case of the non-adiabatic phase. Some
explicit examples of geometric phases are discussed to illustrate this
re-formulation.Comment: 30 pages. Some clarifying sentences have been added in abstract and
in the body of the paper. A new additional reference and some typos have been
corrected. To appear in Int. J. Mod. Phys.
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
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
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
Bosonization in d=2 from finite chiral determinants with a Gauss decomposition
We show how to bosonize two-dimensional non-abelian models using finite
chiral determinants calculated from a Gauss decomposition. The calculation is
quite straightforward and hardly more involved than for the abelian case. In
particular, the counterterm , which is normally motivated from gauge
invariance and then added by hand, appears naturally in this approach.Comment: 4 pages, Revte
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.
The BPHZ renormalised BV master equation and Two-loop Anomalies in Chiral Gravities
Anomalies and BRST invariance are governed, in the context of Lagrangian
Batalin-Vilkovisky quantization, by the master equation, whose classical limit
is . Using Zimmerman's normal products and the BPHZ renormalisation
method, we obtain a corresponding local quantum operator equation, which is
valid to all orders in perturbation theory. The formulation implies a
calculational method for anomalies to all orders that is useful also outside
the BV context and that remains completely within regularised perturbation
theory. It makes no difference in principle whether the anomaly appears at one
loop or at higher loops. The method is illustrated by computing the one- and
two-loop anomalies in chiral gravity.Comment: 44 pages, LaTex. 4 figures, epsf. Discussion in section 4 extended,
assorted small modifications, 3 references added. As it will be published in
NP
Global Anomalies in the Batalin Vilkovisky Quantization
The Batalin Vilkovisky (BV) quantization provides a general procedure for
calculating anomalies associated to gauge symmetries. Recent results show that
even higher loop order contributions can be calculated by introducing an
appropriate regularization-renormalization scheme. However, in its standard
form, the BV quantization is not sensible to quantum violations of the
classical conservation of Noether currents, the so called global anomalies. We
show here that the BV field antifield method can be extended in such a way that
the Ward identities involving divergencies of global Abelian currents can be
calculated from the generating functional, a result that would not be obtained
by just associating constant ghosts to global symmetries. This extension,
consisting of trivially gauging the global Abelian symmetries, poses no extra
obstruction to the solution of the master equation, as it happens in the case
of gauge anomalies. We illustrate the procedure with the axial model and also
calculating the Adler Bell Jackiw anomaly.Comment: We emphasized the fact that our procedure only works for the case of
Abelian global anomalies. Section 3 was rewritten and some references were
added. 12 pages, LATEX. Revised version that will appear in Phys. Rev.
Fermion Condensates of massless at Finite Density in non-trivial Topological Sectors
Vacuum expectation values of products of local bilinears are
computed in massless at finite density. It is shown that chiral
condensates exhibit an oscillatory inhomogeneous behaviour depending on the
chemical potential. The use of a path-integral approach clarifies the
connection of this phenomenon with the topological structure of the theory.Comment: 16 pages, no figures, To be published in Phys.Rev.
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