198 research outputs found
Anomalies in Ward Identities for Three-Point Functions Revisited
A general calculational method is applied to investigate symmetry relations
among divergent amplitudes in a free fermion model. A very traditional work on
this subject is revisited. A systematic study of one, two and three point
functions associated to scalar, pseudoscalar, vector and axial-vector densities
is performed. The divergent content of the amplitudes are left in terms of five
basic objects (external momentum independent). No specific assumptions about a
regulator is adopted in the calculations. All ambiguities and symmetry
violating terms are shown to be associated with only three combinations of the
basic divergent objects. Our final results can be mapped in the corresponding
Dimensional Regularization calculations (in cases where this technique could be
applied) or in those of Gertsein and Jackiw which we will show in detail. The
results emerging from our general approach allow us to extract, in a natural
way, a set of reasonable conditions (e.g. crucial for QED consistency) that
could lead us to obtain all Ward Identities satisfied. Consequently, we
conclude that the traditional approach used to justify the famous triangular
anomalies in perturbative calculations could be questionable. An alternative
point of view, dismissed of ambiguities, which lead to a correct description of
the associated phenomenology, is pointed out.Comment: 26 pages, Revtex, revised version, Refs. adde
Consistency in Perturbative Calculations and Radiatively Induced Lorentz and CPT Violations
The origin of the radiatively induced Lorentz and CPT violations, in
perturbative evaluations, of an extended version of QED, is investigated. Using
a very general calculational method, concerning the manipulations and
calculations involving divergent amplitudes, we clearly identify the possible
sources of contributions for the violating terms. We show that consistency in
the perturbative calculations, in a broader sense, leaves no room for the
existence of radiatively induced contributions which is in accordance with what
was previously conjectured and recently advocated by some authors supported on
general arguments.Comment: 8 pages, Revte
From arbitrariness to ambiguities in the evaluation of perturbative physical amplitudes and their symmetry relations
A very general calculational strategy is applied to the evaluation of the
divergent physical amplitudes which are typical of perturbative calculations.
With this approach in the final results all the intrinsic arbitrariness of the
calculations due to the divergent character is still present. We show that by
using the symmetry properties as a guide to search for the (compulsory) choices
in such a way as to avoid ambiguities, a deep and clear understanding of the
role of regularization methods emerges. Requiring then an universal point of
view for the problem, as allowed by our approach, very interesting conclusions
can be stated about the possible justifications of most intriguing aspect of
the perturbative calculations in quantum field theory: the triangle anomalies.Comment: 16 pages, no figure
A predictive formulation of the Nambu--Jona-Lasinio model
A novel strategy to handle divergences typical of perturbative calculations
is implemented for the Nambu--Jona-Lasinio model and its phenomenological
consequences investigated. The central idea of the method is to avoid the
critical step involved in the regularization process, namely the explicit
evaluation of divergent integrals. This goal is achieved by assuming a
regularization distribution in an implicit way and making use, in intermediary
steps, only of very general properties of such regularization. The finite parts
are separated of the divergent ones and integrated free from effects of the
regularization. The divergent parts are organized in terms of standard objects
which are independent of the (arbitrary) momenta running in internal lines of
loop graphs. Through the analysis of symmetry relations, a set of properties
for the divergent objects are identified, which we denominate consistency
relations, reducing the number of divergent objects to only a few ones. The
calculational strategy eliminates unphysical dependencies of the arbitrary
choices for the routing of internal momenta, leading to ambiguity-free, and
symmetry-preserving physical amplitudes. We show that the imposition of scale
properties for the basic divergent objects leads to a critical condition for
the constituent quark mass such that the remaining arbitrariness is removed.
The model become predictive in the sense that its phenomenological consequences
do not depend on possible choices made in intermediary steps. Numerical results
are obtained for physical quantities at the one-loop level for the pion and
sigma masses and pion-quark and sigma-quark coupling constants.Comment: 38 pages, 1 figure, To appear in Phy.Rev.
Consistency in Regularizations of the Gauged NJL Model at One Loop Level
In this work we revisit questions recently raised in the literature
associated to relevant but divergent amplitudes in the gauged NJL model. The
questions raised involve ambiguities and symmetry violations which concern the
model's predictive power at one loop level. Our study shows by means of an
alternative prescription to handle divergent amplitudes, that it is possible to
obtain unambiguous and symmetry preserving amplitudes. The procedure adopted
makes use solely of {\it general} properties of an eventual regulator, thus
avoiding an explicit form. We find, after a thorough analysis of the problem
that there are well established conditions to be fulfiled by any consistent
regularization prescription in order to avoid the problems of concern at one
loop level.Comment: 22 pages, no figures, LaTeX, to appear in Phys.Rev.
A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits
Leakage outside of the qubit computational subspace poses a threatening
challenge to quantum error correction (QEC). We propose a scheme using two
leakage-reduction units (LRUs) that mitigate these issues for a transmon-based
surface code, without requiring an overhead in terms of hardware or QEC-cycle
time as in previous proposals. For data qubits we consider a microwave drive to
transfer leakage to the readout resonator, where it quickly decays, ensuring
that this negligibly affects the coherence within the computational subspace
for realistic system parameters. For ancilla qubits we apply a
pulse conditioned on the measurement
outcome. Using density-matrix simulations of the distance-3 surface code we
show that the average leakage lifetime is reduced to almost 1 QEC cycle, even
when the LRUs are implemented with limited fidelity. Furthermore, we show that
this leads to a significant reduction of the logical error rate. This LRU
scheme opens the prospect for near-term scalable QEC demonstrations
Influence of Lorentz- and CPT-violating terms on the Dirac equation
The influence of Lorentz- and CPT-violating terms (in "vector" and "axial
vector" couplings) on the Dirac equation is explicitly analyzed: plane wave
solutions, dispersion relations and eigenenergies are explicitly obtained. The
non-relativistic limit is worked out and the Lorentz-violating Hamiltonian
identified in both cases, in full agreement with the results already
established in the literature. Finally, the physical implications of this
Hamiltonian on the spectrum of hydrogen are evaluated both in the absence and
presence of a magnetic external field. It is observed that the fixed
background, when considered in a vector coupling, yields no qualitative
modification in the hydrogen spectrum, whereas it does provide an effective
Zeeman-like splitting of the spectral lines whenever coupled in the axial
vector form. It is also argued that the presence of an external fixed field
does not imply new modifications on the spectrum.Comment: 13 pages, no figures, revtex4 styl
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