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

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

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.

Late Holocene records of fire and human presence in New Zealand

New Zealand, and the South Island in particular, can be considered an excellent test site for the study of the\ud early impact of humans on the environment for two main reasons: the Polynesian settlement occurred only\ud about 700-800 y BP and resulted in abrupt and huge landscape modifications. Burning forest for land clearance\ud impacted dramatically on an ecosystem that was not adapted to fire, changing the composition of the vegetation\ud as documented by sedimentary charcoal and pollen records. Although charcoal data give incontrovertible\ud evidence of some unprecedented fire events right after the arrival of the Maori, its significance as a tracer for local\ud and anthropogenic fire events has been questioned, stressing the need for new markers to confirm and complete the information about human presence and its effective impact.\ud In the present work, faecal sterols and polycyclic aromatic hydrocarbons (PAHs) were individuated as suitable\ud molecular markers and analyzed by GC-MS in a sediment core from Lake Kirkpatrick, located in the Lake\ud Wakatipu catchment at 570 m a.s.l. in the South Island of New Zealand. Coprostanol accounts for about 60%\ud of total sterol content in human faeces, being much less relevant in animal dejections. Together with its\ud degradation product epi-coprostanol, it is well conserved in sedimentary archives and can be highly useful in\ud paleoenvironmental reconstructions of human settlements. PAHs are produced in relevant amounts by combustion in conditions of oxygen depletion, and diagnostic ratios (DR) between specific molecules can be used for inferring fuel and sources.\ud The charcoal record for Lake Kirkpatrick shows major fire episodes around AD 1350, confirmed by corresponding high levels of PAHs ascribable to biomass burning (as further evidenced by DR) at c. AD 1350. Moreover, the same trend is observed also in the fluxes of coprostanol and epi-coprostanol, whose sum results in two peaks at c. AD 1346 and 1351. This finding confirms not only the massive presence of humans in the area and the large use of fire at the time, but also complements and refines the reconstructions enabled by charcoal analysis

Stationary solutions for the parity-even sector of the CPT-even and Lorentz-covariance-violating term of the standard model extension

In this work, we focus on some properties of the parity-even sector of the CPT-even electrodynamics of the standard model extension. We analyze how the six non-birefringent terms belonging to this sector modify the static and stationary classical solutions of the usual Maxwell theory. We observe that the parity-even terms do not couple the electric and magnetic sectors (at least in the stationary regime). The Green's method is used to obtain solutions for the field strengths E and B at first order in the Lorentz- covariance-violating parameters. Explicit solutions are attained for point-like and spatially extended sources, for which a dipolar expansion is achieved. Finally, it is presented an Earth-based experiment that can lead (in principle) to an upper bound on the anisotropic coefficients as stringent as $(\widetilde{\kappa}_{e-}) ^{ij}<2.9\times10^{-20}.$Comment: 8 pages, revtex style, revised published version, to appear in EPJC (2009

Chiral Anomaly and CPT invariance in an implicit momentum space regularization framework

This is the second in a series of two contributions in which we set out to establish a novel momentum space framework to treat field theoretical infinities in perturbative calculations when parity-violating objects occur. Since no analytic continuation on the space-time dimension is effected, this framework can be particularly useful to treat dimension-specific theories. Moreover arbitrary local terms stemming from the underlying infinities of the model can be properly parametrized. We (re)analyse the undeterminacy of the radiatively generated CPT violating Chern-Simons term within an extended version of $QED_4$ and calculate the Adler-Bardeen-Bell-Jackiw triangle anomaly to show that our framework is consistent and general to handle the subtleties involved when a radiative corretion is finite.Comment: 16 pages, LaTeX, version to appear in PR

On the equivalence between Implicit Regularization and Constrained Differential Renormalization

Constrained Differential Renormalization (CDR) and the constrained version of Implicit Regularization (IR) are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods which have rather distinct basis have been successfully applied to several calculations which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum space procedures of Implicit Regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to the regularized ones.Comment: 16 page

Symmetry preserving regularization with a cutoff

A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms carrying Lorentz indices, e.g. proportional to k_{\mu}k_{\nu}. The remaining scalar integrals are calculated with a four dimensional momentum cutoff. The finite terms (independent of the cutoff) are unambiguous and agree with the result of dimensional regularization.Comment: 12 pages, 1 figure, v2 references adde

Implicit Regularization and Renormalization of QCD

We apply the Implicit Regularization Technique (IR) in a non-abelian gauge theory. We show that IR preserves gauge symmetry as encoded in relations between the renormalizations constants required by the Slavnov-Taylor identities at the one loop level of QCD. Moreover, we show that the technique handles divergencies in massive and massless QFT on equal footing.Comment: (11 pages, 2 figures

Macroscopic and microscopic electron transfer kinetics of HOPG and graphite intercalated compound investigated by cyclic voltammetry and SECM

Highly oriented pyrolytic graphite (HOPG) is one of the most used host materials for obtaining and investigating graphite intercalated compounds, because of the high degree structural order of this polycrystal. Experiments on electrochemically intercalated HOPG in sulphuric acid have a model character, as the results obtained can be usefully generalised, not only with respect to other graphite compounds but also for the intercalation of other layered host lattices. In addition, the HOPG/H2SO4 system has an attractive potential for the possibility of electrochemically producing graphite oxide, ideally, by reversible oxidation/reduction cycles, which is of interest for energy storage and graphene production on an industrial scale. However, the oxidation/reduction cycles in such electrochemical intercalation process are not reversible and topotactic, so that the HOPG structure is considerably altered. This alteration may affect, for instance, the quality of the electrochemically produced graphene. In particular, the impact the electrochemical intercalation has on the conductivity of basal planes of HOPG, and so on graphene sheets, is still debated. In this work, we investigated both the macroscopic and microscopic electron transfer (ET) kinetics of the HOPG surface, before and after the intercalation of 1&nbsp;M H2SO4 to obtain graphite intercalated compound, by using cyclic voltammetry (CV) and scanning electrochemical microscopy (SECM), respectively. The heterogeneous kinetic constant (k0) of the HOPG was evaluated quantitatively by using the redox systems [Fe(CN)6]3–/4– and [Ru(NH3)6]3+/2+. The morphology of the samples was also investigated by atomic force microscopy (AFM), which revealed a widespread formation of blisters and precipitates during the HOPG intercalation process. The CV and SECM results indicate that, upon intercalation, the electrochemical behaviour of the HOPG changes sensibly and the ET decreases sensibly. However, this effect depends on the redox mediators employed and it results more dramatic for the [Fe(CN)6]3–/4– system, for which a decrease of k0 by orders of magnitude was obtained. The decrease of ET can be correlated to the blisters and precipitates, which occur during the HOPG intercalation, as observed by AFM