Fields on Paracompact Manifold and Anomalies

In Continuum Light Cone Quantization (CLCQ) the treatment of scalar fields as operator valued distributions and properties of the accompanying test functions are recalled. Due to the paracompactness property of the Euclidean manifold these test functions appear as decomposition of unity. The approach is extended to QED Dirac fields in a gauge invariant way. With such test functions the usual triangle anomalies are calculated in a simple and transparent way.Comment: 25 Octobre 2003, LC03 proceeding

Quantum Fields as Operator Valued Distributions and Causality

Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in understanding its renormalization structure, which was a major and somehow fatal disease to its widespread use in the seventies. In keeping with the usual way of definition of integrals of differential forms, fields are defined through integrals over the whole manifold, which are given an atlas-independent meaning with the help of the partition of unity. Using such partition of unity test functions turns out to be the key to the fulfilment of the Poincar\'e commutator algebra as well as to provide a direct Lorentz invariant scheme to the Epstein-Glaser extension procedure of singular distributions. These test functions also simplify the analysis of QFT behaviour both in the UV and IR domains, leaving only a finite renormalization at a point related to the arbitrary scale present in the test functions. Some well known UV and IR cases are examplified. Finally the possible implementation of Epstein-Glaser approach in light-front field theory is discussed, focussing on the intrinsic non-pertubative character of the initial light-cone interaction Hamiltonian and on the expected benefits of a divergence-free procedure with only finite RG-analysis on physical observables in the end.Comment: 20 pages,2 figure

QED Fermi-Fields as Operator Valued Distributions and Anomalies

The treatment of fields as operator valued distributions (OPVD) is recalled with the emphasis on the importance of causality following the work of Epstein and Glaser. Gauge invariant theories demand the extension of the usual translation operation on OPVD, thereby leading to a generalized $QED$ formulation. At D=2 the solvability of the Schwinger model is totally preserved. At D=4 the paracompactness property of the Euclidean manifold permits using test functions which are decomposition of unity and thereby provides a natural justification and extension of the non perturbative heat kernel method (Fujikawa) for abelian anomalies. On the Minkowski manifold the specific role of causality in the restauration of gauge invariance (and mass generation for $QED_{2}$) is examplified in a simple way.Comment: soumis le 22/09/200

Aspects of fine-tuning of the Higgs mass within finite field theories

We reanalyze the perturbative radiative corrections to the Higgs mass within the Standard Model in the light of the Taylor-Lagrange renormalization scheme. This scheme naturally leads to completely finite corrections, depending on an arbitrary scale. The formulation avoids very large individual corrections to the Higgs mass. This illustrates the fact that the so-called fine-tuning problem in the Standard Model is just an artifact of the regularization scheme. It should therefore not lead to any physical interpretation in terms of the energy scale at which new physics should show up, nor in terms of a new symmetry. We analyze the intrinsic physical scales relevant for the description of these radiative corrections.Comment: 9 pages. arXiv admin note: substantial text overlap with arXiv:1011.174

Asset Prices in Taylor Rules: Specification, Estimation, and Policy Implications for the ECB

This paper estimates standard and extended Taylor rules for core countries in the euro area, namely France, Germany and Italy, as well as for the ECB. Forward, backward and forecast-based rules are estimated for a variety of samples since the late 1970s. We are particularly interested in the impact of adding asset prices to the standard Taylor rule specification. Since forward-looking Taylor rules are usually estimated via GMM we perform extensive tests for over-identifying restrictions and instrument relevance, a practice generally eschewed in previous work. We find that asset prices can be highly relevant as instruments rather than as separate arguments in policy rules. Backwardlooking Taylor rules, however, cannot be rejected outright. Forecast-based rules perform best using the root mean squared error metric but produce coefficients implying that central banks may be too aggressive at fighting inflation. Encompassing tests are therefore required to select the ?best? policy rule and these suggest that policy rules need to have a mix of forward and forecast-based elements. Furthermore too aggressive reactions to stock prices in particular would have led to an implausible monetary policy. Hence, asset prices appear at best to serve as indicators of the direction of interest rates and not as a variable that the ECB directly reacts to. --reaction function,asset prices

Did the Bundesbank React to Stock Price Movements?

In this paper, we investigate the relationship between stock returns and short-term interest rates. Identification of the stock return-interest rate relation is solved by using a new technique that relies on the heteroskedasticity of shocks to stock market returns. We suggest some improvements to the identification technique and its justification, as well as providing some new findings. In particular, we ask whether the Bundesbank, prior to the European Central Bank taking responsibility for monetary policy in 1999, reacted systematically to stock price movements. In contrast to the results for the US, our empirical findings for the 1985 - 1998 period show a positive, but statistically insignificant, parameter for the relationship between German stock returns and short-term interest rates at the daily frequency. The same result is found at the monthly frequency. Nevertheless, the confidence bands are wide enough that we cannot entirely exclude the possibility of a reaction at lower frequencies. The results are extremely robust to alternative methods used to identify changes in heteroskedasticity. The evidence is, therefore, inconsistent with the hypothesis of a systematic reaction of the Bundesbank to every wiggle in German stock prices. Both the historical and institutional evidence are supportive of this conclusion. -- In diesem Diskussionspapier untersuchen wir den Zusammenhang zwischen Aktienkursveränderungen und Veränderungen der kurzfristigen Zinssätze. Die ökonometrische Identifikation dieses Zusammenhangs erfolgt mit Hilfe eines neuen Verfahrens, das die Heteroskedastie von Aktienkursveränderungen ausnutzt. Wir schlagen einige Verbesserungen und Rechtfertigungen zu diesem Verfahren vor und liefern neue empirische Befunde. Im Vordergrund der Betrachtungen steht die Frage, ob die Bundesbank vor der Übernahme der geldpolitischen Entscheidungen durch die Europäische Zentralbank im Jahre 1999 systematisch auf Veränderungen der Aktienkurse reagiert hat. Im Unterschied zu den verfügbaren Ergebnissen für die Vereinigten Staaten von Amerika, finden wir auf Basis von Tagesdaten zwar einen positiven, aber statistisch nicht signifikanten Parameter für die Reaktion des kurzfristigen Zinssatzes auf Änderungen des Aktienkurses. Auf der Grundlage von Monatsdaten ist der Parameter ebenfalls positiv und statistisch insignifikant. Die Konfidenzintervalle sind aber sehr breit, so dass eine Reaktion auf der niedrigeren Frequenz nicht völlig ausgeschlossen werden kann. Die empirischen Resultate sind sehr robust gegenüber unterschiedlichen Modellspezifikationen. Die empirische Evidenz widerspricht somit der These einer systematischen Reaktion der Bundesbank auf jede Bewegung am Aktienmarkt, was durch die historischen und institutionellen Gegebenheiten gestützt wird.