Is the axial anomaly really determined in a continuous non-perturbative regularization?

In the framework of a gauge invariant continuous and non-perturbative regularization scheme based on the smearing of point like interactions by means of cutoff functions, we show that the axial anomaly, though cutoff independent, depends on the shape of the cutoff functions. The standard value for the strength of the axial anomaly is recovered if we assume that the regularized gauge invariant axial current is in addition local.Comment: 12 pages, 1 figure, some typos corrected, to be published in European Physical Journal

Annealing diffusions in a slowly growing potential

We consider a continuous analogue of the simulated annealing algorithm in $R^d$. We prove a convergence result, under hypotheses weaker than the usual ones. In particular, we cover cases where the gradient of the potential goes to zero at infinity. The proof follows an idea of L. Miclo, but we replace the Poincar\'e and log-Sobolev inequalities (which do not hold in our setting) by weak Poincar\'e inequalities. We estimate the latter with measure-capacity criteria. We show that, despite the absence of a spectral gap, the convergence still holds for the "classical" schedule t = c/ ln(t), if c is bigger than a constant related to the potential

Enhancing the Effectiveness of Social Dialogue Articulation in Europe (EESDA) Project No. VS/2017/0434 Social Dialogue Articulation and Effectiveness: Country Report for France

This report presents a country study analysing the articulation and effectiveness of social dialogue in France. The methodological approach relies on desk research and semi-structured interviews with social partners in France, aiming at obtaining deeper insights into how issues are articulated in French social dialogue, actors are interacting, and how social dialogue outcomes are achieved – and ultimately implemented. Following a brief historical background on the industrial relations system and the evolutions in the French context after a series of reforms, the report then provides both a cross-sectoral overview of social dialogue articulation and the interaction with European-level social dialogue. It also offers a sectoral perspective by looking at four sectors with a particular focus on four occupations within these sectors: commerce (sales agents), construction (construction workers), education (teachers) and healthcare (nurses). The research suggests a diversity of experiences both in cross-sectoral and sectoral social dialogue articulation and their effectiveness depending on the type of actor (e.g. trade unions, employer organisations, etc.) and on the sector of focus. The perceptions of social dialogue effectiveness are mixed in the face of continuous reforms over the last decades. Interactions with European-level social dialogue and social partners is considered as important (particularly in some sectors), but the intensity of the interaction is limited when it comes to involvement in the European Semester process

Path integral regularization of pure Yang-Mills theory

In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.Comment: LaTeX file, 24 pages, improved version, to be published in Phys. Rev.

Change and Continuity in European Governance

Since the mid 1990s, European governance has evolved substantially, particularly in thedirection of fewer constraints: flexibility, coordination, peer monitoring, and soft law havebecome fashionable themes. The literature on new modes of governance (or NMGs) hasflourished alongside these transformations. But is the existence of new instruments ofgovernance necessarily synonymous with an innovative way of doing things? Is it really thecase that NMGs now play a central role in EU policy-making? Are we witnessing theemergence of an entirely new system of governance at the European level? In order toaddress these questions, this paper begins by briefly making the point that the concept ofgovernance is better suited to describing the way public policy is conducted in the EuropeanUnion, than that of government. It then moves to a discussion of the main trends that areidentified as NMGs in order to assess to what extent they can properly be described asnew. This is followed by an overview of more traditional forms of EU action, which showsthat old governance has far from disappeared.The European system of governance is thus a good example of change in continuity: oldand new are not mutually exclusive and this hybrid situation may in part be due to the greatcontiguity that exists between new modes of governance and their forerunners. New modesof governance are best analysed as an accentuation of the original features of the system,rather than as outright innovations. Both were largely conceived to respond to the sameneed, to provide a framework for interstate cooperation without leading to an unwanteddegree of centralisation. This is not without analogy with the metaphor of the marble cake,used over a century ago by Morton Grodzins to describe the coexistence of several varietiesof federalism in American government. Pure innovations are rare in the world of governance.directives; European law; governance; legitimacy; multilevel governance; open coordination; policy coordination; soft law