The Gribov horizon and spontaneous BRST symmetry breaking

An equivalent formulation of the Gribov-Zwanziger theory accounting for the gauge fixing ambiguity in the Landau gauge is presented. The resulting action is constrained by a Slavnov-Taylor identity stemming from a nilpotent exact BRST invariance which is spontaneously broken due to the presence of the Gribov horizon. This spontaneous symmetry breaking can be described in a purely algebraic way through the introduction of a pair of auxiliary fields which give rise to a set of linearly broken Ward identities. The Goldstone sector turns out to be decoupled. The underlying exact nilpotent BRST invariance allows to employ BRST cohomology tools within the Gribov horizon to identify renormalizable extensions of gauge invariant operators. Using a simple toy model and appropriate Dirac bracket quantization, we discuss the time-evolution invariance of the operator cohomology. We further comment on the unitarity issue in a confining theory, and stress that BRST cohomology alone is not sufficient to ensure unitarity, a fact, although well known, frequently ignored.Comment: 13 pages. v2: corrected typ

Representations of the Heisenberg algebra on holomorphic functions and Krein structures

Representations of CCR algebras in spaces of entire functions are classified on the basis of isomorphisms between the Heisenberg CCR algebra A_H and star algebras of holomorphic operators. To each representations of such algebras, satisfying a regularity and a reality condition, one can associate isomorphisms and inner products so that they become Krein star representations of A_H, with the gauge transformations implemented by a continuous U(1) group of Krein isometries. Conversely, any holomorphic Krein representation of A_H, having the gauge transformations implemented as before and no null subrepresentation, is shown to be contained in a direct sum of the above representations. The analysis is extended to infinite dimensional CCR algebras, under a spectral condition for the implementers of the gauge transformations.Comment: LateX, with additional results, especially on the infinite dimensional cas

Localization and symmetries

The violation of the Noether relation between symmetries and charges is reduced to the time dependence of the charge associated to a conserved current. For the U(1) gauge symmetry a non-perturbative control of the charge commutators is obtained by an analysis of the Coulomb charged fields. From this, in the unbroken case we obtain a correct expression for the electric charge on the Coulomb states, its superselection and the presence of massless vector bosons; in the broken case, we obtain a general non-perturbative version of the Higgs phenomenon, i.e. the absence of massless Goldstone bosons and of massless vector bosons. The conservation of the (gauge dependent) current associated to the U(1) axial symmetry in QCD is shown to be compatible with the time dependence of the corresponding charge commutators and a non-vanishing eta' mass, as a consequence of the non locality of the (conserved) current.Comment: Invited contribution to ``The Quantum Universe'', dedicated to G. Ghirardi for his 70th birthda

Tricalcium phosphate endosseous implants in dentistry: ultrastructural findings

β-Tricalcium phosphate magnesium substitued (β-TCMP), consisting of one part small unsintered and one part large sintered granules was placed in upper and lower jaw surgical cavities of monkeys. At light and transmission electron microscope the biopsies taken at 2, 4, 8 and 24 weeks showed that both sintered and unsintered granules were well tolerated by the host tissue and result biodegradable over time.β-TCMP may stimulate the direction of bone growth enhancing osteoblasts activity and new bone deposition in direct contact and in the micropores of the biomaterial. β-TCMP containing Mg ions reabsorbs slowly when in sintered granules form and rapidly as unsintered granules. When it is placed in bone cavities, if bone reabsorption is biologically necessary, the biomaterial can be reabsorbed with bone, while if osteogenesis is required β-TCMP provides a more durable matrix to support new bone growth.Le β-phosphate tricalcique contenant à ions Mg (β-TCMP) et constitué à parts égales de fins granules non frittés et de larges granules frittés, est introduit dans des cavités chirurgicales pratiquées dans les maxillaires supérieurs et inférieurs de singes.Des biopsies pratiquées à 2, 4, 8 et 24 semaines ont été examinées au microscope optique et électronique à transmission.Les granules frittés et non frittés sont bien tolérés par les tissus hôtes et sont biodégradés avec le temps.Les observations histologiques montrent aussi que le β-TCMP peut orienter la direction de la croissance osseuse en stimulant l’activité des ostéoblastes et le dépôt d’os nouveau aussi bien autour des biomatériaux que dans leur micropores. Le β-TCMP contenant les ions Mg est réabsorbé lentement lorsqu’il se présente sous la forme de granules frittés, et rapidement lorsqu’il est sous la forme de granules non frittés.Lorsqu’il est introduit dans les cavités osseuses, si la réabsorption osseuse est biologiquement nécessaire, le biomatériau peut être réabsorbé avec l’os, tandis que si c’est l’ostéogenèse qui est sollicitée, β-TCMP fournit une matrice durable comme support à la croissance d’os nouveau

Quantum mechanics on manifolds and topological effects

A unique classification of the topological effects associated to quantum mechanics on manifolds is obtained on the basis of the invariance under diffeomorphisms and the realization of the Lie-Rinehart relations between the generators of the diffeomorphism group and the algebra of infinitely differentiable functions on the manifold. This leads to a unique ("Lie-Rinehart") C* algebra as observable algebra; its regular representations are shown to be locally Schroedinger and in one to one correspondence with the unitary representations of the fundamental group of the manifold. Therefore, in the absence of spin degrees of freedom and external fields, the first homotopy group of the manifold appears as the only source of topological effects.Comment: A few comments have been added to the Introduction, together with related references; a few words have been changed in the Abstract and a Note added to the Titl

Mathematical structure of the temporal gauge

The mathematical structure of the temporal gauge of QED is critically examined in both the alternative formulations characterized by either positivity or regularity of the Weyl algebra. The conflict between time translation invariance and Gauss law constraint is shown to lead to peculiar features. In the positive case only the correlations of exponentials of fields exist (non regularity), the space translations are not strongly continuous, so that their generators do not exist, a theta vacuum degeneracy occurs, associated to a spontaneous symmetry breaking. In the indefinite case the spectral condition only holds in terms of positivity of the energy, gauge invariant theta-vacua exist on the observables, with no extension to time translation invariant states on the field algebra, the vacuum is faithful on the longitudinal algebra and a KMS structure emerges. Functional integral representations are derived in both cases, with the alternative between ergodic measures on real random fields or complex Gaussian random fields.Comment: Late

Topological mass mechanism and exact fields mapping

We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the other model in closed expressions. These expressions provide the mappings of their actions as well as the mappings of their propagators. For a general class of models in which the topological model becomes the BF model the mappings present arbitrary functions which otherwise are absent for Chern-Simons like actions. This work generalizes the results of [1] for arbitrary dimensions.Comment: 11 page

No Eigenvalue in Finite Quantum Electrodynamics

We re-examine Quantum Electrodynamics (QED) with massless electron as a finite quantum field theory as advocated by Gell-Mann-Low, Baker-Johnson, Adler, Jackiw and others. We analyze the Dyson-Schwinger equation satisfied by the massless electron in finite QED and conclude that the theory admits no nontrivial eigenvalue for the fine structure constant.Comment: 13 pages, Late

A prospective evaluation of persistence on antihypertensive treatment with different antihypertensive drugs in clinical practice

Persistence on treatment affects the efficacy of antihypertensive treatment. We prospectively investigated the persistence on therapy and the extent of blood pressure (BP) control in 347 hypertensive patients (age 59.4 +/- 6 years) randomly allocated to a first-line treatment with: angiotensin-converting enzyme (ACE) inhibitors, calcium-channel blockers (CCBs), beta-blockers, angiotensin-II receptor blockers (ARBs), or diuretics and followed-up for 24-months. Persistence on treatment was higher in patients treated with ARBs (68.5%) and ACE inhibitors (64.5%) vs CCBs (51.6%; p < 0.05), beta-blockers (44.8%, p < 0.05), and diuretics (34.4%, p < 0.01). No ARB, ACE inhibitor, beta-blocker, or diuretic was associated with a higher persistence in therapy compared with the other molecules used in each therapeutic class. The rate of persistence was significantly higher in patients treated with lercanidipine vs others CCBs (59.3% vs 46.6%, p < 0.05). Systolic and diastolic BP was decreased more successfully in patients treated with ARBs (-11.2/-5.8 mmHg), ACE inhibitors (-10.5/-5.1 mmHg), and CCBs (-8.5/-4.6 mmHg) compared with beta-blockers (-4.0/-2.3 mmHg p < 0.05) and diuretics (-2.3/-2.1 mmHg, p < 0.05). No ARB, ACE inhibitor, beta-blocker, or diuretic was associated with a higher BP control compared with the other molecules used in each therapeutic class. A trend toward a better BP control was observed in response to lercanidipine vs other CCBs (p = 0.059). The present results confirm the importance of persistence on treatment for the management of hypertension in clinical practice