Renormalization of the Yang-Mills theory in the ambiguity-free gauge

The renormalization procedure for the Yang-Mills theory in the gauge free of the Gribov ambiguity is constructed. It is shown that all the ultraviolet infinities may be removed by renormalization of the parameters entering the classical Lagrangian and the local redefinition of the fields.Comment: 20 pages. Some explanations extended, one reference added. Final version published in the journa

Generalized gaugings and the field-antifield formalism

We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to an infinitely reducible algebra. We connect the embedding tensor formalism to the field-antifield (or Batalin-Vilkovisky) formalism, which is the most general formulation known for general gauge theories and their quantization. The structure equations of the embedding tensor formalism are included in the master equation of the field-antifield formalism.Comment: 42 pages; v2: some clarifications and 1 reference added; version to be published in JHE

Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

Is soft breaking of BRST symmetry consistent?

A definition of soft breaking of BRST symmetry in the field-antifield formalism is proposed, valid for general gauge theories and arbitrary gauge fixing. The Ward identities for the generating functionals of Green's functions are derived, and their gauge dependence is investigated. We discuss the Gribov-Zwanziger action for the one-parameter family of R_xi gauges. It is argued that gauge theories with a soft breaking of BRST symmetry are inconsistent.Comment: 1+16 pages; v2: example of section 5 changed to R_xi gauges; v3: small corrections to section 5, one reference added, published versio

The study of Priapulus caudatus reveals conserved molecular patterning underlying different gut morphogenesis in the Ecdysozoa

Background The digestive systems of animals can become highly specialized in response to their exploration and occupation of new ecological niches. Although studies on different animals have revealed commonalities in gut formation, the model systems Caenorhabditis elegans and Drosophila melanogaster, which belong to the invertebrate group Ecdysozoa, exhibit remarkable deviations in how their intestines develop. Their morphological and developmental idiosyncrasies have hindered reconstructions of ancestral gut characters for the Ecdysozoa, and limit comparisons with vertebrate models. In this respect, the phylogenetic position, and slow evolving morphological and molecular characters of marine priapulid worms advance them as a key group to decipher evolutionary events that occurred in the lineages leading to C. elegans and D. melanogaster. Results In the priapulid Priapulus caudatus, the gut consists of an ectodermal foregut and anus, and a mid region of at least partial endodermal origin. The inner gut develops into a 16-cell primordium devoid of visceral musculature, arranged in three mid tetrads and two posterior duplets. The mouth invaginates ventrally and shifts to a terminal anterior position as the ventral anterior ectoderm differentially proliferates. Contraction of the musculature occurs as the head region retracts into the trunk and resolves the definitive larval body plan. Despite obvious developmental differences with C. elegans and D. melanogaster, the expression in P. caudatus of the gut-related candidate genes NK2.1, foxQ2, FGF8/17/18, GATA456, HNF4, wnt1, and evx demonstrate three distinct evolutionarily conserved molecular profiles that correlate with morphologically identified sub-regions of the gut. Conclusions The comparative analysis of priapulid development suggests that a midgut formed by a single endodermal population of vegetal cells, a ventral mouth, and the blastoporal origin of the anus are ancestral features in the Ecdysozoa. Our molecular data on P. caudatus reveal a conserved ecdysozoan gut-patterning program and demonstrates that extreme morphological divergence has not been accompanied by major molecular innovations in transcriptional regulators during digestive system evolution in the Ecdysozoa. Our data help us understand the origins of the ecdysozoan body plan, including those of C. elegans and D. melanogaster, and this is critical for comparisons between these two prominent model systems and their vertebrate counterparts

On the algebraic structure of the BRST symmetry

info:eu-repo/semantics/publishe