The reduced phase space of Palatini-Cartan-Holst theory

General relativity in four dimensions can be reformulated as a gauge theory, referred to as Palatini-Cartan-Holst theory. This paper describes its reduced phase space using a geometric method due to Kijowski and Tulczyjew and its relation to that of the Einstein-Hilbert approach.Comment: Revised version comprising new results, a correction of Th 4.22 and the arguments leading to it. Manuscript accepted for publication in AHP. 31 page

On time

This note describes the restoration of time in one-dimensional parameterization-invariant (hence timeless) models, namely the classically-equivalent Jacobi action and gravity coupled to matter. It also serves as a timely introduction by examples to the classical and quantum BV-BFV formalism as well as to the AKSZ method.Comment: 36 pages. Improved exposition. To appear in Lett. Math. Phy

BV-BFV approach to General Relativity: Palatini-Cartan-Holst action

We show that the Palatini--Cartan--Holst formulation of General Relativity in tetrad variables must be complemented with additional requirements on the fields when boundaries are taken into account for the associated BV theory to induce a compatible BFV theory on the boundary.Comment: 22 pages. Corrected typos in some formulae. Minor aesthetic fixe

BV-equivalence between triadic gravity and BF theory in three dimensions

The triadic description of General Relativity in three dimensions is known to be a BF theory. Diffeomorphisms, as symmetries, are easily re- covered on shell from the symmetries of BF theory. This note describes an explicit off-shell BV symplectomorphism between the BV versions of the two theories, each endowed with their natural symmetries

BV-BFV approach to General Relativity, Einstein-Hilbert action

The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any $d + 1 \not= 2$ (pseudo-) Riemannian manifold M with space-like or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered in a straightforward way.Comment: 16 page

General Relativity and the AKSZ construction

In this note the AKSZ construction is applied to the BFV description of the reduced phase space of the Einstein-Hilbert and of the Palatini--Cartan theories in every space-time dimension greater than two. In the former case one obtains a BV theory for the first-order formulation of Einstein--Hilbert theory, in the latter a BV theory for Palatini--Cartan theory with a partial implementation of the torsion-free condition already on the space of fields. All theories described here are BV versions of the same classical system on cylinders. The AKSZ implementations we present have the advantage of yielding a compatible BV-BFV description, which is the required starting point for a quantization in presence of a boundary.Comment: Improved version with new results about Palatini-Cartan theory. 41 Page

Boundary structure of General Relativity in tetrad variables

An explicit, geometric description of the first-class constraints and their Poisson brackets for gravity in the Palatini-Cartan formalism (in space-time dimension greater than three) is given. The corresponding Batalin- Fradkin-Vilkovisky (BFV) formulation is also developed.Comment: Accepted manuscript. Few exposition and stylistic improvements. 32 page

Gravity with torsion as deformed BF theory

We study a family of (possibly non topological) deformations of BF theory for the Lie algebra obtained by quadratic extension of so(3, 1) by an orthogonal module. The resulting theory, called quadratically extended General Relativity (qeGR), is shown to be classically equivalent to certain models of gravity with dynamical torsion. The classical equivalence is shown to promote to a stronger notion of equivalence within the Batalin–Vilkovisky formalism. In particular, both Palatini–Cartan gravity and a deformation thereof by a dynamical torsion term, called (quadratic) generalised Holst theory, are recovered from the standard Batalin–Vilkovisky formulation of qeGR by elimination of generalised auxiliary fields.&#xD

BV equivalence with boundary

An extension of the notion of classical equivalence of equivalence in the Batalin–Vilkovisky (BV) and Batalin–Fradkin–Vilkovisky (BFV) frameworks for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in both a strict and a lax sense, distinguished by the compatibility between the BV data for a field theory and its boundary BFV data, necessary for quantisation. In this context, the first- and second-order formulations of nonabelian Yang–Mills and of classical mechanics on curved backgrounds, all of which admit a strict BV–BFV description, are shown to be pairwise equivalent as strict BV–BFV theories. This in particular implies that their BV complexes are quasi-isomorphic. Furthermore, Jacobi theory and one-dimensional gravity coupled with scalar matter are compared as classically equivalent reparametrisation-invariant versions of classical mechanics, but such that only the latter admits a strict BV–BFV formulation. They are shown to be equivalent as lax BV–BFV theories and to have isomorphic BV cohomologies. This shows that strict BV–BFV equivalence is a strictly finer notion of equivalence of theories

Complications After Systematic, Random and Image-guided Prostate Biopsy

CONTEXT: Prostate biopsy (PB) represents the gold standard method to confirm the presence of cancer. In addition to traditional random or systematic approaches, a magnetic resonance imaging (MRI)-guided technique has been introduced recently. OBJECTIVE: To perform a systematic review of complications after transrectal ultrasound (TRUS)-guided, transperineal, and MRI-guided PB. EVIDENCE ACQUISITION: We performed a systematic literature search of Web of Science, Embase, and Scopus databases up to October 2015, according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Complications and mortality following random, systematic, and image-guided PBs were reviewed. Eighty-five references were included. EVIDENCE SYNTHESIS: The most frequent complication after PB was minor and self-limiting bleeding (hematuria and hematospermia), regardless of the biopsy approach. Occurrence of rectal bleeding was comparable for traditional TRUS-guided and image-guided PBs. Almost 25% of patients experienced lower urinary tract symptoms, but only a few had urinary retention, with higher rates after a transperineal approach. Temporary erectile dysfunction was not negligible, with a return to baseline after 1-6 mo. The incidence of infective complications is increasing, with higher rates among men with medical comorbidities and older age. Transperineal and in-bore MRI-targeted biopsy may reduce the risk of severe infectious complications. Mortality after PB is uncommon, regardless of biopsy technique. CONCLUSIONS: Complications after PB are frequent but often self-limiting. The incidence of hospitalization due to severe infections is continuously increasing. The patient's general health status, risk factors, and likelihood of antimicrobial resistance should be carefully appraised before scheduling a PB. PATIENT SUMMARY: We reviewed the variety and incidence of complications after prostate biopsy. Even if frequent, complications seldom represent a problem for the patient. The most troublesome complications are infections. To minimize this risk, the patient's medical condition should be carefully evaluated before biopsy