Sachs Group Research Articles

Homogeneous Projective Coordinates for the Bondi–Metzner–Sachs Group

This paper studies the Bondi–Metzner–Sachs group in homogeneous projective coordinates because it is then possible to write all transformations of such a group in a manifestly linear way. The 2-sphere metric, the Bondi–Metzner–Sachs metric, asymptotic Killing vectors, generators of supertranslations as well as boosts and rotations of Minkowski spacetime are all re-expressed in homogeneous projective coordinates. Lastly, the integral curves of vector fields which generate supertranslations are evaluated in detail. This work paves the way for more advanced applications of the geometry of asymptotically flat spacetime in projective coordinates by virtue of the tools provided from complex analysis in several variables and projective geometry.

On the structure and applications of the Bondi–Metzner–Sachs group

On the structure and applications of the Bondi–Metzner–Sachs group

On the structure and applications of the Bondi–Metzner–Sachs group

This work is a pedagogical review dedicated to a modern description of the Bondi–Metzner–Sachs (BMS) group. Minkowski space-time has an interesting and useful group of isometries, but, for a generic space-time, the isometry group is simply the identity and hence provides no significant informations. Yet symmetry groups have important role to play in physics; in particular, the Poincaré group describing the isometries of Minkowski space-time plays a role in the standard definitions of energy-momentum and angular-momentum. For this reason alone it would seem to be important to look for a generalization of the concept of isometry group that can apply in a useful way to suitable curved space-times. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work, the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of “asymptotic simplicity” are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the BMS group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the BMS group, e.g. its algebra and the possibility to obtain as its subgroup the Poincaré group, as we may expect. The paper ends with a review of the BMS invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.

On the representation theory of the Bondi–Metzner–Sachs group and its variants in three space–time dimensions

The original Bondi–Metzner–Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian radiating 4-dim space–times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, McCarthy classified all relativistic B-invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here we introduce the analogue B(2, 1) of the BMS group B in 3 space–time dimensions. B(2, 1) itself admits thirty-four analogues both real in all signatures and in complex space–times. In order to find the IRS of both B(2, 1) and its analogues, we need to extend Wigner–Mackey’s theory of induced representations. The necessary extension is described and is reduced to the solution of three problems. These problems are solved in the case where B(2, 1) and its analogues are equipped with the Hilbert topology. The extended theory is necessary in order to construct the IRS of both B and its analogues in any number d of space–time dimensions, d≥3, and also in order to construct the IRS of their supersymmetric counterparts. We use the extended theory to obtain the necessary data in order to construct the IRS of B(2, 1). The main results of the representation theory are as follows: The IRS are induced from “little groups” which are compact. The finite “little groups” are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.

Representations of the Bondi—Metzner—Sachs group in three space—time dimensions

The original Bondi–Metzner–Sachs group B is the common asymptotic symmetry group of all asymptotically at Lorentzian 4–dim space–times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthy classified all relativistic B–invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here, we construct the IRS of B(2, 1), the analogue of B, in 3 space–time dimensions. The IRS are induced from ‘little groups’ which are compact. The finite ‘little groups’ are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.

Identification and Characterization of Intercritical Heat-Affected Zone in As-Welded Grade 91 Weldment

A metallurgical method is proposed for locating the intercritical heat-affected zone in the as-welded Grade 91 steel. New austenitic grains, preferentially formed along the original prior austenite grain boundaries, are characterized to contain finer M23C6 carbides and higher strain levels than the original prior austenite grains. Kurdjumov–Sachs Group 1 variant pairs, with a low misorientation of 7 deg within a martensitic block, are identified as the dominant variants in the new PAGs.

Conformal Carroll groups and BMS symmetry

The Bondi–Metzner–Sachs group is shown to be the conformal extension of Lévy-Leblond’s ‘Carroll’ group. Further extension to the Newman–Unti group is also discussed in the Carroll framework.

The Bondi–Sachs 4-momentum in non-axisymmetric Robinson–Trautman spacetimes

We derive the Bondi–Sachs 4-momentum conservation laws that regulate the emission of gravitational waves in non-axisymmetric Robinson–Trautman spacetimes. Although Robinson–Trautman spacetimes describe the exterior vacuum gravitational field of a bounded system radiating gravitational waves, the Robinson–Trautman metrics do not satisfy the appropriate Bondi–Sachs boundary conditions formulated for radiating systems. We therefore derive the transformations between Robinson–Trautman and Bondi–Sachs coordinates which allow us to obtain some of the basic Bondi–Sachs physical quantities, namely the news functions and the Bondi–Sachs energy–momentum fluxes of the gravitational waves. These quantities are fundamental to the description of the radiative transfer processes involved in the generation and emission of gravitational waves by the system. The Bondi–Sachs 4-momentum conservation laws are covariant under the transformations of the Bondi–Metzner–Sachs group. The section of this paper containing the derivation of the coordinate transformations extends the work of von der Gönna and Kramer done for the case of axisymmetric Robinson–Trautman spacetimes. We discuss some possible applications of the conservation laws in numerical simulations of black hole systems emitting gravitational waves, and also future research of Bondi–Sachs conservation laws for twisting Robinson–Trautman-type spacetimes.

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II: The search of the interface between QFT and QG

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper.

Tolerance Versus Immunosuppression: A Perspective

To the Editor: It was with general agreement that we read your editorial and cautionary credo ‘do not try this at home’ (1Halloran PF Bromberg J Kaplan B et al.Tolerance versus immunosuppression: A perspective.Am J Transplant. 2008; 8: 1365-1366Abstract Full Text Full Text PDF PubMed Scopus (20) Google Scholar). Tolerance-inducing protocols as routine are ‘not yet ready for prime time’ before more mechanisms are clarified. To attempt to reproduce the landmark neonatal mice tolerance work in 1953 of Billingham, Brent and Medawar in a human with a mature immune system, it seems obvious that an initial immunoablative state that entails some risk must be introduced. Where we disagree with you is in your statement referring to the work of Hofmann et al. ‘that such mice (chimeric from your previous sentence) accept third party heart transplants, that is, are immunosuppressed’. Admittedly, there may be an early spread of a nonspecific regulatory cell effect even in neonatal chimeric tolerance. Indeed, a regulatory effect of recipient suppressor cells was even described by Brent himself in adult mice years after their initial observations (2Kilshaw PJ Brent L Pinto M Suppressor cells in mice made unresponsive to skin allografts.Nature. 1975; 255: 489-491Crossref PubMed Scopus (111) Google Scholar). Certainly regulatory cells by their very nature are (nonspecifically) infectious (bystander inducing) in their local surroundings. However, even the more extensive earlier work by West and Tau of that same group (3West LJ Tao K. Acceptance of thirdparty cardiac but not skin allografts induced by neonatal exposure to semi-allogeneic lymphohematopoietic cells.Am J Transplant. 2002; 2: 733-744Crossref PubMed Scopus (16) Google Scholar) should not be interpreted as being associated with longlasting or even shortterm chimerism. Moreover, even in their skin graft survival data, 30% of the specific (BALB/c) donor (of the bone marrows and spleens) skin grafts were lost in the first 2 weeks and no longterm data after 60 days were reported (3West LJ Tao K. Acceptance of thirdparty cardiac but not skin allografts induced by neonatal exposure to semi-allogeneic lymphohematopoietic cells.Am J Transplant. 2002; 2: 733-744Crossref PubMed Scopus (16) Google Scholar). This may well mean that chimerism was not established, just as it could not be in many of the initial experiments by Medawar’s group between several fully MHC mismatched strains, that is, it did not work in many combinations. The Hofmann animals indeed may well not have been long-term chimeras, that is, keeping their grafts due to tolerance induced by (total) clonal deletion, but more by some active regulatory mechanism. This might have been associated with an element of ‘linked’ or infectious inhibition to nonspecific antigenic stimuli of third party heart grafts due to the ‘proximity’ of (bystanding) regulatory cells, perhaps what you referred to as ‘immunosuppressed’. In addition, there might have been the not inconsiderable positive effect of the evolution toward graft quiescence (absence of inflammation/danger) in the longer term accepted skin grafts (4Matzinger P Tolerance, danger, and the extended family.Annu Rev Immunol. 1994; 12: 991-1045Crossref PubMed Scopus (4013) Google Scholar). Were true long-term mixed chimerism established, implying bi-directional tolerance of these cells residing in the recipient, perhaps one might expect more donor specificity long term (Medawar chimerism model). As such, the earlier nonspecific ‘immunosuppression’ brought on by regulatory cell bystander effects might be minimized long term. This may even have occurred in our previous clinical reports of longer term results of simultaneous donor bone marrow and kidney transplantation in which an early immunosuppressed state appears to have resolved 1 or 2 years after transplantation (5Ciancio G Miller J Garcia-Morales RO et al.Six-year clinical effect of donor bone marrow infusions in renal transplant patients.Transplantation. 2001; 71: 827-835Crossref PubMed Scopus (120) Google Scholar). However, it may or may not have occurred in the groundbreaking tolerance work of the Cosimi, Sykes and Sachs group to which you addressed your editorial and to which they responded in the next (August) issue of the Journal.

On extracting physical content from asymptotically flat spacetime metrics

A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g. degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates), or from solutions that have symmetries or approximate symmetries. In the present work, we will be concerned with asymptotically flat spacetimes where the approximate symmetry is the Bondi–Metzner–Sachs group. For these spaces the Bondi 4-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy–momentum of the interior source and the energy–momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat spacetimes, we give kinematic meaning to the Bondi 4-momentum. In other words, we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux.

Structural consequences of amino acid substitutions causing Tay–Sachs disease

To determine the structural changes in the α-subunit of β-hexosaminidase due to amino acid substitutions causing Tay–Sachs disease, we built structural models of mutant α-subunits resulting from 33 missense mutations (24 infantile and 9 late-onset), and analyzed the influence of each amino acid replacement on the structure by calculating the number of atoms affected and determining the solvent-accessible surface area of the corresponding amino acid residue in the wild-type α-subunit. In the infantile Tay–Sachs group, the number of atoms influenced by a mutation was generally larger than that in the late-onset Tay–Sachs group in both the main chain and the side chain, and residues associated with the mutations found in the infantile Tay–Sachs group tended to be less solvent-accessible than those in the late-onset Tay–Sachs group. Furthermore, color imaging determined the distribution and degree of the structural changes caused by representative amino acid substitutions, and that there were also differences between the infantile and late-onset Tay–Sachs disease groups. Structural study is useful for elucidating the basis of Tay–Sachs disease.

Two Points of Anecdotal Evidence Do Not Make a Trend

In his article Care: The Next Generation, Michael Sachs has used some evidence from a few marketplaces to create a trend. This trend, however, is not supported by hard evidence but rather by anecdotal evidence. The Sachs Group does great research, and I use that research all the time, but this time Sachs' trying to be a futurist misses its mark. The reason is fairly simple. With penetration below 30 percent, we as yet do not have managed care in this country. When we speak of managed care, however, we have never defined it. Some will claim you are receiving managed care if you are in an HMO or PPOdepending on who is doing the research. Yet, as one travels from west to east, it becomes readily apparent that what is called managed care by some managed care companies is in essence volume discounting. They use little if any managed care techniques to effect care. In short, they are indemnity insurance companies in disguise. Sachs' two models, the Economic and Care Delivery Models, are in my mind the initial stages of managed financing. Having been an executive both of major teaching hospitals and an HMO, and having consulted as well as having been a trustee of an academic medical center, I do not believe that our hospital industry's attempting to position itself as integrated delivery systems will present a viable answer to creating managed care for a population. This is like relying on the fox to guard the chicken coop. Hospitals and their subsidiaries have always tried, and will always continue to try, to maximize their revenues. They even started their own insurance product now known as Blue Cross to make sure they got paid when the pure fee-for-service system did not support those who walked through their door. Today, after having been for more than 15 years on the fixed payment system known as diagnosis-related groups, few hospitals and their physicians (both owned and privileged) know the actual cost of treatment, much less how to price on the margin. Try to find an epidemiologist within an integrated delivery systemor even an actuary or underwriter! Have not the past fiascoes-such as creating holding companies that own hospital companies, forming integrated delivery systems that do not integrate, creating physician hospital organizations that cannot agree, and buying physician practices that have been able to erode the bottom line-taught us that the brick and mortar of the healthcare industry is not where our employers and government wish to bet their future? Managed care today is hastily built on the smoking ruins of the fee-for-service industry. I have not stumbled across so much as one expose or scorecard report that truthfully characterizes the fee-for-service system as an insatiable user of resources that, for too long, has greedily ingested more of our gross domestic product than has any other healthcare system in any other civilized nation. Nor do we often enough hear how a feefor-service reimbursement scheme has created a healthcare system that, through ever-increasing premiums, has caused an oversupply of medically trained personnel. Choice at any cost! was the battle cry of the professionals who were only too happy to receive the fees. Unfortunately for these professionals, who today are grabbing the short end of the managed care stick, the benefits of choice were not passed along to the employers and governments who were footing the bill. …

Borel multipliers for the Bondi–Metzner–Sachs group

It is shown that there exist only two cohomology classes of Borel multipliers for the Bondi–Metzner–Sachs group B when the subgroup of ’’supertranslations’’ is the additive group of a separable real Hilbert space. This implies that all Borel multipliers for the universal covering group ? of B are coboundaries and so every continuous unitary projective representation of B can be obtained from a continuous unitary (ordinary) representation of ?.

Lifting of projective representations of the Bondi—Metzner—Sachs group

Following some motivating remarks on the role of group theory in physics, it is explained how a systematic study of the asymptotic symmetry group of general relativity, the Bondi-Metzner-Sachs group, can give some very general insights into the nature of the energy, momentum and angular momentum structure of curved (asymptotically flat) space-times, as well as of quantum theory in these space-times. In particular, a classical ‘ Bondi angular momentum ’ vector is defined for any 5-in variant classical system. However, the representations which arise in any fundamental study of this (or any other) quantum theory are projective rather than linear. This paper is devoted to the problem of showing th at each continuous projective representation arises from (that is, can be ‘lifted’ to) a continuous linear (in fact, unitary) representation of the universal covering group. An almost complete proof of this is given for the two very different cases in which the group is given a Hilbert or nuclear topology. This reduces the study of the group in quantum theory to an ordinary unitary representation problem which has already been studied, and implies, for example, that nothing more general than ‘two-valued representations’ need be considered. Some remarks are made on the physical interpretation of the known irreducibles, and on outstanding problems of this representation theory.

The Bondi—Metzner—Sachs group in the nuclear topology

The Bondi-Metzner-Sachs group is topologized as a nuclear Lie group, and it is shown th at irreducible representations arise from either (i) transitive SL{2,C) actions on supermomentum space, or (ii) cylinder measures in supermomentum space with respect to which the SL(2,C) action is strictly ergodic. The irreducibles arising from transitive actions are shown to be induced, and most of the theorems from a previous analysis (in which the group was given a Hilbert topology) are generalized so as to apply here. All non-discrete closed subgroups of 2, C) are found, and this analysis is used to construct all induced representations whose little groups are not both discrete and infinite. In the previous analysis, there were exactly two connected little groups, SU{2) and r (T double covers $0(2)). In the present analysis, exactly one additional connected little group A (which double covers E{2)) arises for faithful representations (that is, those for which the mass squared is defined); the associated mass squared value is zero. Exactly one further connected little group arises;

Representations of the Bondi—Metzner—Sachs group I. Determination of the representations

Following a historical introduction, it is suggested that irreducible unitary representations of the Bondi-Metzner-Sachs group may be used to classify elementary particles in a quantum theory which takes ‘asymptotically flat5 gravitational fields into account. The unitary representations of the group induced from irreducible unitary representations of the connected little groups are all determined. It is shown that the connected little groups are all compact, so that the ‘spins’ of the corresponding particles are necessarily discrete, and the wave functions have a finite number of components. Furthermore, the spins are of precisely the observed type. This is in striking contrast to the situation for the Poincare group, for which the spins may be discrete or continuous. (The continuous spin wave functions are infinite-component.) It is concluded that the B.M.S. group may provide an explanation for the observed discreteness of the spins of elementary particles.

Breaking the Green Washing Wave: The Need for ESG-Friendly Securities Fraud Class Action Standards Post-Goldman Sachs Group, Inc. v. Arkansas Teacher Retirement System

Breaking the Green Washing Wave: The Need for ESG-Friendly Securities Fraud Class Action Standards Post-Goldman Sachs Group, Inc. v. Arkansas Teacher Retirement System