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Recent work on the Bondi-Metzner-Sachs group introduced a class of functions sYlm(θ, φ) defined on the sphere and a related differential operator ð. In this paper the sYlm are related to the representation matrices of the rotation group R3 and the properties of ð are derived from its relationship to an angular-momentum raising operator. The relationship of the sTlm(θ, φ) to the spherical harmonics of R4 is also indicated. Finally using the relationship of the Lorentz group to the conformal group of the sphere, the behavior of the sTlm under this latter group is shown to realize a representation of the Lorentz group.

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.Comment: Latex file. 34 pages. (Trivial) misprints corrected. To appear in Nucl. Phys.

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Summary Intravenous lidocaine is used widely for its effect on postoperative pain and recovery but it can be, and has been, fatal when used inappropriately and incorrectly. The risk‐benefit ratio of i.v. lidocaine varies with type of surgery and with patient factors such as comorbidity (including pre‐existing chronic pain). This consensus statement aims to address three questions. First, does i.v. lidocaine effectively reduce postoperative pain and facilitate recovery? Second, is i.v. lidocaine safe? Third, does the fact that i.v. lidocaine is not licensed for this indication affect its use? We suggest that i.v. lidocaine should be regarded as a ‘high‐risk’ medicine. Individual anaesthetists may feel that, in selected patients, i.v. lidocaine may be beneficial as part of a multimodal peri‐operative pain management strategy. This approach should be approved by hospital medication governance systems, and the individual clinical decision should be made with properly informed consent from the patient concerned. If i.v. lidocaine is used, we recommend an initial dose of no more than 1.5 mg.kg‐1, calculated using the patient’s ideal body weight and given as an infusion over 10 min. Thereafter, an infusion of no more than 1.5 mg.kg‐1.h‐1 for no longer than 24 h is recommended, subject to review and re‐assessment. Intravenous lidocaine should not be used at the same time as, or within the period of action of, other local anaesthetic interventions. This includes not starting i.v. lidocaine within 4 h after any nerve block, and not performing any nerve block until 4 h after discontinuing an i.v. lidocaine infusion.

Total hip arthroplasty (THA) is amenable to a variety of regional anaesthesia (RA) techniques that may improve patient outcome. We sought to answer whether RA decreased mortality, cardiovascular morbidity, deep venous thrombosis (DVT) and pulmonary embolism (PE), blood loss, duration of surgery, pain, opioid-related adverse effects, cognitive defects, and length of stay. We also questioned whether RA improved rehabilitation. To do so, we performed a systematic review of the contemporary literature to compare general anaesthesia (GA) and RA and also systemic and regional analgesia for THA. To reflect contemporary surgical and anaesthetic practice, only randomized controlled trials (RCTs) from 1990 onward were included. We identified 18 studies involving 1239 patients. Only two of the 18 trials were of Level I quality. There is insufficient evidence from RCTs alone to conclude if anaesthetic technique influenced mortality, cardiovascular morbidity, or the incidence of DVT and PE when using thromboprophylaxis. Blood loss may be reduced in patients receiving RA rather than GA for THA. Our review suggests that there is no difference in duration of surgery in patients who receive GA or RA. Compared with systemic analgesia, regional analgesia can reduce postoperative pain, morphine consumption, and nausea and vomiting. Length of stay is not reduced and rehabilitation does not appear to be facilitated by RA or analgesia for THA.

BackgroundThere is heterogeneity in the names and anatomical descriptions of regional anesthetic techniques. This may have adverse consequences on education, research, and implementation into clinical practice. We aimed to produce standardized nomenclature for abdominal wall, paraspinal, and chest wall regional anesthetic techniques.MethodsWe conducted an international consensus study involving experts using a three-round Delphi method to produce a list of names and corresponding descriptions of anatomical targets. After long-list formulation by a Steering Committee, the first and second rounds involved anonymous electronic voting and commenting, with the third round involving a virtual round table discussion aiming to achieve consensus on items that had yet to achieve it. Novel names were presented where required for anatomical clarity and harmonization. Strong consensus was defined as ≥75% agreement and weak consensus as 50% to 74% agreement.ResultsSixty expert Collaborators participated in this study. After three rounds and clarification, harmonization, and introduction of novel nomenclature, strong consensus was achieved for the names of 16 block names and weak consensus for four names. For anatomical descriptions, strong consensus was achieved for 19 blocks and weak consensus was achieved for one approach. Several areas requiring further research were identified.ConclusionsHarmonization and standardization of nomenclature may improve education, research, and ultimately patient care. We present the first international consensus on nomenclature and anatomical descriptions of blocks of the abdominal wall, chest wall, and paraspinal blocks. We recommend using the consensus results in academic and clinical practice.

Total knee arthroplasty (TKA) is amenable to various regional anesthesia techniques that may improve patient outcome. We sought to answer whether regional anesthesia decreased mortality, cardiovascular morbidity, deep venous thrombosis and pulmonary embolism, blood loss, duration of surgery, pain, opioid-related adverse effects, cognitive defects, and length of stay. We also questioned whether regional anesthesia improved rehabilitation. To do so, we performed a systematic review of the contemporary literature comparing general anesthesia and/or systemic analgesia with regional anesthesia and/or regional analgesia for TKA. To reflect contemporary surgical and anesthetic practice, only randomized, controlled trials from 1990 onward were included. We identified 28 studies involving 1538 patients. There was insufficient evidence from randomized, controlled trials alone to conclude if anesthetic technique influenced mortality, cardiovascular morbidity other than postoperative hypotension, or the incidence of deep venous thrombosis and pulmonary embolism when using thromboprophylaxis. Our review suggests there was no difference in perioperative blood loss or duration of surgery in patients who received general anesthesia versus regional anesthesia. Compared with general anesthesia and/or systemic analgesia, regional anesthesia and/or analgesia reduced postoperative pain, morphine consumption, and opioid-related adverse effects. Length of stay may be reduced and rehabilitation facilitated for patients undergoing regional anesthesia and analgesia for TKA.