A gauge theoretical view of the charge concept in Einstein gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension $\hbar/l^2$, the mass parameter of a particle dimension $\hbar/l$, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi-electric monopole charge of the time translation whereas the NUT parameter is a quasi-magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio

Geodesic Deviation in Regge Calculus

Geodesic deviation is the most basic manifestation of the influence of gravitational fields on matter. We investigate geodesic deviation within the framework of Regge calculus, and compare the results with the continuous formulation of general relativity on two different levels. We show that the continuum and simplicial descriptions coincide when the cumulative effect of the Regge contributions over an infinitesimal element of area is considered. This comparison provides a quantitative relation between the curvature of the continuous description and the deficit angles of Regge calculus. The results presented might also be of help in developing generic ways of including matter terms in the Regge equations.Comment: 9 pages. Latex 2e with 5 EPS figures. Submitted to CQ

Gauge Formalism for General Relativity and Fermionic Matter

A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and spinors. An appropriate gauge structure is also given to General Relativity, replacing the metric field with spin frames. Finally, conserved quantities and superpotentials are calculated under a general covariant form.Comment: 18 pages, Plain TEX, revision, explicit expression for superpotential has been adde

Ataxia with oculomotor apraxia type 2: clinical, biological and genotype/phenotype correlation study of a cohort of 90 patients

Ataxia with oculomotor apraxia type 2 (AOA2) is an autosomal recessive disease due to mutations in the senataxin gene, causing progressive cerebellar ataxia with peripheral neuropathy, cerebellar atrophy, occasional oculomotor apraxia and elevated alpha-feto-protein (AFP) serum level. We compiled a series of 67 previously reported and 58 novel ataxic patients who underwent senataxin gene sequencing because of suspected AOA2. An AOA2 diagnosis was established for 90 patients, originating from 15 countries worldwide, and 25 new senataxin gene mutations were found. In patients with AOA2, median AFP serum level was 31.0 mu g/l at diagnosis, which was higher than the median AFP level of AOA2 negative patients: 13.8 mu g/l, P = 0.0004; itself higher than the normal level (3.4 mu g/l, range from 0.5 to 17.2 mu g/l) because elevated AFP was one of the possible selection criteria. Polyneuropathy was found in 97.5% of AOA2 patients, cerebellar atrophy in 96%, occasional oculomotor apraxia in 51%, pyramidal signs in 20.5%, head tremor in 14%, dystonia in 13.5%, strabismus in 12.3% and chorea in 9.5%. No patient was lacking both peripheral neuropathy and cerebellar atrophy. The age at onset and presence of occasional oculomotor apraxia were negatively correlated to the progression rate of the disease (P = 0.03 and P = 0.009, respectively), whereas strabismus was positively correlated to the progression rate (P = 0.03). An increased AFP level as well as cerebellar atrophy seem to be stable in the course of the disease and to occur mostly at or before the onset of the disease. One of the two patients with a normal AFP level at diagnosis had high AFP levels 4 years later, while the other had borderline levels. The probability of missing AOA2 diagnosis, in case of sequencing senataxin gene only in non-Friedreich ataxia non-ataxia-telangiectasia ataxic patients with AFP level >= 7 mu g/l, is 0.23% and the probability for a non-Friedreich ataxia non-ataxia-telangiectasia ataxic patient to be affected with AOA2 with AFP levels >= 7 mu g/l is 46%. Therefore, selection of patients with an AFP level above 7 mu g/l for senataxin gene sequencing is a good strategy for AOA2 diagnosis. Pyramidal signs and dystonia were more frequent and disease was less severe with missense mutations in the helicase domain of senataxin gene than with missense mutations out of helicase domain and deletion and nonsense mutations (P = 0.001, P = 0.008 and P = 0.01, respectively). The lack of pyramidal signs in most patients may be explained by masking due to severe motor neuropathy

Particle Physics from Almost Commutative Spacetimes

Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the ideas and concepts from noncommutative geometry using physicists' terminology, gearing towards the predictions that can be derived from the noncommutative description. Focusing on a light package of noncommutative geometry (so-called 'almost commutative manifolds'), we shall introduce in steps: electrodynamics, the electroweak model, culminating in the full Standard Model. We hope that our approach helps in understanding the role noncommutative geometry could play in describing particle physics models, eventually unifying them with Einstein's (geometrical) theory of gravity.Comment: 104 pages, 5 figures, version 2 (minor changes and some additional references

Efficacy and safety of rozanolixizumab in moderate to severe generalized myasthenia gravis : a phase 2 randomized control trial

OBJECTIVE: To explore the clinical efficacy and safety of subcutaneous (SC) rozanolixizumab, an anti-neonatal Fc receptor humanized monoclonal antibody, in patients with generalized myasthenia gravis (gMG). METHODS: In this phase 2a, randomized, double-blind, placebo-controlled, 2-period, multicenter trial (NCT03052751), patients were randomized (1:1) in period 1 (days 1-29) to 3 once-weekly (Q1W) SC infusions of rozanolixizumab 7 mg/kg or placebo. In period 2 (days 29-43), patients were re-randomized to either rozanolixizumab 7 mg/kg or 4 mg/kg (3 Q1W SC infusions), followed by an observation period (days 44-99). Primary endpoint was change from baseline to day 29 in Quantitative Myasthenia Gravis (QMG) score. Secondary endpoints were change from baseline to day 29 in MG-Activities of Daily Living (MG-ADL) and MG-Composite (MGC) scores and safety. RESULTS: Forty-three patients were randomized (rozanolixizumab 21, placebo 22 [period 1]). Least squares (LS) mean change from baseline to day 29 for rozanolixizumab vs placebo was as follows: QMG (LS mean -1.8 vs -1.2, difference -0.7, 95% upper confidence limit [UCL] 0.8; p = 0.221; not statistically significant), MG-ADL (LS mean -1.8 vs -0.4, difference -1.4, 95% UCL -0.4), and MGC (LS mean -3.1 vs -1.2, difference -1.8, 95% UCL 0.4) scores. Efficacy measures continued to improve with rozanolixizumab 7 mg/kg in period 2. The most common adverse event in period 1 was headache (rozanolixizumab 57%, placebo 14%). CONCLUSION: Whereas change from baseline in QMG was not statistically significant, the data overall suggest rozanolixizumab may provide clinical benefit in patients with gMG and was generally well tolerated. Phase 3 evaluation is ongoing (NCT03971422). CLASSIFICATION OF EVIDENCE: This study provides Class I evidence that for patients with gMG, rozanolixizumab is well-tolerated, but did not significantly improve QMG score

Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge

We define the {\it rest-frame instant form} of tetrad gravity restricted to Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of gauge transformations generated by the 14 first class constraints of the theory, we define and solve the multitemporal equations associated with the rotation and space diffeomorphism constraints, finding how the cotriads and their momenta depend on the corresponding gauge variables. This allows to find quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal gauges and to find the Dirac observables for superspace in these gauges. The construction of the explicit form of the transformation and of the solution of the rotation and supermomentum constraints is reduced to solve a system of elliptic linear and quasi-linear partial differential equations. We then show that the superhamiltonian constraint becomes the Lichnerowicz equation for the conformal factor of the 3-metric and that the last gauge variable is the momentum conjugated to the conformal factor. The gauge transformations generated by the superhamiltonian constraint perform the transitions among the allowed foliations of spacetime, so that the theory is independent from its 3+1 splittings. In the special 3-orthogonal gauge defined by the vanishing of the conformal factor momentum we determine the final Dirac observables for the gravitational field even if we are not able to solve the Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted to this completely fixed gauge.Comment: RevTeX file, 141 page

New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split

I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. [This is also known as variation with natural boundary conditions.] Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose corresponding velocities are, respectively, the abovementioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations, which shall be provided in a second paper.Comment: 11 page

High-throughput imaging of ATG9A distribution as a diagnostic functional assay for adaptor protein complex 4-associated hereditary spastic paraplegia

Adaptor protein complex 4-associated hereditary spastic paraplegia is caused by biallelic loss-of-function variants in AP4B1, AP4M1, AP4E1 or AP4S1, which constitute the four subunits of this obligate complex. While the diagnosis of adaptor protein complex 4-associated hereditary spastic paraplegia relies on molecular testing, the interpretation of novel missense variants remains challenging. Here, we address this diagnostic gap by using patient-derived fibroblasts to establish a functional assay that measures the subcellular localization of ATG9A, a transmembrane protein that is sorted by adaptor protein complex 4. Using automated high-throughput microscopy, we determine the ratio of the ATG9A fluorescence in the trans-Golgi-network versus cytoplasm and ascertain that this metric meets standards for screening assays (Z'-factor robust >0.3, strictly standardized mean difference >3). The `ATG9A ratio' is increased in fibroblasts of 18 well-characterized adaptor protein complex 4-associated hereditary spastic paraplegia patients [mean: 1.54 +/- 0.13 versus 1.21 +/- 0.05 (standard deviation) in controls] and receiver-operating characteristic analysis demonstrates robust diagnostic power (area under the curve: 0.85, 95% confidence interval: 0.849-0.852). Using fibroblasts from two individuals with atypical clinical features and novel biallelic missense variants of unknown significance in AP4B1, we show that our assay can reliably detect adaptor protein complex 4 function. Our findings establish the 'ATG9A ratio' as a diagnostic marker of adaptor protein complex 4-associated hereditary spastic paraplegia