Perturbative Construction of Models of Algebraic Quantum Field Theory

We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.Comment: 38 page

A note on the peeling theorem in higher dimensions

We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of the Weyl tensor, and the asymptotic structure at null infinity, in higher dimensions.Comment: 5 pages, to appear in Class. Quantum Gra

Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime

We prove that the singularity structure of all n-point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to the real free scalar field and the result has applications in perturbative quantum field theory, showing that the class of all Hadamard states is the state space of interest. In our proof we assume that the field is a generalised free field, i.e. that it satisies scalar (c-number) commutation relations, but it need not satisfy an equation of motion. The same argument also works for anti-commutation relations and it can be generalised to vector-valued fields. To indicate the strengths and limitations of our assumption we also prove the analogues of a theorem by Borchers and Zimmermann on the self-adjointness of field operators and of a very weak form of the Jost-Schroer theorem. The original proofs of these results in the Wightman framework make use of analytic continuation arguments. In our case no analyticity is assumed, but to some extent the scalar commutation relations can take its place.Comment: 18 page

Supersymmetric Field-Theoretic Models on a Supermanifold

We propose the extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general spacetime manifold so as to include superfield models on a supermanifold. We only deal with the limited class of supermanifolds which admit the existence of a smooth body manifold structure. Our considerations are based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In particular, we show that the class of supermanifolds constructed by Bonora-Pasti-Tonin satisfies the criterions which guarantee that a supermanifold admits a Hausdorff body manifold. This construction is the closest to the physicist's intuitive view of superspace as a manifold with some anticommuting coordinates, where the odd sector is topologically trivial. The paper also contains a new construction of superdistributions and useful results on the wavefront set of such objects. Moreover, a generalization of the spectral condition is formulated using the notion of the wavefront set of superdistributions, which is equivalent to the requirement that all of the component fields satisfy, on the body manifold, a microlocal spectral condition proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy

Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory

On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum field theory. The crucial technical ingredient is a proof that the renormalized time-ordered product is equivalent to the pointwise product of classical field theory. The renormalized Batalin-Vilkovisky algebra is then the classical algebra but written in terms of the time-ordered product, together with an operator which replaces the ill defined graded Laplacian of the unrenormalized theory. We identify it with the anomaly term of the anomalous Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps.Comment: 34 page

A systematic review of approaches to modelling lower limb muscle forces during gait : applicability to clinical gait analyses

Computational methods to estimate muscle forces during walking are becoming more common in biomechanical research but not yet in clinical gait analysis. This systematic review aims to identify the current state-of-the-art, examine the differences between approaches, and consider applicability of the current approaches in clinical gait analysis. A systematic database search identified studies including estimated muscle force profiles of the lower limb during healthy walking. These were rated for quality and the muscle force profiles digitised for comparison. From 13.449 identified studies, 22 were finally included which used four modelling approaches: static optimisation, enhanced static optimisation, forward dynamics and EMG-driven. These used a range of different musculoskeletal models, muscle-tendon characteristics and cost functions. There is visually broad agreement between and within approaches about when muscles are active throughout the gait cycle. There remain considerable differences (CV 7% to 151%, range of timing of peak forces in gait cycle 1% to 31%) in patterns and magnitudes of force between and within modelling approaches. The main source of this variability is not clear. Different musculoskeletal models, experimental protocols, and modelling approaches will clearly have an effect as will the variability of joint kinetics between healthy individuals. Limited validation of modelling approaches, particularly at the level of individual participants, makes it difficult to conclude if any of the approaches give consistently better estimates than others. While muscle force modelling has clear potential to enhance clinical gait analyses future research is needed to improve validation, accuracy and feasibility of implementation in clinical practice

Protecting the conformal symmetry via bulk renormalization on Anti deSitter space

The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi^2 with bulk interaction Phi^4.Comment: 40 page

Immediate Effect of Voluntary-induced Stepping Response Training on Protective Stepping in Persons with Chronic Stroke: A Randomized Controlled Trial

Purpose: To compare the immediate effects of voluntary-induced stepping response training (VSR) and DynSTABLE perturbation training (DST) on protective stepping in patients with stroke. Methods: A randomized controlled trial (registration number: TCTR20170827001) was conducted in 34 patients with chronic stroke who were randomly allocated to the VSR (n = 17) or DST (n = 17) group. The VSR group was instructed to lean forward to induce protective stepping, while the DST group experienced support surface translation. All participants received one session of training (3 set, 10 min for each set with 10-minute rest in between). Step length, step width, number of steps and center of mass (CoM) position during protective stepping were assessed using a computer-assisted rehabilitation environment (CAREN) system prior to and immediately after training. Two-way ANOVA was used to compare between groups and times. Results: Both types of training resulted in an increase in step width, but step length increased and there was a more positive COM position exhibited following DST (p < .05) than following VSR. Single-step incidence increased, whereas multiple-step incidence decreased significantly in both groups. Only participants in the VSR group generated protective stepping with the affected leg in a larger percentage of trials (27%) after training than before training. Conclusion: Both DST and VSR led to changes in protective stepping parameters after a single session of training. VSR may be a feasible alternative to equipment-based training but requires further study. • Implication for Rehabilitation • VSR and DST trainings improved protective stepping in stroke. • Step length and CoM control at foot touchdown increased after DST training. • VSR training for 50 minutes led to increase affected stepping and reduce grasping. • Step width, affected step length, and single step increased after both trainings. • Without instrument, VSR increased steps execution and performance similar to DST