IR/UV mixing from local similarity maps of scalar non-Hermitian field theories

We propose to "gauge" the group of similarity transformations that acts on a space of non-Hermitian scalar theories. We introduce the "similarity gauge field", which acts as a gauge connection on the space of non-Hermitian theories characterized by (and equivalent to a Hermitian) real-valued mass spectrum. This extension leads to new effects: if the mass matrix is not the same in distant regions of space, but its eigenvalues coincide pairwise in both regions, the particle masses stay constant in the whole spacetime, making the model indistinguishable from a standard, low-energy and scalar Hermitian one. However, contrary to the Hermitian case, the high-energy scalar particles become unstable at a particular wavelength determined by the strength of the emergent similarity gauge field. This instability corresponds to momentum-dependent exceptional points, whose locations cannot be identified from an analysis of the eigenvalues of the coordinate-dependent squared mass matrix in isolation, as one might naively have expected. For a doublet of scalar particles with masses of the order of 1 MeV and a similarity gauge rotation of order unity at distances of 1 meter, the corrections to the masses are about 10^{-7}eV, which makes no experimentally detectable imprint on the low-energy spectrum. However, the instability occurs at 10^{18} eV, suggestively in the energy range of detectable ultra-high-energy cosmic rays, thereby making this truly non-Hermitian effect and its generalizations of phenomenological interest for high-energy particle physics.Comment: 14 pages, 4 figures; v2 matches the published versio

Anomalous dispersion, superluminality, and instabilities in two-flavor theories with local non-Hermitian mass mixing

Pseudo-Hermitian field theories possess a global continuous “similarity” symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavor scalar or fermion mixing and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities, and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterized by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties.<br/

Anomalous dispersion, superluminality and instabilities in two-flavour theories with local non-Hermitian mass mixing

Pseudo-Hermitian field theories possess a global continuous ``similarity'' symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavour scalar or fermion mixing, and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterised by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties

Consistent description of field theories with non-Hermitian mass terms

We review how to describe a field theory that includes a non-Hermitian mass term in the region of parameter space where the Lagrangian is PT-symmetric. The discrete symmetries of the system are essential for understanding the consistency of the model, and the link between conserved current and variation of the Lagrangian has to be revisited in the case of continuous symmetries

Self-consistent solitons for vacuum decay in radiatively generated potentials

We use a Green’s function approach in order to develop a method for calculating the tunneling rate between radiatively generated nondegenerate vacua. We apply this to a model that exhibits spontaneous symmetry breaking via the Coleman-Weinberg mechanism, where we determine the self-consistent tunneling configuration and illustrate the impact of gradient effects that arise from accounting for the underlying space-time inhomogeneity

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given

High Street 2020: An Analysis for Morecambe

Overall, footfall in UK town centres is falling and Morecambe’s footfall is falling at nearly twice the average rate1. This indicates that the town centre is ‘at risk’ – and that it is likely to be less resilient to shocks such as increased edge-of-town competition. Morecambe’s footfall profile most closely matches that of a ‘holiday town’ meaning that leisure and distinctive retail need to be an important part of the overall offer. Nevertheless, the identity of Morecambe is confused – there seems to be little overall vision and leadership to enable the town to adapt to change in a proactive, positive way to create a more positive and differentiated identity. In our opinion, based on the High Street 2020 research we have undertaken, the proposed Bay Shopping Park will have a negative impact on the existing centre as it is too far away to generate linked trips – and there are no plans to integrate it in a way that could complement the existing offer. Retailers will be attracted to the Bay Park’s larger units, 1 Over a 30 month period ending May 2014 better road access and convenient car-parking – and this will further reduce the comparison offer in the existing town centre. In this respect, the Bay Shopping Park will impact in a similar manner to out-of-town development – which, as our model demonstrates, diverts up to 30% of footfall. As a result of the newly built Morrison’s supermarket and other developments, there is no doubt some of this diversion has already taken place. However, the spiral of decline that will come with more vacant retail units and less footfall after the opening of the Bay Shopping Park will eventually impact upon Morecambe’s ability to sustain its traditional centre. To what extent is the Council willing to sacrifice the traditional centre to the new shopping park development? Our research also demonstrates the proposed development could also be detrimental to overall rateable value. Nevertheless, whilst we predict the Bay Shopping Park would have a detrimental impact, we are aware that the existing centre is also not serving the resident catchment or visitors/tourists effectively. Newspaper reports refer to the Arndale Centre as ‘a disgrace’ and our own High Street UK 2020 project points out the negative impact that out-of-date and out-of-scale in-town development has on vitality and viability. In order to strengthen the existing town centre, all stakeholders have to work together – under a shared vision for the future – and New River Retail must make the necessary investment, to improve the retail offer (both comparison and convenience) through their Arndale Centre. Our research demonstrates the role a channel anchor, such as a shopping centre, can take in coordinating and supporting place change. The town also needs to improve the overall customer experience and create an appropriate and differentiated identity, with the traditional town centre at the heart of these developments

Histopathological evaluation of placentas after diagnosis of maternal SARS-CoV-2 infection.

Background:The impact of maternal SARS-CoV-2 infection on placental histopathology is not well known. Objectives:To determine if significant placental histopathological changes occur after diagnosis of SARS-CoV-2 infection in pregnancy and whether these changes are correlated with the presence or absence of symptoms associated with infection. Study Design:Retrospective cohort study of women diagnosed with SARS-CoV-2 infection who delivered at a single center from April 9th to April 27th, 2020, and had placental specimens reviewed by pathology. Women with singleton gestations and laboratory-confirmed SARS-CoV-2 infection were eligible for inclusion. Historical controls selected from a cohort of women who delivered 6 months prior to the study period were matched in a 1:1 fashion by week of gestation at delivery. Histopathological characteristics were evaluated in each placenta and the incidence of these findings were compared between placentas after diagnosis of maternal SARS-CoV-2 infection and historical controls, as well as between placentas from patients with or without typical symptoms related to infection. Statistical analysis included use of Wilcoxon rank sum test and Fisher\u27s exact test for comparison of categorical and continuous variables. Statistical significance was defined as P value \u3c 0.05. Results:A total of 50 placentas after diagnosis of maternal SARS-CoV-2 infection and 50 historical controls were analyzed. Among placentas from patients diagnosed with SARS-CoV-2 infection, 3 (6%) were preterm (33 3/7, 34 6/7 and 36 6/7 weeks of gestation), 16 (32%) were from patients with typical symptoms related to infection and 34 (68%) were from patients without typical symptoms related to the infection. All patients had diagnosis of SARS-CoV-2 infection in the third trimester. Decidual vasculopathy was not visualized in any of the placentas from patients diagnosed with SARS-CoV-2 infection. There was no statistically significant difference in placental histopathological characteristics between the groups. SARS-CoV-2 testing for all neonates at 24 hours of life was negative. Conclusions:Based on our data, there are no significant placental histopathological changes that occur after diagnosis of SARS-CoV-2 infection in the third trimester of pregnancy compared to a gestational age-matched historical control group. Similar incidences of histopathological findings were also discovered when comparing placentas from patients with SARS-CoV-2 infection with or without the presence of symptoms typically related to infection

Towns and Cities as Multifunctional Centres

Whilst omni-channel retailing and the digital high street may be two of the latest talking points in the retail property industry, our towns and city centres have always been shaped by a series of technological, social and political revolutions. The purpose of this report is to examine how, after many years of mono-functionality focused upon retailing, our centres are experiencing something of a renaissance, and remerging as multi-functional ones, supporting leisure and recreation, employment, tourism, heritage, culture, housing, employment, education, health and wellbeing as well as retail. A multi-functional centre means a diverse offer, and, therefore, traditional economic indicators will not, on their own, act as a sensible yardstick of performance or tool for decision-making. For the multi-functional centre, activity levels are the key performance indicators. How much is the centre used, when and for what? Multi-functional centres draw people in for a much wider ‘bundle of benefits’ than just shopping. This requires all stakeholders to work together much more effectively to deliver a better collective experience in locations, to the commuter who may want to choose and collect at different times of the day, depending on their personal transport options and shift patterns, to the carer who may want to combine exercise and top-up shopping near to reliable respite care. Many of the newfound uses for underused or redundant retail space have resulted from structural changes in the retail sector, as well as from a more tightly gripped public purse. This has opened up the possibility for much more community involvement in the redevelopment and reuse of space. Sometimes this influx of creativity is only temporary, but it still demonstrates what an important asset an engaged community can be to a place, and what a difference it can make to vitality and viability. We think the retail property sector should work harder to integrate more local entrepreneurship and civic practice into both the development of new centres and the management of existing ones. The successful multi-functional centre will have both a multitude of users as well as a multitude of caretakers. Most of all, our report argues that all retail developments (both new and existing) have to integrate more effectively into the overall offer of the multi-functional centre. Decision making and management must become less hierarchical and myopic and more place-based and ‘porous’ to allow more intelligence and input from the location

High Street UK 2020 Interim Project Report: Identifying factors that influence vitality and viability

The purpose of this document is to report the progress of the High Street UK2020 (HSUK2020) project. Started in January 2014, HSUK2020 aims to bring evidence to 10 UK High Streets, to improve local decision making that will improve vitality and viability. The 10 partner locations are Alsager, Altrincham, Ballymena, Barnsley, Bristol (St George), Congleton, Holmfirth, Market Rasen, Morley and Wrexham. The report outlines the background to the project, the methods we have employed, the results we have found and a brief overview of how some of our partner towns are using these findings. By undertaking a systematic review of the literature and, through adopting a more ‘engaged’ model of scholarship, the project has identified 201 factors that influence the performance of the UK High Street. This has enabled us to classify the top 25 priorities for action our partner towns should focus on