Spin jj Dirac Operators on the Fuzzy 2-Sphere

The spin 1/2 Dirac operator and its chirality operator on the fuzzy 2-sphere $S^2_F$ can be constructed using the Ginsparg-Wilson(GW) algebra [arxiv:hep-th/0511114]. This construction actually exists for any spin $j$ on $S^2_F$, and have continuum analogues as well on the commutative sphere $S^2$ or on $\mathbb{R}^{2}$. This is a remarkable fact and has no known analogue in higher dimensional Minkowski spaces. We study such operators on $S^2_F$ and the commutative $S^2$ and formulate criteria for the existence of the limit from the former to the latter. This singles out certain fuzzy versions of these operators as the preferred Dirac operators. We then study the spin 1 Dirac operator of this preferred type and its chirality on the fuzzy 2-sphere and formulate its instanton sectors and their index theory. The method to generalize this analysis to any spin $j$ is also studied in detail.Comment: 16 pages, 1 tabl

Quantum Geons and Noncommutative Spacetimes

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group $S_N$. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the commutative spacetime algebras of geons as well to noncommutative algebras. The latter support twisted actions of diffeos of geon spacetimes and associated twisted statistics. The notion of covariant fields for geons is formulated and their twisted versions are constructed from their untwisted versions. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli principle, seem to be the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out.Comment: 41 page

Skyrmions, Spectral Flow and Parity Doubles

It is well-known that the winding number of the Skyrmion can be identified as the baryon number. We show in this paper that this result can also be established using the Atiyah-Singer index theorem and spectral flow arguments. We argue that this proof suggests that there are light quarks moving in the field of the Skyrmion. We then show that if these light degrees of freedom are averaged out, the low energy excitations of the Skyrmion are in fact spinorial. A natural consequence of our approach is the prediction of a $(1/2)^{-}$ state and its excitations in addition to the nucleon and delta. Using the recent numerical evidence for the existence of Skyrmions with discrete spatial symmetries, we further suggest that the the low energy spectrum of many light nuclei may possess a parity doublet structure arising from a subtle topological interaction between the slow Skyrmion and the fast quarks. We also present tentative experimental evidence supporting our arguments.Comment: 22 pages, LaTex. Uses amstex, amssym

Distributed Consensus to Enable Merging and Spacing of UAS in an Urban Environment

This paper presents a novel approach to enable multiple Unmanned Aerial Systems approaching a common intersection to independently schedule their arrival time while maintaining a safe separation. Aircraft merging at a common intersection are grouped into a network and each aircraft broadcasts its arrival time interval to the network. A distributed consensus algorithm elects a leader among the aircraft approaching the intersection and helps synchronize the information received by each aircraft. The consensus algorithm ensures that each aircraft computes a schedule with the same input information. The elected leader also dictates when a schedule must be computed, which may be triggered when a new aircraft joins the network. Preliminary results illustrating the collaborative behavior of the vehicles are presented

Quantum Fields with Noncommutative Target Spaces

Quantum field theories (QFT's) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT's with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [1], and others [2,3,4,5,6,7,8]. The twisted spectra of their free Hamiltonians has been found earlier by Carmona et al [9,10]. We review their derivation and then compute the partition function of one such typical theory. It leads to a deformed black body spectrum, which is analysed in detail. The difference between the usual and the deformed black body spectrum appears in the region of high frequencies. Therefore we expect that the deformed black body radiation may potentially be used to compute a GZK cut-off which will depend on the noncommutative parameter $\theta$.Comment: 20 pages, 5 figures; Abstract changed. Changes and corrections in the text. References adde

Novel Studies on the \eta' Effective Lagrangian

The effective Lagrangian for \eta' incorporating the effect of the QCD \theta-angle has been developed previously. We revisit this Lagrangian and carry out its canonical quantization with particular attention to the test function spaces of constraints and the topology of the \eta'-field. In this way, we discover a new chirally symmetric coupling of this field to chiral multiplets which involves in particular fermions. This coupling violates P and T symmetries. In a subsequent paper, we will evaluate its contribution to the electric dipole moment (EDM) of fermions. Our motivation is to test whether the use of mixed states restores P and T invariance, so that EDM vanishes. This calculation will be shown to have striking new physical consequences.Comment: 14 pages, 1 figure; V2: NEW TITLE; revised version to be published in JHEP; references adde

Solid Waste Management Approaches in Trincomalee Urban Council Area

Solid Waste Management is one of the major challenges encountered by the urban areas of Sri Lanka. As a result of inappropriate disposal of solid waste in the open spaces; ecological, health, socio economic problems arise. No research has been undertaken regarding the solid waste management in Trincomalee Urban Council (UC) area of Sri Lanka. This research is carried out with the objectives of identifying the existing solid waste management system of Trincomalee UC area, assessing the problems and challenges in the solid waste management system and proposing recommendations to manage solid wastes properly. Primary data were collected through direct field observation, questionnaire survey with 200 respondents were selected based on purposive sampling, discussion and the secondary data were obtained from resource profiles, statistical handbooks, official websites and published journals. Data was collected from 02.09.2019 to 02.12.2019 and analysed through descriptive statistical method. “SPSS” software is used to analyse the questionnaires. Research revealed that the municipal solid waste generation in Trincomalee UC area has increased temporally due to population increase, expansion of commercial activities, growth of tourism and development activities. 73 tons of municipal solid waste has been generated daily, among them 54% produced from commercial centres and 38% from residential areas. 85% of the waste are degradable organic and 15% are inorganic. Unsorted solid wastes of Trincomalee UC area are disposed at Kanninya open space without any intermediate treatment activities. There is a shortage in appropriate technology, finance and cadres at Trincomalee UC to pursue the recycle activities and the participation of community is low. This situation is the root for the variety of ecological, health and socio-economic problems. Proposed recommendations were included in the conclusion. In this context, this study is the starting point for the policy makers and researchers of solid waste management.DOI: https://doi.org/10.31357/fhss/vjhss.v05i01.03

Influence of Locational Characteristics on the Sustainability of Underserved Settlements in Jaffna Municipality and its Urban Fringe

In developing countries, ineffective land-use planning and unplanned development have spread underserved settlements, particularly in Sri Lanka. These settlements have grown to be an important supplement to cities' insufficient formal housing supply, and they spontaneously formed spatial patterns that significantly impact sustainability. This study examines the locational characteristics of underserved settlements and their influence on their sustainability in the Jaffna Municipal area and its urban fringe. Primary data were collected through a questionnaire survey with 341 underserved settlements using a stratified random sampling technique; focus group discussions with representatives of community-based organizations and ground-level officers; interviews with administrative officers of government institutions, local authorities, academics, and social activists, while secondary data were obtained from Google Earth and government departments. The collected data were analyzed using spatial, descriptive statistics, and qualitative methods. SPSS statistical software was used to analyze the data collected via a questionnaire survey, and ArcGIS 10.4 mapping software was used to create maps. According to the results, underserved settlements' locational characteristics, specifically their location in flood-inundation areas, land reservations, and irregular road networks with poor accessibility, weaken the development potential and negatively impact the sustainability of underserved settlements as well as the urban environment. On the other hand, the current location is crucial for the livelihoods of the underserved settlements. As a result, this study emphasizes the importance of aligning underserved settlements with spatial development and sustainable development goals to reduce problems in underserved settlements and establish cities without underserved areas. Accordingly, this study is expected to be useful for developers, urban planners, and policymakers in prioritizing housing programs and livelihood asset development activities to control the emergence and growth of underserved settlements and minimize existing problems.                                       KEYWORDS: Underserved settlements, Locational characteristics, Influence, Sustainability, Jaffna Municipality, Urban fring