Gauge Symmetries on θ\theta-Deformed Spaces

A Hamiltonian formulation of gauge symmetries on noncommutative ($\theta$ deformed) spaces is discussed. Both cases- star deformed gauge transformation with normal coproduct and undeformed gauge transformation with twisted coproduct- are considered. While the structure of the gauge generator is identical in either case, there is a difference in the computation of the graded Poisson brackets that yield the gauge transformations. Our analysis provides a novel interpretation of the twisted coproduct for gauge transformations.Comment: LaTex, 20 pages, no figure

Remarks on the Noncommutative Gravitational Quantum Well

A planar phase space having both position and momentum noncommutativity is defined in a more inclusive setting than that considered elsewhere. The dynamics of a particle in a gravitational quantum well in this space is studied. The use of the WKB approximation and the virial theorem enable analytic discussions on the effect of noncommutativity. Consistent results are obtained following either commutative space or noncommutative space descriptions. Comparison with recent experimental data with cold neutrons at Grenoble imposes an upper bound on the noncommutative parameter. Also, our results are compared with a recent numerical analysis of a similar problem.Comment: Latex, 17 pages, Title changed, minor modifications, 3 new references added, To appear in Phys. Rev.

Study on Noncommutative Representations of Galilean Generators

The representations of Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under noncommutative phase space transformations is constructed. The Dirac brackets of this model reproduce the original noncommutative algebra. Also, the generators in terms of noncommutative phase space variables are abstracted from this model in a consistent manner. Finally, the role of Jacobi identities is emphasised to produce the noncommuting structure that occurs when an electron is subjected to a constant magnetic field and Berry curvature.Comment: Title changed, new references added, published in Int. J. Mod. Phys.

Self-reported oral health status and self-care practices among mid-life women at a secondary care hospital in a rural area of Delhi, India

Background: Poor oral health status is more likely among socioeconomically disadvantaged women and low literacy due to poor oral hygiene. Onset of menopausal symptoms also triggers hormonal changes, adversely influencing oral health. The study objective was to determine the self-reported oral health status and self-care practices among perimenopausal women attendees of the medical outpatient department of a government hospital in Delhi, India  Methods: We conducted a cross-sectional study at a secondary care hospital among 136 women aged 40-59 years, having either perimenopause symptoms or with menopause. Data were collected through face-to-face interviews using the Hindi version of the WHO Steps Module on Oral Health. A p-value < 0.05 was considered statistically significant. Results: Sixty-nine (51.2%) participants had not received any schooling. Oral health status was reported as average or poor by 61 (44.85%) and 59 (43.4) participants for their teeth and gums, respectively. Pain or discomfort in teeth was reported by 77 (56.6%) participants, along with chewing 66 (48.5%) and speech difficulties 21 (15.4%). Most participants 114 (83.8%) brushed their teeth only once a day, and rarely (3.7%) flossed.  Participants with low education and a greater number of missing teeth were significantly more likely to report suboptimal dental health status. Conclusion: A large proportion of mid-life socioeconomically vulnerable women in India report poor oral health and hygiene with self-perceived suboptimal teeth or gum status. Visually oriented information, education, and communication (IEC) campaigns for oral health promotion should be evaluated in public health facilities

Noncommutative Black Hole Thermodynamics

We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=\frac{\cal K}{2\pi}$ connecting the black hole temperature ($T_h$) with the surface gravity ($\cal K$), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi classical regime i. e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space time. The effects of back reaction are also included. For such a black hole the Hawking temperature is computed in a closed form. A graphical analysis reveals interesting features regarding the variation of the Hawking temperature (including corrections due to noncommutativity and back reaction) with the small radius of the black hole. The entropy and tunneling rate valid for the leading order in the noncommutative parameter are calculated. We also show that the noncommutative Bekenstein-Hawking area law has the same functional form as the usual one.Comment: LaTex, 17 pages, 2 figures, minor changes, references added, to appear in Phys. Rev.

Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics

We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge (reparametrisation) independent derivation of Snyder's algebra from such models is given. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided. Finally, an alternative form of an action yielding Snyder's algebra is discussed where the mass of a relativistic particle gets identified with the inverse of the noncommutativity parameter.Comment: 19 pages; Latex; title changed, 3 new references added and minor changes; to appear in JHE