Path integral action of a particle in κ\kappa-Minkowski spacetime

In this letter, we derive the path integral action of a particle in $\kappa$-Minkowski spacetime. The equation of motion for an arbitrary potential due to the $\kappa$-deformation of the Minkowski spacetime is then obtained. The action contains a dissipative term which owes its origin to the $\kappa$-Minkowski deformation parameter $a$. We take the example of the harmonic oscillator and obtain the frequency of oscillations in the path integral approach as well as operator approach upto the first order in the deformation parameter $a$. For studying this, we start with the $\kappa$-deformed dispersion relation which is invariant under the undeformed $\kappa$-Poincar$\acute{e}$ algebra and take the non-relativistic limit of the $\kappa$-deformed dispersion relation to find the Hamiltonian. The propagator for the free particle in the $\kappa$-Minkowski spacetime is also computed explicitly. In the limit, $a\rightarrow 0$, the commutative results are recovered.Comment: 5 pages, To appear in Euro.Phys. Let

Particle Dynamics and Lie-algebraic type of Non-commutativity of space-time

In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$ and treat both as configuration space variables. Here, $\tau$ is a monotonic increasing parameter and the system evolves with this parameter. After constraint analysis, we find the deformed Dirac brackets similar to the $\kappa$-deformed space-time and also, get the deformed Hamilton's equations of motion. Moreover, we study the effect of non-commutativity on the generators of Galilean group and Poincare group and find undeformed form of the algebra. Also, we work on the extended space analysis in the Lagrangian formalism. We find the primary as well as the secondary constraints. Strikingly on calculating the Dirac brackets among the phase space variables, we obtain the classical version of $\kappa$-Minkowski algebra.Comment: 15 page

Characteristics of Fatal Cases of Pandemic Influenza A (H1N1) from September 2009 to January 2010 in Saurashtra Region, India

Background: India reported first case of 2009 pandemic influenza A (H1N1) virus infection in May, 2009 and Saurashtra region in August, 2009. We describe the characteristics of fatal cases of 2009 influenza A (H1N1) infection reported in Saurashtra region. Methods: From September, 2009 to January, 2010, we observed 71 fatal cases that were infected with 2009 influenza A (H1N1) virus and admitted in different hospitals in Rajkot city. Real-time reverse-transcriptase-polymerase-chain-reaction (RT-PCR) testing was used to confirm infection; the clinico-epidemiological features were observed and documented. Results: Median age of the deceased (71) was 29 years, and 57.7% were females. Median time observed was 5 days from onset of illness to diagnosis of influenza A (H1N1), and 57.7% were referred from general practitioner (OR=0.42, CI=0.24-0.74). Median hospital stay reported was 3 days. All admitted patients received oseltamivir, but only 16.9% received it within 2 days of onset of illness. The most common symptoms were cough (97.2%), fever (93%), sore throat and shortness of breath. Co-morbid conditions were present in almost half of the patients who ultimately died, the most common of which was pregnancy (OR=0.15, CI=0.04-0.52). Radiological pneumonia was reported in 98% patients. Conclusion: Residing in urban area, delayed referral from general practitioner, presence of co-existing condition, especially pregnancy was responsible for mortality among influenza A (H1N1) infected positive