SIM(2) and supergraphs

We construct Feynman rules and Supergraphs in SIM(2) superspace. To test our methods we perform a one-loop calculation of the effective action of the SIM(2) supersymmetric Wess-Zumino model including a term which explicitly breaks Lorentz invariance. The renormalization of the model is also discussed.Comment: 28 page

Sim(2) and SUSY

The proposal of hep-ph/0601236, that the laws of physics in flat spacetime need be invariant only under a SIM(2) subgroup of the Lorentz group, is extended to include supersymmetry. $\mathcal{N}=1$ SUSY gauge theories which include SIM(2) couplings for the fermions in chiral multiplets are formulated. These theories contain two conserved supercharges rather than the usual four.Comment: 10 pages, revtex4. Note added and sign correcte

Estimating selection pressures on HIV-1 using phylogenetic likelihood models

Human immunodeficiency virus (HIV-1) can rapidly evolve due to selection pressures exerted by HIV-specific immune responses, antiviral agents, and to allow the virus to establish infection in different compartments in the body. Statistical models applied to HIV-1 sequence data can help to elucidate the nature of these selection pressures through comparisons of non-synonymous (or amino acid changing) and synonymous (or amino acid preserving) substitution rates. These models also need to take into account the non-independence of sequences due to their shared evolutionary history. We review how we have developed these methods and have applied them to characterize the evolution of HIV-1 in vivo.To illustrate our methods, we present an analysis of compartment-specific evolution of HIV-1 env in blood and cerebrospinal fluid and of site-to-site variation in the gag gene of subtype C HIV-1

Gravitational Radiation from Nonaxisymmetric Instability in a Rotating Star

We present the first calculations of the gravitational radiation produced by nonaxisymmetric dynamical instability in a rapidly rotating compact star. The star deforms into a bar shape, shedding $\sim 4\%$ of its mass and $\sim 17\%$ of its angular momentum. The gravitational radiation is calculated in the quadrupole approximation. For a mass $M \sim 1.4$ M$_{\odot}$ and radius $R \sim 10$ km, the gravitational waves have frequency $\sim 4$ kHz and amplitude $h \sim 2 \times 10^{-22}$ at the distance of the Virgo Cluster. They carry off energy $\Delta E/M \sim 0.1\%$ and radiate angular momentum $\Delta J/J \sim 0.7\%$.Comment: 16 pages, LaTeX with REVTEX macros, reprints available - send mailing address to [email protected]. Published: PRL 72, 1314 (1994

Characterization of Riesz spaces with topologically full center

Let $E$ be a Riesz space and let $E^{\sim}$ denote its order dual. The orthomorphisms $Orth(E)$ on $E,$ and the ideal center $Z(E)$ of $E,$ are naturally embedded in $Orth(E^{\sim})$ and $Z(E^{\sim})$ respectively. We construct two unital algebra and order continuous Riesz homomorphisms $$\gamma:((Orth(E))^{\sim})_{n}^{\sim}\rightarrow Orth(E^{\sim})\text{ }$$ and $$m:Z(E)^{\prime\prime}\rightarrow Z(E^{\sim})$$ that extend the above mentioned natural inclusions respectively. Then, the range of $\gamma$ is an order ideal in $Orth(E^{\sim})$ if and only if $m$ is surjective. Furthermore, $m$ is surjective if and only if $E$ has a topologically full center. (That is, the $\sigma(E,E^{\sim})$-closure of $Z(E)x$ contains the order ideal generated by $x$ for each $x\in E_{+}.$) As a consequence, $E$ has a topologically full center $Z(E)$ if and only if $Z(E^{\sim})=\pi\cdot Z(E)^{\prime\prime}$ for some idempotent $\pi\in Z(E)^{\prime\prime}.

Deforming the Maxwell-Sim Algebra

The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim$_b$, where $b$ is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force.Comment: Appendix on Lifshitz and Schrodinger algebras adde