Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators

Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators

Given a semidirect product $\frak{g}=\frak{s}\uplus\frak{r}$ of semisimple Lie algebras $\frak{s}$ and solvable algebras $\frak{r}$, we construct polynomial operators in the enveloping algebra $\mathcal{U}(\frak{g})$ of $\frak{g}$ that commute with $\frak{r}$ and transform like the generators of $\frak{s}$, up to a functional factor that turns out to be a Casimir operator of $\frak{r}$. Such operators are said to generate a virtual copy of $\frak{s}$ in $\mathcal{U}(\frak{g})$, and allow to compute the Casimir operators of $\frak{g}$ in closed form, using the classical formulae for the invariants of $\frak{s}$. The behavior of virtual copies with respect to contractions of Lie algebras is analyzed. Applications to the class of Hamilton algebras and their inhomogeneous extensions are given.Comment: 20 pages, 2 Appendice

Projective Representations of the Inhomogeneous Hamilton Group: Noninertial Symmetry in Quantum Mechanics

Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary representations of the central extension of the group. The formulation of the inertial states of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group, and its nonrelativistic limit in terms of the Galilei group, are fundamental examples. Interestingly, neither of these symmetries includes the Weyl-Heisenberg group; the hermitian representations of its algebra are the Heisenberg commutation relations that are a foundation of quantum mechanics. The Weyl-Heisenberg group is a one dimensional central extension of the abelian group and its unitary representations are therefore a particular projective representation of the abelian group of translations on phase space. A theorem involving the automorphism group shows that the maximal symmetry that leaves invariant the Heisenberg commutation relations are essentially projective representations of the inhomogeneous symplectic group. In the nonrelativistic domain, we must also have invariance of Newtonian time. This reduces the symmetry group to the inhomogeneous Hamilton group that is a local noninertial symmetry of Hamilton's equations. The projective representations of these groups are calculated using the Mackey theorems for the general case of a nonabelian normal subgroup

Light Sheets and the Covariant Entropy Conjecture

We examine the holography bound suggested by Bousso in his covariant entropy conjecture, and argue that it is violated because his notion of light sheet is too generous. We suggest its replacement by a weaker bound.Comment: 5 pages, to appear in Classical and Quantum Gravit

A balloon-borne 1 meter telescope for far-infrared astronomy

The flight of a balloon-borne one-meter telescope for infrared astronomy in the wavelength interval of 40 to 240 microns is discussed. The gyro-stabilized telescope mapped the intensity of the far infrared radiation from NGC 7538, Mars, the Orion Nebula, and W3 with a resolution of one minute and from selected regions of these sources with a resolution of 30 seconds. The infrared detection is described and its capabilities are analyzed. The instrumentation, orientation system, and modes of observation of the telescope are defined

The Riemann Surface of a Static Dispersion Model and Regge Trajectories

The S-matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy $\omega$ in the plane with cuts $(-\infty,-1],[+1,+\infty)$. In the elastic case it reduces to N functions $S_{i}(\omega)$ connected by the crossing symmetry matrix A. The scattering of a neutral pseodoscalar meson with an arbitrary angular momentum l at a source with spin 1/2 is considered (N=2). The Regge trajectories of this model are explicitly found.Comment: 5 pages, LaTe

Ballistic-Ohmic quantum Hall plateau transition in graphene pn junction

Recent quantum Hall experiments conducted on disordered graphene pn junction provide evidence that the junction resistance could be described by a simple Ohmic sum of the n and p mediums' resistances. However in the ballistic limit, theory predicts the existence of chirality-dependent quantum Hall plateaus in a pn junction. We show that two distinctively separate processes are required for this ballistic-Ohmic plateau transition, namely (i) hole/electron Landau states equilibration and (ii) valley iso-spin dilution of the incident Landau edge state. These conclusions are obtained by a simple scattering theory argument, and confirmed numerically by performing ensembles of quantum magneto-transport calculations on a 0.1um-wide disordered graphene pn junction within the tight-binding model. The former process is achieved by pn interface roughness, where a pn interface disorder with a root-mean-square roughness of 10nm was found to suffice under typical experimental conditions. The latter process is mediated by extrinsic edge roughness for an armchair edge ribbon and by intrinsic localized intervalley scattering centers at the edge of the pn interface for a zigzag ribbon. In light of these results, we also examine why higher Ohmic type plateaus are less likely to be observable in experiments.Comment: 9 pages, 6 figure

Sintering of titanium with yttrium oxide additions for the scavenging of chlorine impurities

Chloride impurities in titanium powders are extremely difficult to remove and present a long-standing problem in titanium powder metallurgy. We show that the detrimental effects of chlorides on the sintering of titanium can be mitigated with trace additions of yttrium oxide, which has a high affinity for the normally volatile species and forms highly stable oxychloride reaction products. Compacts that would otherwise exhibit gross swelling and excessive porosity due to chloride impurities can be now sintered to near full density by liquid phase sintering. The potency of yttrium oxide additions is observable at levels as low as 500 ppm. The scavenging of chlorine by YO appears to be independent of alloy composition and sintering regime. It is effective when used with high-chloride powders such as Kroll sponge fines but ineffective when used with powders containing NaCl impurities or during solid-state sintering. The identification of highly potent chlorine scavengers may enable the future development of chloride-tolerant powder metallurgy (PM) alloys aimed at utilizing low-cost, high-chloride powder feedstocks

What if the Higgs couplings to W and Z bosons are larger than in the Standard Model?

We derive a general sum rule relating the Higgs coupling to W and Z bosons to the total cross section of longitudinal gauge boson scattering in I=0,1,2 isospin channels. The Higgs coupling larger than in the Standard Model implies enhancement of the I=2 cross section. Such an enhancement could arise if the Higgs sector is extended by an isospin-2 scalar multiplet including a doubly charged, singly charged, and another neutral Higgs.Comment: 11 pages, no figures. v2: comments and references added. v3: early QCD references adde

Real space first-principles derived semiempirical pseudopotentials applied to tunneling magnetoresistance

In this letter we present a real space density functional theory (DFT) localized basis set semi-empirical pseudopotential (SEP) approach. The method is applied to iron and magnesium oxide, where bulk SEP and local spin density approximation (LSDA) band structure calculations are shown to agree within approximately 0.1 eV. Subsequently we investigate the qualitative transferability of bulk derived SEPs to Fe/MgO/Fe tunnel junctions. We find that the SEP method is particularly well suited to address the tight binding transferability problem because the transferability error at the interface can be characterized not only in orbital space (via the interface local density of states) but also in real space (via the system potential). To achieve a quantitative parameterization, we introduce the notion of ghost semi-empirical pseudopotentials extracted from the first-principles calculated Fe/MgO bonding interface. Such interface corrections are shown to be particularly necessary for barrier widths in the range of 1 nm, where interface states on opposite sides of the barrier couple effectively and play a important role in the transmission characteristics. In general the results underscore the need for separate tight binding interface and bulk parameter sets when modeling conduction through thin heterojunctions on the nanoscale.Comment: Submitted to Journal of Applied Physic