11,192 research outputs found
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 of semisimple
Lie algebras and solvable algebras , we construct
polynomial operators in the enveloping algebra of
that commute with and transform like the generators of
, up to a functional factor that turns out to be a Casimir operator
of . Such operators are said to generate a virtual copy of
in , and allow to compute the Casimir operators of
in closed form, using the classical formulae for the invariants of
. 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 in the plane with
cuts . In the elastic case it reduces to N functions
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
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
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
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
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