4,522 research outputs found
Two-Dimensional Conformal Models of Space-Time and Their Compactification
We study geometry of two-dimensional models of conformal space-time based on
the group of Moebius transformation. The natural geometric invariants, called
cycles, are used to linearise Moebius action. Conformal completion of the
space-time is achieved through an addition of a zero-radius cycle at infinity.
We pay an attention to the natural condition of non-reversibility of time arrow
in order to get a correct compactification in the hyperbolic case.Comment: 8 pages,AMS-LaTeX, 18 PS figures; v2--small corrections; v3--add two
coments on notations and multidimensional generalisation
Superselection Structure of Massive Quantum Field Theories in 1+1 Dimensions
We show that a large class of massive quantum field theories in 1+1
dimensions, characterized by Haag duality and the split property for wedges,
does not admit locally generated superselection sectors in the sense of
Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1+1
dimensions due to Fredenhagen, Rehren and Schroer is vacuous for such theories.
Even charged representations which are localizable only in wedge regions are
ruled out. Furthermore, Haag duality holds in all locally normal
representations. These results are applied to the theory of soliton sectors.
Furthermore, the extension of localized representations of a non-Haag dual net
to the dual net is reconsidered. It must be emphasized that these statements do
not apply to massless theories since they do not satisfy the above split
property. In particular, it is known that positive energy representations of
conformally invariant theories are DHR representations.Comment: latex2e, 21 pages. Final version, to appear in Rev. Math. Phys. Some
improvements of the presentation, but no essential change
Testing the Hubble Law with the IRAS 1.2 Jy Redshift Survey
We test and reject the claim of Segal et al. (1993) that the correlation of
redshifts and flux densities in a complete sample of IRAS galaxies favors a
quadratic redshift-distance relation over the linear Hubble law. This is done,
in effect, by treating the entire galaxy luminosity function as derived from
the 60 micron 1.2 Jy IRAS redshift survey of Fisher et al. (1995) as a distance
indicator; equivalently, we compare the flux density distribution of galaxies
as a function of redshift with predictions under different redshift-distance
cosmologies, under the assumption of a universal luminosity function. This
method does not assume a uniform distribution of galaxies in space. We find
that this test has rather weak discriminatory power, as argued by Petrosian
(1993), and the differences between models are not as stark as one might expect
a priori. Even so, we find that the Hubble law is indeed more strongly
supported by the analysis than is the quadratic redshift-distance relation. We
identify a bias in the the Segal et al. determination of the luminosity
function, which could lead one to mistakenly favor the quadratic
redshift-distance law. We also present several complementary analyses of the
density field of the sample; the galaxy density field is found to be close to
homogeneous on large scales if the Hubble law is assumed, while this is not the
case with the quadratic redshift-distance relation.Comment: 27 pages Latex (w/figures), ApJ, in press. Uses AAS macros,
postscript also available at
http://www.astro.princeton.edu/~library/preprints/pop682.ps.g
A Unified Treatment of the Characters of SU(2) and SU(1,1)
The character problems of SU(2) and SU(1,1) are reexamined from the
standpoint of a physicist by employing the Hilbert space method which is shown
to yield a completely unified treatment for SU(2) and the discrete series of
representations of SU(1,1). For both the groups the problem is reduced to the
evaluation of an integral which is invariant under rotation for SU(2) and
Lorentz transformation for SU(1,1). The integrals are accordingly evaluated by
applying a rotation to a unit position vector in SU(2) and a Lorentz
transformation to a unit SO(2,1) vector which is time-like for the elliptic
elements and space-like for the hyperbolic elements in SU(1,1). The details of
the procedure for the principal series of representations of SU(1,1) differ
substantially from those of the discrete series.Comment: 31 pages, RevTeX, typos corrected. To be published in Journal of
Mathematical Physic
A Linearization Beam-Hardening Correction Method for X-Ray Computed Tomographic Imaging of Structural Ceramics
Computed tomographic (CT) imaging with both monochromatic and polychromatic x-ray sources can be a powerful NDE method for characterization (e. g., measurement of density gradients) as well as flaw detection (e. g., detection of cracks, voids, inclusions) in ceramics. However, the use of polychromatic x-ray sources can cause image artifacts and overall image degradation through beam hardening (BH) effects [1]. Beam hardening occurs because (i) x-ray attenuation in a given material is energy dependent and (ii) data collection in CT systems is not energy selective. Without an appropriate correction, the BH effect prevents the establishment of an absolute scale for density measurement. Thus, quantitative density comparisons between samples of the same material but of different geometrical shape becomes unreliable [2]
QED in external fields from the spin representation
Systematic use of the infinite-dimensional spin representation simplifies and
rigorizes several questions in Quantum Field Theory. This representation
permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily
projective: we compute its cocycle at the group level, and obtain Schwinger
terms and anomalies from infinitesimal versions of this cocycle. Quantization,
in this framework, depends on the choice of the ``right'' complex structure on
the space of solutions of the Dirac equation. We show how the spin
representation allows one to compute exactly the S-matrix for fermions in an
external field; the cocycle yields a causality condition needed to determine
the phase.Comment: 32 pages, Plain TeX, UCR-FM-01-9
On localization and position operators in Moebius-covariant theories
Some years ago it was shown that, in some cases, a notion of locality can
arise from the group of symmetry enjoyed by the theory, thus in an intrinsic
way. In particular, when Moebius covariance is present, it is possible to
associate some particular transformations to the Tomita Takesaki modular
operator and conjugation of a specific interval of an abstract circle. In this
context we propose a way to define an operator representing the coordinate
conjugated with the modular transformations. Remarkably this coordinate turns
out to be compatible with the abstract notion of locality. Finally a concrete
example concerning a quantum particle on a line is also given.Comment: 19 pages, UTM 705, version to appear in RM
Segal-Bargmann-Fock modules of monogenic functions
In this paper we introduce the classical Segal-Bargmann transform starting
from the basis of Hermite polynomials and extend it to Clifford algebra-valued
functions. Then we apply the results to monogenic functions and prove that the
Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform
for monogenic functionals. This kernel is also the reproducing kernel for the
monogenic Bargmann module.Comment: 11 page
Large-scale structure and the redshift-distance relation
In efforts to demonstrate the linear Hubble law v = Hr from galaxy
observations, the underlying simplicity is often obscured by complexities
arising from magnitude-limited data. In this paper we point out a simple but
previously unremarked fact: that the shapes and orientations of structures in
redshift space contain in themselves independent information about the
cosmological redshift-distance relation.
The orientations of voids in the CfA slice support the Hubble law, giving a
redshift-distance power index p = 0.83 +/- 0.36 (void data from Slezak, de
Lapparent, & Bijoui 1993) or p = 0.99 +/- 0.38 (void data from Malik &
Subramanian 1997).Comment: 11 pages (AASTeX), 4 figures, to appear in the Astrophysical Journal
Letter
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