Scientific and Technical Aerospace Reports Volume 39 April 6, 2001
Scientific and Technical Aerospace Reports Volume 39 April 6, 2001
Scientific and Technical Aerospace Reports Volume 39 April 6, 2001
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We construct explicit solutions of a conditionally quantum conformal invariant q-d’Alembert equation proposed earlier by<br />
one of us. We give two types of solutions - polynomial solutions <strong>and</strong> a q-deformation of the plane wave. The latter is a formal<br />
power series in the noncommutative coordinates of q-Minkowski space-time <strong>and</strong> four-momenta. This q-plane wave has analogous<br />
properties to the classical one, in particular, it has the properties of q- Lorentz covariance, <strong>and</strong> it satisfies the q-d’Alembert equation<br />
on the q-Lorentz covariant momentum cone. On the other h<strong>and</strong>, our q-plane wave is not an exponent or q-exponent. Thus, it differs<br />
conceptually from the classical plane wave <strong>and</strong> may serve as a regularization. (author). 11 refs.<br />
NTIS<br />
Deformation; Coordinates; Covariance; Conformal Mapping<br />
<strong>2001</strong>0026243 Abdus Salam International Centre for Theoretical Physics, Trieste, Italy<br />
Aspects of U-duality in matrix theory<br />
Blau, M.; OLoughlin, M.; Dec. 31, 1997; 19p; In English<br />
Report No.(s): DE98-621491; IC-97/198; HEP-TH-9712047; No Copyright; Avail: Department of Energy Information Bridge<br />
We explore various aspects of implementing the full M-theory U-duality group E(sub d+1), <strong>and</strong> thus Lorentz invariance, in<br />
the finite N matrix theory (DLCQ of M-theory) describing toroidal IIA-compactifications on d-tori: (1) We generalize the analysis<br />
of Elitzur et al. (hep-th/9707217) from E(sub d) to E(sub d+1) <strong>and</strong> identify the highest weight states unifying the momentum <strong>and</strong><br />
flux E(sub d)-multiplets into one E(sub d+1)-orbit, (2) We identify the new symmetries, in particular the Weyl group symmetry<br />
associated to the (d+1)’th node of the E(sub d+1) Dynkin diagram, with Nahm-duality-like symmetries (N- duality) exchanging<br />
the rank N of the matrix theory gauge group with other (electric, magnetic, ...) quantum numbers. (3) We describe the action of<br />
N- duality on BPS bound states, thus making testable predictions for the Lorentz invariance of matrix theory. (4) We discuss the<br />
problems that arise in the matrix theory limit for BPS states with no top-dimensional branes, i.e. configurations with N = 0. (5)<br />
We show that N-duality maps the matrix theory SYM picture to the matrix string picture <strong>and</strong> argue that, for d even, the latter should<br />
be thought of as an M-theory membrane description (which appears to be well defined even for d > 5). (6) We find a compact<br />
<strong>and</strong> unified expression for a U-duality invariant of E(sub d+1) for all d <strong>and</strong> show that in d = 5,6 it reduces to the black hole entropy<br />
cubic E(sub 6)- <strong>and</strong> quartic E(sub 7)- invariants respectively. (7) Finally, we describe some of the solitonic states in d = 6,7 <strong>and</strong><br />
give an example (a ’rolled-up’ Taub-NUT 6-brane) of a configuration exhibiting the unusual 1/g(sup 3)(sub s)-behaviour. (author).<br />
<strong>39</strong> refs.<br />
NTIS<br />
Matrix Theory; Matrices (Mathematics)<br />
<strong>2001</strong>0026244 Abdus Salam International Centre for Theoretical Physics, Trieste, Italy<br />
Quantum mechanical potential for the prime numbers<br />
Mussardo, G.; Dec. 31, 1997; 10p; In English<br />
Report No.(s): DE98-621492; IC-97/199; ISAS/EP-97/153; No Copyright; Avail: Department of Energy Information Bridge<br />
A simple criterion is derived in order that a number sequence S(sub n) is a permitted spectrum of a quantized system. The<br />
sequence of the prime numbers fulfills the criterion <strong>and</strong> the corresponding one-dimensional quantum potential is explicitly computed<br />
in a semi-classical approximation. The existence of such a potential implies that the primality testing can in principle be<br />
resolved by the sole use of physical laws.<br />
NTIS<br />
Quantum Mechanics; Criteria; Laws<br />
<strong>2001</strong>0026246 Abdus Salam International Centre for Theoretical Physics, Trieste, Italy<br />
Signatures of non-universal soft breaking sfermion masses at Hadron colliders<br />
Datta, A.; Datta, A.; Parida, M. K.; Dec. 31, 1997; 9p; In English<br />
Report No.(s): DE98-621494; IC-97/207; No Copyright; Avail: Department of Energy Information Bridge<br />
We identify several mass patterns, within the framework of N = 1 SUGRA with nonuniversal soft breaking masses for the<br />
sfermions, which may significantly alter SUSY signals <strong>and</strong> the current squark-gluino mass limits from the Tevatron. These effects<br />
are illustrated in a SO(10) SUSY GUT with an intermediate mass scale, but the conclusions are also valid in SUSU SO(10) models<br />
with gr<strong>and</strong> deserts. (author). 21 refs, 2 figs, 2 tabs.<br />
NTIS<br />
Fermions; Particle Accelerators; Elementary Particles<br />
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