The standard model on non-commutative space-time

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter . No new particles are introduced; the structure group is . We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. Received: 29 November 2001 / Published online: 25 January 2002     

The two-dimensional quantum Euclidean algebra

The algebra dual to Woronowicz's deformation of the two-dimensional Euclidean group is constructed. The same algebra is obtained from SU _q (2) via contraction on both the group and algebra levels.     

Use of solid-phase extraction to enable enhanced detection of acyl homoserine lactones (AHLs) in environmental samples

A challenge for understanding the role of bacterial cell–cell signalling in the environment is the detection of those signals, which are often present in low (nmol L⁻¹) concentrations. We describe here a simple purification method, solid-phase extraction (SPE), for increasing the sensitivity of detection for one such group of signals, acyl homoserine lactones (AHLs), in environmental samples. Spiking of dried marine sponge tissue (Stylinos sp.) with AHLs resulted in detection down to 0.01 ppm for 3-oxo-hexanoyl homoserine lactone (3-oxo C₆-HSL) and 1 ppm for hexanoyl homoserine lactone (C₆-HSL). Compared with liquid extraction methods use of SPE resulted in twofold and tenfold improvements in sensitivity, respectively.     

The standard model on non-commutative space-time: strong interactions included

This paper is a direct extension of our earlier work on electroweak currents and the Higgs sector in the standard model on non-commutative space-time, now with strong interactions included. Apart from the non-commutative corrections to standard model strong interactions, several new interactions appear. The most interesting ones are gluonic interactions with the electroweak sector. They are elaborated here in detail and the Feynman rules for interactions up to are provided.Received: 18 March 2005, Revised: 13 May 2005, Published online: 19 July 2005     

The photon-neutrino interaction induced by non-commutativity and astrophysical bounds

In this work we propose a possible mechanism of left- and right-handed neutrino couplings to photons, which arises quite naturally in non-commutative field theory. We estimate the predicted additional energy-loss in stars induced by space-time non-commutativity. The usual requirement that any new energy-loss mechanism in globular stellar clusters should not excessively exceed the standard neutrino losses implies a scale of non-commutative gauge theory above the scale of weak interactions.Received: 2 April 2004, Published online: 14 July 2004     

Remarkable properties of alkali halides and new techniques for determining Debye--Waller factors

We have used 70 Ci ¹⁸³Ta Mössbauer sources to measure the Debye--Waller factors of NaCl, KCl, and KBr single crystals for several of the (h00) and (nnn) Bragg reflections. We have found that the procedure used to analyze data by earlier workers leads to incorrect parameters in the Debye--Waller factor exponent, and we use a procedure that eliminates the need to introduce an empirical parameter to account for thermal expansion effects. We observe that both the cations and anions in NaCl and KBr have identical Debye--Waller factors in the [nnn] direction. We observe Q⁴ terms in NaCl and KCl, with some evidence for a Q⁴ term in KBr. The size of this contribution varies with the direction of momentum transfer and will be reported. We observe that the Debye temperature and the coefficient of the anharmonic Q² term also vary with direction of momentum transfer. We believe this to be the first definitive evidence for a non-spherical thermal cloud in a cubic crystal; the ions have a larger amplitude of oscillation in the [h00] direction than in the [nnn] direction. This effect is temperature dependent and greater at lower temperatures.     

The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms

Let F _k be a free group of rank k ≥ 2 with a fixed set of free generators. We associate to any homomorphism φ from F _k to a group G with a left-invariant semi-norm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation where φ: F _k → Aut(X) corresponds to a free action of F _k on a simplicial tree X, in particular, where φ corresponds to the action of F _k on its Cayley graph via an automorphism of F _k . In this case we are able to obtain some detailed “arithmetic” information about the possible values of λ = λ(φ). We show that λ ≥ 1 and is a rational number with 2kλ ∈ ℤ[1/(2k − 1)] for every φ ∈ Aut(F _k ). We also prove that the set of all λ(φ), where φ varies over Aut(F _k ), has a gap between 1 and 1+(2k−3)/(2k ²−k), and the value 1 is attained only for “trivial” reasons. Furthermore, there is an algorithm which, when given φ, calculates λ(φ). The second and the third author were supported by the NSF grant DMS#0404991 and the NSA grant DMA#H98230-04-1-0115.     

Precision measurements of recoil-free fraction and interference with hundred Curie sources

We discuss our experiences with exceptionally intense Mössbauer sources (of order 100 Ci) and their use in making precision determinations of line shape parameters. We review our measurements of interference and recoilless fraction using conventional transmission geometry. Fitting simultaneous sets of data with known constraints greatly improves the efficiency of line-shape determination. Measurements of interference have been made using a two-absorber technique first introduced by Mössbauer and coworkers. Our results indicate that the method can be useful for determining interference, but that incorrect line shape parameters are obtained if powder samples are used which do not comply well with the assumption of thickness uniformity in the absorber.