The Simultaneous Coupling Scheme for SU(3)

We present a simple method for calculating the Clebsch-Gordan coefficients for the tensor product of two unitary irreducible representations of SU(3). The calculation given here is an application and extension of the simultaneous coupling scheme proposed in 2010 for the rotation group SU(2).     

The time reversal operator for semigroup evolutions

A quantum theory combining an irreversible time evolution semigroup with a time reversal operator is presented.     

Perturbations of unitary representations of the Galilei group: Mass operators with continuous spectra

We present a systematic procedure for constructing mass operators with continuous spectra for a system of particles in a manner consistent with Galilean relativity. These mass operators can be used to construct what may be called point-form Galilean dynamics. As in the relativistic case introduced by Dirac, the point-form dynamics for the Galilean case is characterized by both the Hamiltonian and momenta being altered by interactions. An interesting property of such perturbative terms to the Hamiltonian and momentum operators is that, while having well-defined transformation properties under the Galilei group, they also satisfy Maxwell’s equations. This result is an alternative to the well-known Feynman-Dyson derivation of Maxwell’s equations from non-relativistic quantum physics.     

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner–Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated in quantum theory.     

Natural dissolved organic matter affects electrospray ionization during analysis of emerging contaminants by mass spectrometry

Dissolved organic matter (DOM), present in many forms in water, can interfere with analysis of organic contaminants by atmospheric pressure ionization–mass spectrometry. A quantitative analysis of this interference, or matrix effect, on organic contaminant target analyte measurements was carried out using un-fractionated and fractionated dissolved natural organic matter from the Suwannee River, GA (SROM), a standard reference material, that was directly infused into the tandem mass spectrometer during multiple reaction monitoring (MRM) of a suite of endocrine disrupting compounds–pharmaceuticals and personal care products (EDC/PPCPs). Most target analytes suffered signal suppression in the presence of both fractionated and un-fractionated SROM, however greater interferences were measured with fractionated relative to bulk SROM. This finding is consistent with the view of organic matter as a supramolecular association of low molecular mass components having separate charged and structural features revealed only after dissociation.     

Analysis of deprotonated acids with silicon nanoparticle-assisted laser desorption/ ionization mass spectrometry

Chemically modified silicon nanoparticles were applied for the laser desorption/negative ionization of small acids. A series of substituted sulfonic acids and fatty acids was studied. Compared to desorption ionization on porous silicon (DIOS) and other matrix-less laser desorption/ionization techniques, silicon nanoparticle-assisted laser desorption/ionization (SPALDI) mass spectrometry allows for the analysis of acids in the negative ion mode without the observation of multimers or cation adducts. Using SPALDI, detection limits of many acids reached levels down to 50 pmol/μl. SPALDI of fatty acids with unmodified silicon nanoparticles was compared to SPALDI using the fluoroalkyl silylated silicon powder, with the unmodified particles showing better sensitivity for fatty acids, but with more low-mass background due to impurities and surfactants in the untreated silicon powder. The fatty acids exhibited a size-dependent response in both SPALDI and unmodified SPALDI, showing a signal intensity increase with the chain length of the fatty acids (C12-C18), leveling off at chain lengths of C18-C22. The size effect may be due to the crystallization of long chain fatty acids on the silicon. This hypothesis was further explored and supported by SPALDI of several, similar sized, unsaturated fatty acids with various crystallinities. Fatty acids in milk lipids and tick nymph samples were directly detected and their concentration ratios were determined by SPALDI mass spectrometry without complicated and time-consuming purification and esterification required in the traditional analysis of fatty acids by gas chromatography (GC). These results suggest that SPALDI mass spectrometry has the potential application in fast screening for small acids in crude samples with minimal sample preparation.     

Synthesis of histidinoalanine: a comparison of β-lactone and sulfamidate electrophiles

Previous syntheses of histidinoalanine (HAL) have led to mixtures of regioisomers and/or stereoisomers. For example, opening of N-Cbz-D-serine-β-lactone (6) with Boc-L-His-OMe (5) gave a 2:1 mixture of τ- and π-regioisomers. The sulfamidate 10, derived from N-benzyl-D-serine methyl ester (11), was reacted with Boc-L-His-OMe (5) to give the τ-HAL derivative 17 as a single isomer in 57% yield. A similarly prepared τ-HAL 19, bearing protecting groups that were all hydrogenolytically labile, led to the free bis-amino acid, τ-L-histidinyl-D-alanine (τ-4), as a salt-free standard for amino acid analysis.     

Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations

This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle as well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics.     

Galilean and dynamical invariance of entanglement in particle scattering

Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.