A Theory of Quantized Fields Based on Orthogonal and Symplectic Clifford Algebras

The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the role of quantum mechanical operators that satisfy the Heisenberg equations of motion. For quadratic Hamiltonians, the latter equations are obtained from the classical equations of motion, rewritten in terms of the phase space coordinates and the corresponding basis vectors. Then, assuming that such equations hold for arbitrary path, i.e., that coordinates and momenta are undetermined, we arrive at the equations that contains basis vectors and their time derivatives only. According to this approach, quantization of a classical theory, formulated in phase space, is replacement of the phase space variables with the corresponding basis vectors (operators). The basis vectors, transformed into the Witt basis, satisfy the bosonic or fermionic (anti)commutation relations, and can create spinor states of all minimal left ideals of the corresponding Clifford algebra. We consider some specific actions for point particles and fields, formulated in terms of commuting and/or anticommuting phase space variables, together with the corresponding symplectic or orthogonal basis vectors. Finally we discuss why such approach could be useful for grand unification and quantum gravity.     

Parametrized Field Theory

A theory is presented in which a field depends not only on spacetime coordinates x, but also on a Lorentz-invariant parameter . Such a theory is conceptually and technically simple and manifestly covariant at every step. The generator of evolution and the generator of spacetime translations and Lorentz transformations are obtained in a straightforward way. In the quantized theory the Heisenberg equation of motion is written in a covariant form and is equivalent to the field equation. The equal commutator between the field and its canonically conjugate momentum is just proportional to the spacetime function. Finally comparison with the conventional field theory is done, and it is found that the expectation value of the momentum operator in the on shell states is the same.     

Zintl‐Phase Sr3LiAs2H: Crystal Structure and Chemical Bonding Analysis by the Electron Localizability Approach

The compound Sr₃LiAs₂H was synthesized by reaction of elemental strontium, lithium, and arsenic, as well as LiH as hydrogen source. The crystal structure was determined by single‐crystal X‐ray diffraction: space group Pnma; Pearson symbol oP28; a = 12.0340(7), b = 4.4698(2), c = 12.5907(5) Å; V = 677.2(1) ų; R_F = 0.047 for 1021 reflections and with 36 parameters refined. The positions of the hydrogen atoms were first revealed by the electron localizability indicator and subsequently confirmed by crystal structure refinement. In the crystal structure of Sr₃LiAs₂H the metal atoms are arranged in a Gd₃NiSi₂‐type motif, whereas the hydrogen atoms are arranged in a distorted tetrahedral environment formed by strontium. The calculated band structure revealed that Sr₃LiAs₂H is a semiconductor, which is in agreement with its diamagnetic behavior. Thus, Sr₃LiAs₂H is considered as a (charge‐balanced) Zintl phase.     

Diversity‐Oriented Synthesis of Drug‐Like Macrocyclic Scaffolds Using an Orthogonal Organo‐ and Metal Catalysis Strategy

Small‐molecule modulators of biological targets play a crucial role in biology and medicine. In this context, diversity‐oriented synthesis (DOS) provides strategies toward generating small molecules with a broad range of unique scaffolds, and hence three‐dimensionality, to target a broad area of biological space. In this study, an organocatalysis‐derived DOS library of macrocycles was synthesized by exploiting the pluripotency of aldehydes. The orthogonal combination of multiple diversity‐generating organocatalytic steps with alkene metathesis enabled the synthesis of 51 distinct macrocyclic structures bearing 48 unique scaffolds in only two to four steps without the need for protecting groups. Furthermore, merging organocatalysis and alkene metathesis in a one‐pot protocol facilitated the synthesis of drug‐like macrocycles with natural‐product‐like levels of shape diversity in a single step.     

Mechanochemistry as a versatile and scalable tool for nanomaterials synthesis: Recent achievements in Košice,Slovakia

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Long range corrections in inhomogeneous simulations

An improved method for the treatment of the long range corrections in molecular simulations of inhomogeneous systems with planar interfaces is presented. To evaluate the quality of this approach, Monte Carlo simulations of the Lennard-Jones fluid are performed in the temperature range T* is an element of <0.7, 1.25>. The attention is focused especially on the values of the surface tension, which represents a property significantly sensitive to the truncation of the intermolecular interactions. When the presented approach is employed, the values of coexisting densities and surface tensions obtained with the cutoff distance R(c) = 2.5sigma are within experimental errors identical with those obtained for cutoff distance R(c) = 5.5sigma.     

Global intercompany assessment of ICIEF platform comparability for the characterization of therapeutic proteins

An international team spanning 19 sites across 18 biopharmaceutical and in vitro diagnostics companies in the United States, Europe, and China, along with one regulatory agency, was formed to compare the precision and robustness of imaged CIEF (ICIEF) for the charge heterogeneity analysis of the National Institute of Standards and Technology (NIST) mAb and a rhPD-L1-Fc fusion protein on the iCE3 and the Maurice instruments. This information has been requested to help companies better understand how these instruments compare and how to transition ICIEF methods from iCE3 to the Maurice instrument. The different laboratories performed ICIEF on the NIST mAb and rhPD-L1-Fc with both the iCE3 and Maurice using analytical methods specifically developed for each of the molecules. After processing the electropherograms, statistical evaluation of the data was performed to determine consistencies within and between laboratory and outlying information. The apparent isoelectric point (pI) data generated, based on two-point calibration, for the main isoform of the NIST mAb showed high precision between laboratories, with RSD values of less than 0.3% on both instruments. The SDs for the NIST mAb and the rhPD-L1-Fc charged variants percent peak area values for both instruments are less than 1.02% across different laboratories. These results validate the appropriate use of both the iCE3 and Maurice for ICIEF in the biopharmaceutical industry in support of process development and regulatory submissions of biotherapeutic molecules. Further, the data comparability between the iCE3 and Maurice illustrates that the Maurice platform is a next-generation replacement for the iCE3 that provides comparable data.