A recent application of an index relation of the form, dim ker M − dim ker M † = ν, to the generation of chiral fermions in a vector-like gauge theory is reviewed. In this scheme the chiral structure arises from a mass term with a non-trivial index.The essence of the generalized Pauli-Villars reg-ularization of chiral gauge theory,which is based on this mechanism,is also clarified.

Chirality is widespread in natural systems, and artificial reproduction of chiral recognition is a major scientific challenge, especially owing to various potential applications ranging from catalysis to sensing and separation science. In this context, molecular imprinting is a well-known approach for generating materials with enantioselective properties, and it has been successfully employed u...

Mutual chiral recognition of four stereoisomers of tadalafil and three pairs of enantiomers of proton pump inhibitors (PPIs) including pantoprazole, lansoprazole, and omeprazole, as well as quantitative analysis of enantiomeric excess is achieved on the basis of the competitive fragmentation of doubly charged trimeric NiII cluster ions. Compared with a singly charged trimeric cluster ion, a dou...

In life sciences, diastereomeric chiral molecule/chiral receptor complexes are held together by a different combination of intermolecular forces and are therefore endowed with different stability and reactivity. Determination of these forces, which are normally affected in the condensed phase by solvent and supramolecular interactions, can be accomplished through the generation of diastereomeri...

Despite the tremendous advances of the past four decades, chemists are far from being able to use chiral catalysts to control the stereoselectivity of any desired reaction. New concepts for the construction and mode of operation of chiral catalysts have the potential to open up previously inaccessible reaction space. The recognition and categorization of distinct approaches seems to play a role...

Two-dimensional supramolecular chirality is often achieved by confining molecules against a solid surface. The sergeants-soldiers principle is a popular strategy to fabricate chiral surfaces using predominantly achiral molecules. In this method, achiral molecules (the soldiers) are forced to assemble in a chiral fashion by mixing them with a small percentage of structurally similar chiral molec...

Unravelling the main initial dynamics responsible for chiral recognition is a key step in the understanding of many biological processes. However, this challenging task requires a sensitive enantiospecific probe to investigate molecular dynamics on their natural femtosecond time scale. Here we show that, in the gas phase, the ultrafast relaxation dynamics of photoexcited chiral molecules can be...

A chiral amino acid-based monomeric and polymeric surfactant, sodium oleyl-L-leucylvalinate) (L-SOLV) and poly(sodium oleyl-L-leucylvalinate) (poly-L-SOLV) were synthesized and used for chiral separations in micellar electrokinetic chromatography (MEKC). Poly-L-SOLV was used successfully in the separation of various enantiomers of neutral, acidic, and basic analytes such as 1,1'-bi-2-napthol, 1...