Parity violation

Abstract

Violation of (space) parity in atomic physics, molecular physics and chemistry is briefly reviewed. The review is structured by frequently asked questions related to the concept of space parity, its violation and the consequences thereof in physics, chemistry and biology. This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy Structure and Mechanism > Molecular Structures Theoretical and Physical Chemistry > Thermochemistry K E Y W O R D S chirality, electroweak quantum chemistry, fundamental symmetries, parity violation, periodic system of fundamental particles, relativistic quantum chemistry 1 | WHAT IS (SPACE) PARITY?In mathematics, the concept of even and odd parity is related to integer numbers and their behavior under division by the number two. Those integers which can be divided by two without remainder are called even, those that are divided by two with remainder one are called odd. Consequently, one can speak of a given integer to possess either even parity or odd parity (see also Reference 1). In quantum mechanics, instead, the term parity is used for the transformation properties of states and operators with respect to discrete symmetry operations such as space inversion, time reversal or charge conjugation. Space inversion (in conventional three-dimensional space) implies reflection of spatial coordinates of all particles at the origin, time reversal implies reversal of all particle momenta and charge conjugation implies change from particles to their anti-particles and vice versa. States that remain unaltered under application of such a discrete symmetry operation are called space parity even (Peven) or charge parity even (C-even), respectively, those which change sign under application of these discrete symmetry operations are called space parity odd (P-odd) or charge parity odd (C-odd). Time reversal is special in this regard as the corresponding operator describing time reversal is an antiunitary operator which does not have eigenvalues. In contrast to states, operators can be classified as being time parity even (T-even) or time parity odd (T-odd) (see Reference 2 for a more detailed discussion of time-reversal symmetry). When no additional classification is given, the word parity conventionally refers to space parity, and we will use that convention also within this review.An arbitrary quantum state does not necessarily have to possess well-defined parity (P-even or P-odd), but in linear quantum mechanics instead, such a quantum state can be written as a superposition of states with well-defined parity.Elementary particles as quanta of fields are usually described with the help of so-called intrinsic parities (see e.g., Reference 3). One characterizes these fields for instance as scalar fields and vector fields or pseudo-scalar fields and pseudo-scalar fields and vector fields, depending on their behavior with respect to space inversion. Scalar fields and pseudo-vector fields remain

Emerging Methods and Design Principles for Cell‐Penetrant Peptides

“…Rather, they are best-odds strategies based on results from many research groups.They also do not take into account additional effects,s uch as transport kinetics,t issue selectivity,a nd binding kinetics at the cellular target, which medicinal chemistry has shown to be critical for understanding distribution properties for all molecules. [125,[179][180][181][182] Thed ecision of how to modify ap eptide to make it intrinsically cell-penetrant depends on its size,c harge,a nd hydrophobicity.Apeptide might be amenable to ap assive penetration mechanism if the peptide is on the smaller side, defined as molecular volume less than 1500 3 ,which roughly corresponds to ac onstrained peptide of less than 1100-1200 Daltons. [65,135] Passive penetration also limits the number of solvent-exposed hydrogen-bond donors.T hese parameters can often be satisfied for cyclic peptides that have asubstantial portion of non-peptidic or N-modified backbone,o rt hat are structured in away that shields amide protons from solvent.…”

Neue Methoden und Designprinzipien für zellgängige Peptide

“…[172,173] Bei CAPA werden Zellen zunächst mit dem zu untersuchenden, Chloralkan-markierten Molekülg epulst, das bei Erreichen des Zytosols HaloTag kovalent blockiert. [125,[179][180][181][182] Die Entscheidung, wie ein Peptid zu modifizieren ist, um es intrinsisch zellgängig zu machen, hängt von seiner Grçße, Ladung und Hydrophobie ab.E in Peptid kann einem passiven Penetrationsmechanismus unterliegen, wenn es eher klein ist -d efiniert durch ein Molekülvolumen < 1500 3 entsprechend einem Peptid von < 1100-1200 Dalton. CAPA ist nicht markierungsfrei und weist daher alle Probleme der markierungsbasierten Assays auf,w ie sie oben beschrieben wurden.…”

“…[171] HaloTag ist eine modifizierte Halogenalkan-Dehalogenase,die von Wood und Mitarbeitern entwickelt wurde und mit schneller Kinetik und hoher Selektivitätd urch Chloralkane markiert wird. [172,173] Bei CAPA werden Zellen zunächst mit dem zu untersuchenden, [125,[179][180][181][182] Die Entscheidung, wie ein Peptid zu modifizieren ist, um es intrinsisch zellgängig zu machen, hängt von seiner Grçße, Ladung und Hydrophobie ab.E in Peptid kann einem passiven Penetrationsmechanismus unterliegen, wenn es eher klein ist -d efiniert durch ein Molekülvolumen < 1500 3 entsprechend einem Peptid von < 1100-1200 Dalton. [65,135] Füre ine passive Zellpenetration ist auch die Zahl der solvensexponierten Wasserstoffbrückendonoren begrenzt.…”

Chiral Molecules as Sensitive Probes for Direct Detection of P -Odd Cosmic Fields

“…It is well known that such P-odd effects are strongly enhanced in chiral molecules, as the chiral arrangement of the nuclei leads to helicity in the electron cloud (see, e.g., Refs. [33,34]). Such P-odd effects can be measured as energy difference between enantiomers of chiral molecules or as resonance frequency differences between the two nonidentical mirror-image molecules [35,36].…”

“…Such P-odd effects can be measured as energy difference between enantiomers of chiral molecules or as resonance frequency differences between the two nonidentical mirror-image molecules [35,36]. As frequency shifts can be measured very accurately, this appears to be a particularly promising tool to search for P-odd cosmic field interactions (for recent reviews on molecular P violation, see [33,34,[37][38][39][40][41]). In the following we show advantages of the use of chiral molecules to search for P-odd cosmic field interactions.…”