# What is Chiral: Definition and 91 Discussions

Chirality is a property of asymmetry important in several branches of science. The word chirality is derived from the Greek χειρ (kheir), "hand," a familiar chiral object.
An object or a system is chiral if it is distinguishable from its mirror image; that is, it cannot be superimposed onto it. Conversely, a mirror image of an achiral object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called enantiomorphs (Greek, "opposite forms") or, when referring to molecules, enantiomers. A non-chiral object is called achiral (sometimes also amphichiral) and can be superposed on its mirror image.
The term was first used by Lord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club which was published in 1894:

I call any geometrical figure, or group of points, 'chiral', and say that it has chirality if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself.
Human hands are perhaps the most universally recognized example of chirality. The left hand is a non-superimposable mirror image of the right hand; no matter how the two hands are oriented, it is impossible for all the major features of both hands to coincide across all axes. This difference in symmetry becomes obvious if someone attempts to shake the right hand of a person using their left hand, or if a left-handed glove is placed on a right hand. In mathematics, chirality is the property of a figure that is not identical to its mirror image. A molecule is said to be chiral if its all valence is occupied by different atom or group of atoms.

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1. ### I Propagator of massless Weyl field

I have this Lagrangian for a free massless left Weyl spinor, so it’s just the kinetic term, that can be written embedding the field into a larger Dirac spinor and then taking the left projector in this way: $$i \bar{\psi} \cancel{\partial} P_L \psi$$ Srednicki says that the momentum space...
2. ### I Chiral symmetries in E[SUP]^n[/SUP]

As a biochemist, I deal with chirality of molecules all the time. If you have a tetrahedral molecule, for example a carbon atom, and all 4 vertices are labeled differently, as in different atoms on each one, then that molecule has a mirror-symmetric one that cannot be superimposed on the...
3. ### I Why is K an anti-unitary operator in (26)?

Hey all, I just wanted to double check my understanding of (26) in the following notes: https://arxiv.org/pdf/1512.08882.pdf. Is the reason that ##(U_{T}\cdot K) \cdot (U_{C}\cdot K) = U_{T}\cdot U_{C}^{*}## because ##K## is a unitary operators and thus ##(K\cdot U_{C}\cdot K) = U_{C}^{*}## as...
4. ### A Question about chiral molecules

Hello! I started reading a bit about chiral molecules, and I have some questions. For reference, I will use this article for my questions. In Figure 1 in that article they show the energy levels for a typical chiral molecule (my question is for the case in which the left/right enantiomers are...
5. ### Chiral Column Chromatography

"Resolution of enantiomers can be accomplished using column chromatography. When enantiomers are passed through a traditional column, they travel at the same rate because their properties are identical. However, if a chiral adsorbent is used, the enantiomers interact with the adsorbent...
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30. ### Sum of spin for chiral particles?

How does the spin of a pair of particles work if both particles are known to be chiral? generically if I sum the spins of two different (EDIT: spin 1/2, indeed ;-) particles I expect to get a triplet with S=1 \uparrow\uparrow, \uparrow\downarrow+\downarrow\uparrow, \downarrow\downarrow and...
31. ### Chiral gauge theory and C-symmetry

Hi, I have a question in Srednicki's QFT textbook. In p.460 section 75(about Chiral gauge theory), it says "In spinor electrodynamics, the fact that the vector potential is odd under charge conjugation implies that the sum of these diagrams(exact 3photon vertex at one-loop) must vanish."...
32. ### Chiral leptoquarks and vector currents

In a comment http://motls.blogspot.com.es/2014/07/cms-sees-650-gev-leptoquarks.html#comment-1479399237 to Motl's blog, there are some reference to "chiral leptoquarks". I am guessing that this is an object which is not a Dirac fermion, ie it only exists one of the two chiral components of it...
33. ### Constraints on Chiral superfield

Suppose we have a superfield \Phi(x,\theta,\bar{\theta}) this can be expanded in component fields in the standard way as: \Phi(x,\theta,\bar{\theta})= c(x) + \theta \psi(x) + \bar{\theta} \bar{ζ}(x) + \theta^{2} F(x) + \bar{\theta}^{2} Z(x) + \theta \sigma^{\mu} \bar{\theta} u_{\mu}(x) +...
34. ### How Does Chiral Symmetry Breakdown Influence Meson Mass Differences?

Why is the chiral symmetry breakdown determined for the vector/axial current as: V = \frac{m_{π^{+}}-m_{π^{0}}}{m_{π^{0}}+m_{π^{+}}}\approx 0.01 A= \frac{m_{π^{+}}-m_{f^{0}}}{m_{f^{0}}+m_{π^{+}}}\approx 1 ? why do we choose the difference between the pion+ (~140MeV) and pion0 (~135MeV)...
35. ### Chiral life concept - creating mirror image synthetic life?

Imagine mirror image of a cell - built from a scratch using mirror images (enantiomers) of molecules of the original cell. It should work as standard one, but use e.g. L-sugars instead of our D-sugars: article. Some possible applications: - doubling the space of possible enzymes we could...
36. ### Finding Chiral Centres in Ring Structures

How to find chiral centres of rings structures?For example take the following ringhttp://img203.imageshack.us/img203/7994/8vmq.jpg How to calculate no. of chiral centres?? thanks
37. ### Self energy logarithmic divergence due to chiral symmetry.

In peskin at page 319 right above equation (10.6) he writes "If the constant term in a taylor expansion of the self energy were proportional to the cutoff ##\Lambda##, the electron mass shift would also have a term proportional to ##\Lambda##. But the electron mass shift must actually be...
38. ### Chemistry Chirality: why these molecules are not chiral?

Homework Statement Look at the image please. The image shows 3 pairs of compounds. Explain why the first two are not chiral but the last one is chiral. Homework Equations Ar means Aromatic ring Aquirais means aquiral Quirais means chiral The Attempt at a Solution...
39. ### Operator algebra of chiral quasi-primary fields

Studying conformal field theory, I tried to derive general expression for the commutation relations of the modes of two chiral quasi-primary fields. At first, I expressed the modes \phi_{(i)m} and \phi_{(j)n} as contour integrals over each fields, and took commutation relation. I used...
40. ### Relationship between photochemical mechanisms and chiral molecules

I'm way outside my realm of knowledge here so perhaps I need some help polishing my question or the concepts behind it. Thank you for your patience. Does the orientation of circularly polarized light (CPL) as a reaction mechanism influence the chirality of the molecule in a general manner...
41. ### Chiral symmetry and quark condensate

I'm studying chiral symmetry in QCD. I understand that in order for a spontaneous symmetry breaking to occur, there must be some state with a vacuum expectation value different from zero. My question is: can someone prove that is the chiral symmetry is an exact symmetry of the QCD then...
42. ### Chiral Perturbation Theory : pi0 pi0 Z vertex?

Not sure if anyone has any experience with chiral perturbation theory, but I'm trying to see what all of the vertices are for interactions with a single Z boson. I've looked at the lagrangian up to order p^4 so far, and it seems that the Z only interacts with charged pions/kaons. I'm using...
43. ### Achiral and Chiral Compounds - B and D

Compounds B and D both have no chiralaty centers - but it seems to me that B has a plane of symmetry so it's achiral, and D has no plane of symmetry so it's chiral. I always thought though, that if a compound has no chiral centers then you can say with conffidence it's achiral. Is my analysis...
44. ### 2 dimensional chiral boson theory

I am reading the paper "Covariant Action for a D=11 Five-Brane with the Chiral Field" and want to make an analog for the chiral field in 2 dimensions. But I don't know at the starting point, for if I take the local coordinates of the worldvolume to be ##x^m (m=0,1)##, the dual field strength...
45. ### Choose from Unknown - A Chiral Compound

A C8H12 chiral hydrocarbon, X, is reduced by catalytic Hydrogenation to an achiral C8H14. Ozonolysis (Oxidative) of X gave a chiral C8H12O4 dicarboxylic acid. Choose X from the given. Attempt I first determined the chirality of the given alternatives. That rules out the 2nd option, as it...
46. ### Pyrrolidine: Achiral or chiral?

Hi everyone, this is my first time posting to this website. I'm just trying to study for organic chemistry, and I've been having a little trouble trying to grasp the concept of chiral/achiral. The book talks about pyrrolidine,C4H9N, and it asks whether or not pyrrolidine could be used to...
47. ### I don't understand why it's chiral. It's not like any of the phenyl

I don't understand why it's chiral. It's not like any of the phenyl rings are stuck in a single resonance structure.
48. ### Chiral Perturbation Theory : Some quick questions

I just want to make sure that I am doing some things correctly. I'll be using http://www.physics.umd.edu/courses/Phys741/xji/chapter5.pdf from about 5.64 on. The kinetic term : \frac{f^2}{4} Tr[D_{\mu} \Sigma D^{\mu} \Sigma^{\dagger}] Now if I want to expand this out, as \Sigma =e^{i...
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### Understanding Chirality and Enantiomers: Differences and Similarities

What makes something chiral, but not an enantiomer? It seems like they have the exact same definition
50. ### Oxidation state and chiral configurations

I'm doing this same problem found on the following link for a biochemistry homework. http://www.chegg.com/homework-help/questions-and-answers/nucleoside-phosphorothioates-synthetic-nucleotide-analogs-used-enzymology-molecular-biolog-q1481931 My question is regarding both finding the...