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. A

    Chiral Anomaly (calculation)

    I am following Pierre Ramond's book "Field Theory - A Modern Primer", chapter 8, section 8.9, "Anomalies". My question starts in what follows from p.304. Homework Statement He draws the triangular diagram with one axial vector at one of the vertices and, using the standard Feynman rules...
  2. J

    Why and how chiral molecules rotate plane of polarisation?

    I have been studying stereochemistry and it says that optically active molecules(chiral molecules) rotate plane of polarisation. I suppose that's because of the electrons in the molecule. I know that all molecules can rotate the plane of polarisation but when achiral moelcules are present in...
  3. S

    Chiral currents of a Dirac plane wave

    I am currently trying to check the formula for the chiral current of the Dirac equation for a plane wave solution (found here ), that is, j_{R}^\mu = \psi_R^\dagger \sigma^\mu \psi_R j_{L}^\mu = \psi_L^\dagger \sigma^\mu \psi_L With \psi_R = I( \cosh(\frac{\theta}{2}) + \sigma^i...
  4. J

    Are Human Hands Truly Chiral?

    How are our hands chiral?? How are human hands chiral at all. Put them in the praying position and they are superimposable! "The left hand is a non-superposable 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...
  5. L

    Chiral sym breaking questions

    Hi, So to break the axial part of SU(2)_L \times SU(2)_R we use the composite field \chi_{\alpha i} \xi^{\alpha \bar{j}} (since this is Lorentz scalar, colour singlet, and has the right transformation under the flavour symmetries, only breaking the axial part etc). We assume that \langle...
  6. L

    Reading off masses of eight goldstone bosons from chiral Lagrangian mass term

    Hi, If I have three light quark flavours with massses m_u, m_d,m_s , I want to try and calcuate the masses of the eight pseudogoldstone bosons. I have found from my mass term in the Chiral L that: L_{mass}=-2v^3...
  7. L

    Chiral Lagrangian symmetry

    Hi, If I have the Lagrangian L=i\chi^{\dagger\alpha i}\bar{\sigma}^{\mu}(D_{\mu})_{\alpha}^{\beta}\chi_{\beta i}+i\xi^{\dagger}_{\bar{i}\alpha}\bar{\sigma}^{\mu}(\bar{D}_{\mu})^{\alpha}_{\beta}\xi^{\beta i}-1/4 F^{a\mu\nu}F_{\mu\nu}^{a} where \alpha,\beta are colour indices, and i=1,2 is a...
  8. C

    Why is it only chiral molecules that rotate plane polarized light?

    I just read that the reason molecules rotate plane polarized light is because the light interacts with the electron cloud of the molecule. That makes sense but why aren't achiral molecules optically active? Achiral molecules have electron clouds too so why don't their electron clouds cause...
  9. C

    Chemistry Specific Rotation of Chiral Molecules

    Homework Statement Why may the specific rotation of a sample of (R)-(+)-limonene be less than the literature value of (R)-(+)-limonene. Assume that there are so (S) enantiomers present. Homework Equations The Attempt at a Solution There are no (S) enantiomers, but there are some...
  10. M

    Chiral nematic liquid crystals - describing light diffraction

    So my book has an equation describing the wavelengths of light that are diffracted by a chiral nematic liquid crystal in terms of the refractive index (n), the pitch of the helix (p), and the angle (θ) with respect to the surface. The equation is this - λ = np√((1-cos2θ)/n2) If this isn't...
  11. T

    Meso Compounds with an odd number of chiral centers

    I was learning about chirality in my organic chemistry class when we were talking about meso compounds. The professor stated that for a compound to be meso, you needed there to be two or more chiral centers. After thinking about it for a while, I can come up with abstract structures for meso...
  12. C

    Calculating Feynman Rules for Effective Electroweak Chiral Lagrangian

    Hi all, I'm trying to calculate the Feynman Rules for the effective electroweak chiral Lagrangian. For example, this is the first term in the Lagrangian: \begin{eqnarray} \mathcal{L}=\frac{v^2}{4}\text{Tr}(D_{\mu}U D^{\mu}U^{\dagger}) \end{eqnarray} where \begin{eqnarray}...
  13. P

    Neuman stability and chiral question

    Homework Statement I have two questions. I have attached two pictures, 1 for each. 1. For the question about stability, the answer is C, but I thought it should be B. I would imagine the strain of two OH groups would be greater than an OH group with a CH3 group. Can someone explain what...
  14. O

    QFT Dirac Chiral Equations of Motion

    Homework Statement From Mandl and Shaw (exercise 4.5): Deduce the equations of motion for the fields: \psi_L(x)\equiv{1 \over 2} (1-\gamma_5)\psi(x) \psi_R(x)\equiv{1 \over 2} (1+\gamma_5)\psi(x) for non-vanishing mass, and show that they decouple in the limit m=0. Hence show that the...
  15. N

    Constructing Chiral Superfield from Vector Superfields

    Hi, Is it possible to construct chiral superfield from Vectorsuperfields and/or combinations of vector superfield and some another chiral superfield... Thanks
  16. S

    How many Higgsinos are there in the MSSM and what is their structure?

    Question 1: I am aware the Higgs lies in a chiral supermultiplet, but I realized I don't have an intuitive idea of i) how many Higgsinos there are (since the MSSM has 2 complex isodoublets) ii) how many Higgsinos there are after EWSB and you gauge away three of the scalar fields iii) their...
  17. J

    Questions about chiral symmetry breaking

    Hello everyone, I was learning about the topic "chiral symmetry breaking" recently and got couple questions. I try to describe my understandings below, then list the questions: From the QCD Lagrangian level (quark level), I can understand the exact chiral symmetry exists when we take...
  18. L

    Understanding Γ5 & Chiral Symmetry in QFT

    recently i am reading chiral symmetry in QFT. Almost all textbooks define γ5 as a chiral operator without saying some reasons. i am very confused why γ5 has something to do with chiral symmetry, can somebody explain it more intuitively and physically? who first introduce γ5 as a chiral...
  19. P

    Dynamical chiral symmetry breaking

    I don't know if it is the correct sub-forum, if I choose wrong then feel free to move the thread. I was listening to a talk today using DCSB. I think I could get a glimpse on some other parts of the talk and found some ideas intriguing. I would like to understand them better, but I cannot...
  20. J

    Where Can I Find Feynman Rules for Chiral Perturbation Theory?

    Hello, I was wondering whether anyone knows the Feynman rules for Chiral Perturbation theory? I am trying to calculate K->PiPi and have obtained the relevant diagrams but cannot proceed without the relevant feynman rules.
  21. D

    Organic Chemistry: No. of chiral centres in Camphor

    Hello. I have a query regarding organic chemistry. 1. http://tinyurl.com/y9nvg2p See question number 21. 2. Homework Equations : None 3. The first Carbon atom beneath the top-most CH3 group I can tell is a chiral centre, as it has 4 different groups attached to it (C=O, CH2...
  22. H

    Calculation trafo chiral multiplet

    Hello, I'm trying to deduce the suspersymmetry transformation of the chiral multiplet out of the superfield formalism. In doing this I got stuck with this...
  23. E

    Which fermions are chiral besides neutrinos?

    Wen local bosonic emergent string net model states he can give rise to electrons and photons, quarks and gluons but not chiral fermions. I know neutrinos are chiral. Any other fermions? If he can provide an explanation for masses and mixing angles for all SM particles except neutrinos...
  24. E

    Wen bosonic lattice model, chiral interactions, noncommutative space

    Hello, I know that Wen might be able to get W Z gauge bosons and chiral neutrinos using his lattice bosonic models he is unable to get chiral interactions using standard bosonic lattice on minkowski space. If instead he used Connes' noncommutative space would he be able to get chiral...
  25. turin

    Decoupled chiral Lorentz algebras

    Homework Statement Please bare with me; I don't know all of the terminology for this problem. In many textbooks, the six-dimensional Lie algebra of the Lorentz group is identified with the three components of the rotation generator and the three components of the boost generator. Then, the...
  26. G

    Chiral symmetry, quark condensate and self-energy

    Why in QCD chiral symmetry breaking study only the light quarks are taken into account? And why are their masses usually set to zero, Goldstone bosons are found, and then their masses are corrected by letting the quarks have non-zero mass? What happens if one study this symmetry breaking with...
  27. B

    Chiral symmetry breaking and approximate flavour symmetry

    I have 2 questions: 1. When there are no fermion mass terms, the Dirac part of the Lagrangian posseses an SU(N) left X SU(N) right flavour symmetry for N flavours of fermions. This can be "re-arranged" as an SU(N) vector X SU(N) axial symmetry. The axial part is spontaneously broken by the...
  28. V

    What is a Pseudochiral Carbon?

    i am trying to understand what a pseudochiral carbon is? please help thanks in advance
  29. S

    Chiral theories and matter gauges

    Is it true that classical theories tend to treat matter 'in the limit' of large N, or it encodes matter in N_A as N_A(m_e,e) say, and chiral theories need to include \hbar which classicality sees as \{G(h),c\} ? We use 'mass-free' theories that treat charge and spin momentum in circuits =...
  30. L

    Chemistry Where Is the Fifth Asymmetric Center in This Molecule?

    Please help me find an asymmetric center There are 5 asymmetric centers in this molecule. I think I've managed to find 4 of them, but where is the last?
  31. P

    Questions Chiral centers,Markonikov's rule

    I put all of my questions/solutions in the attached file...could someone please check over them before 7:00 am to see if I have them correct? Thanks in advance!
  32. J

    Chiral anomaly, pion to photon decay

    Hello, I understand that the non-zero (or non-small) rate for \pi^0 \rightarrow \gamma\gamma was historically a big motivation for the non-conservation of the axial current. I've been trying to work on problem IV.7.2 (p. 252) in Zee which asks to show that this amplitude vanishes if \partial_\mu...
  33. C

    Chiral Purity (enantiomer excess) for HPLC

    [SOLVED] Chiral Purity (enantiomer excess) for HPLC Hello! When I use HPLC to test Chiral Purity, obtain chromatogra and peak area. How do I calculate with Peak area? thanks!
  34. G

    Representing Chiral cyclohexane on a chair conformation

    For an assignment for organic chem the question asks to convert the structure of a compound into a chair conformation my question is that are equatorial substituents always the ones that are represented as a wedge on a structural diagram? If not could someone please give me tips on how to...
  35. N

    Understanding Chiral Symmetry in QCD for Heavy Ion Collisions

    Homework Statement I'm doing a dissertation on heavy ion collisions and one of the things they look for in the collisions is chiral symmetry resolution - what is it? Homework Equations The Attempt at a Solution I understand that it is a type of symmetry that is usually broken...
  36. marcus

    Exploring Chiral States in Quantum Gravity

    http://arxiv.org/abs/0710.1548 Propagation and interaction of chiral states in quantum gravity Lee Smolin, Yidun Wan 34 pages, 30 figures (Submitted on 5 Oct 2007) "We study the stability, propagation and interactions of braid states in models of quantum gravity in which the states are...
  37. A

    Understanding Chiral Theory & Its Significance

    Could somebody please tell me a workable definition of the term "chiral theory" , and also explain its significance? As far as I know, in a chiral theory not all the fermions obtain a mass but whether this is a definition or a derived result is not clear to me. Thanks in advance
  38. N

    Gents: Combining Chiral Currents with Translational Invariance

    Gents, Is it possible to have the not singular chiral current (singularity is due to the product of fermionic operators) and at the same time the translational invariance. Normaly to get rid of singularity in chiral current one is useing the point splitting regularisation (little shift of...
  39. N

    How Are Goldstone Bosons Formed in Chiral Symmetry Breaking?

    Dear PF, Could anyone help me to understand the following issue: I don't understand the formation of Goldston bosons in chiral symmmetry breaking. Namely - suppose there is only fermion fields Lagrangian and due to some reasons the fermion field obteins VEV - <0|psi^bar psi|0> is non...
  40. E

    Chiral Compounds: Properties and Examples

    From what I understand a chiral compound is one of which that when mirrored it is not identical. Not identical in what way's? Is it not superposable? Not have same properties? I have a multiple choise question asking which of the following is a chiral compound and the ones I choose are not...
  41. arivero

    Separate normalisation of chiral spinors?

    When solving Dirac equation (for free massive particles) we usually impose normalisation conditions upon the eigenfunction in a single stroke. I am wondering, Is it possible/useful to impose separate normalisation conditions upon the left and right spinors? Should we still have a resolution...
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