What is Charge conjugation: Definition and 31 Discussions

In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal).
These discrete symmetries, C, P and T, are symmetries of the equations that describe the known fundamental forces of nature: electromagnetism, gravity, the strong and the weak interactions. Verifying whether some given mathematical equation correctly models nature requires giving physical interpretation not only to continuous symmetries, such as motion in time, but also to its discrete symmetries, and then determining whether nature adheres to these symmetries. Unlike the continuous symmetries, the interpretation of the discrete symmetries is a bit more intellectually demanding and confusing. An early surprise appeared in the 1950's, when Chien Shiung Wu demonstrated that the weak interaction violated P (and thus C) symmetry. For several decades, it appeared that the combined symmetry CP was preserved, until CP-violating interactions were discovered. Both discoveries lead to Nobel prizes.
The C-symmetry is particularly troublesome, physically, as the universe is primarily filled with matter, not anti-matter, whereas the naive C-symmetry of the physical laws suggests that there should be equal amounts of both. It is currently believed that CP-violation during the early universe can account for the "excess" matter, although the debate is not settled. Earlier textbooks on cosmology, predating the 1970's, routinely suggested that perhaps distant galaxies were made entirely of anti-matter, thus maintaining a net balance of zero in the universe.
This article focuses on exposing and articulating the C-symmetry of various important equations and theoretical systems, including the Dirac equation and the structure of quantum field theory. The various fundamental particles can be classified according to behavior under charge conjugation; this is described in the article on C-parity.

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  1. B

    Charge-Conjugation property

    I'm probably just complicating things, but I'm a little bit stuck with this problem. I started with just plugging in the definitions for ##\bar{\Psi}_a^c## and ##\Psi_b^c##. So I get $$\bar{\Psi}_a^c\gamma^{\mu}\Psi_b^c=-\Psi_a^TC^{-1}\gamma^{\mu}C\bar{\Psi}_b^T$$. After this I used...
  2. J

    A Charge conjugation in quantum gravity

    The charge associated with gravitational interactions is the mass. In the Standard Model, charge conjugation is the "flippin" of all kinds of charges (electric, color, etc). So, if we were to, say, incorporate quantum gravity in a beyond the Standard Model theory, what would the full charge...
  3. L

    I C-parity π+ π- π0: Is (-1)^L (+1) Correct?

    The C-parity of π+ π- alone is simply (-1)^L, where L is the angular momentum quantum number for the system. But then what is C-parity of π+ π- π0? Is it simply (-1)^L (+1), where L is the angular momentum quantum number for the π+ π- subsystem (which isn't necessarily the angular momentum of...
  4. The black vegetable

    I Does the Charge Conjugation Operator Affect Gamma Matrices Similarly?

    I have in my notes the charge conjugation operator converts the spinnor into its complex conjugate , ## C\begin{pmatrix} \varepsilon \\ \eta \end{pmatrix}=\begin{pmatrix} \varepsilon^{*}{} \\ \eta ^{*} \end{pmatrix}##when applied to gamma matrix from dirac equation does it do the same...
  5. F

    A G-parity - where does the minus sign come from?

    Hi all, I have a question on G-parity. I know it's defined as ## G = exp(-i\pi I_{y})C ##, with ##I_y## being the second component of the isospin and ##C## is the C-parity. In other words, the G-parity should be the C-parity followed by a 180° rotation around the second axis of the isospin...
  6. G

    A Does Charge Conjugation change the electromagnetic field?

    Is there a difference between the meaning of charge conjugation in Relativistic Quantum Mechanics and its meaning in Quantum Field Theory? In chapter 4.7.5 of "Thomson Modern Particle Physics" the charge conjugation operator is derived without changing the electromagnetic field Aμ. This...
  7. Gene Naden

    I CP transformation, charge conjugation and antimatter

    Many discussions cite CP transformation as the exchange of particles for anitparticles. But other places it says that charge conjugation alone is sufficient to turn a particle into its antiparticle. So, the question is, when you exchange particles for anitparticles, is it a CP transformation or...
  8. diegzumillo

    A Charge conjugation in Peskin and Schroeder

    Hey there I'm trying to reconstruct the entire table of all Dirac bilinears under C, P, T and CPT transformations of page 71 and hit a wall on charge conjugation. It's a computational problem, really. Here's a specific problem: Equation 3.145 we have $$-i\gamma ^2 \left( \psi ^{\dagger...
  9. J

    I Charge conjugation and spatial wave function

    Hi, I'm recently reading something which briefly introduces C symmetry. So the thing that confuses me is that how does the spatial wave function contribute the (-1)^L factor? Thanks!
  10. T

    I Question regarding the charge conjugation operator

    So I am aware the charge conjugation operator changes the sign of all internal quantum numbers. But I was wondering how it acts on a state such as ## \left|\pi^{+} \pi^{-} \right>## when the individual ##\pi's## are not eigenstates of C. I believe the combination of the ##\pi's## has eigenvalue...
  11. C

    I Charge conjugation properties of the gluon

    The intrinsic charge parity of a species is the ##\eta_C## defined in the equation $$\mathcal C |\psi \rangle = \eta_C |\psi \rangle $$ which can take on values ##\pm 1##. Since the gluon carries a colour charge, it is not an eigenstate of the C (charge conjugation) operator. 1) Why do I...
  12. Andrea M.

    I Charge conjugation of Majorana pairs

    I was reading this article (http://arxiv.org/abs/1301.0021) about WIMP pair annihilation. At page six the author says that under charge conjugation a state of Majorana particles with orbital angular momentum ##L## and spin angular momentum ##S## take a phase ##(-1)^{L+S}##. I understand this...
  13. andrex904

    Exploring Parity & Charge Conjugation in Z Boson Decay

    Considering a Z boson decay into a fermion-antifermion pair. How can i say if the process respect parity and charge conjugation?Thanks
  14. S

    Charge conjugation matrix and Dirac equation's solutions

    I saw this somewhere but I think it is wrong... I already read Griffiths' "Introduction to Particle Physics" (the 1st edition) from the page 216 to the page 222 (chapter of Quantum Electrodynamics - section "Solution to the Dirac Equation") and I didn't understood why was there the imaginary...
  15. S

    Does charge conjugation affect parity?

    "Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in the Standard Model." --https://en.wikipedia.org/wiki/C-symmetry The excerpt above seems to...
  16. 1

    Rules of Parity and Charge Conjugation Parity

    I have two related questions to ask relating to statements found in introductory particle physics textbooks. The first is that the "Dirac equation predicts fermions/anti-fermions have opposite intrinsic parity". I have attempted to verify this by applying the parity transformation to free...
  17. G

    List of Charge Conjugation and Parity numbers

    Hi everyone, i am just wondering why I cannot find a list of Charge Conjugation and Parity numbers for all the appropriate particles? I mean, I can look online and sift through sources for individual particles (for example, after some research I have found the the photon has a charge...
  18. Einj

    Charge conjugation and time reversal in the SM

    Hi everyone. I have a doubt on charge conjugation symmetry. Consider the Standard Model lagrangian with just the gauge and the fermionic part (no Higgs and no Yukawa). This is invariant under SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_Y. Moreover, as any other field theory, it is CPT...
  19. C

    [Srednicki] Charge Conjugation of Dirac Spinor

    Homework Statement I am reading Srednicki's QFT up to CPT symmetries of Spinors In eq. 40.42 of http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf I attempted to get the 2nd equation: C^{-1}\bar{\Psi}C=\Psi^{T}C from the first one: C^{-1}\Psi C=\bar{\Psi}^{T}C Homework Equations...
  20. F

    Charge conjugation in Dirac equation

    I need to know the mathematical argument that how the relation is true $(C^{-1})^T\gamma ^ \mu C^T = - \gamma ^{\mu T} $ . Where $C$ is defined by $U=C \gamma^0$ ; $U$= non singular matrix and $T$= transposition. I need to know the significance of these equation in charge conjuration .
  21. L

    Charge conjugation in second quantization

    We know that under charge conjugation the current operator reverses the sign: \hat{C} \hat{\bar{\Psi}} \gamma^{\mu} \hat{\Psi} \hat{C} = - \hat{\bar{\Psi}} \gamma^\mu \hat{\Psi} Here \hat{C} is the unitary charge conjugation operator. I was wondering should we consider gamma matrix...
  22. N

    Charge conjugation for Dirac particles (error in problem?)

    Homework Statement Show that if \psi is a down-spin anti-electron, and we apply charge conjugation, then \psi^C is an up-spin electron. The Attempt at a Solution My calculations suggest that the anti-electron indeed becomes an electron; however, spin does not change for me. Is it possible...
  23. V

    Finding Charge Conjugation Eigenvalues

    I've just recently been introduced to charge conjugation while reading the introductory particle physics texts by Griffiths and Perkins, and neither one really seem to explain how you go about finding the values for C. For example, if I wanted to find the value for the \rho^0 meson (which I...
  24. E

    Charge Conjugation and Internal Symmetry Representations

    Hi All, I am trying to work through a QFT problem for independent study and I can't quite get my head around it. It is 5.16 from Tom Bank's book (http://www.nucleares.unam.mx/~Alberto/apuntes/banks.pdf) which goes as follows: "Show that charge conjugation symmetry implies that the...
  25. F

    Bilinear terms in QED lagrangian under charge conjugation

    Homework Statement I want to check that the QED lagrangian \mathcal{L}=-\frac{1}{4}F^{\alpha\beta}F_{\alpha\beta} + \bar\Psi(i\displaystyle{\not} D - m)\Psi where F^{\alpha\beta} = \partial^\alpha A^\beta - \partial^\beta A^\alpha, \ D^\mu = \partial^\mu - ieA^\mu is invariant under charge...
  26. O

    Charge conjugation of Complex Klein Gordon Lagrangian

    Homework Statement Show that the complex Klein-Gordon Lagrangian density: L=N\left(\partial_\alpha\phi^{\dagger}(x)\partial^\alpha\phi(x)-\mu^2\phi^{\dagger}(x)\phi(x)\right) is invariant under charge conjugation: \phi(x)\rightarrow C\phi(x)C^{-1}=\eta_c \phi^\dagger (x) Where C...
  27. F

    What changes under charge conjugation

    Hi! Which quantum numbers change under the charge conjugation operation? Electric charge - yes Spin - no Isospin - ? z-component of isospin - ? Hypercharge - ? Parity - ?
  28. maverick280857

    Does Charge Conjugation Flip Spin?

    Hi, According to Perkins (4th edition, pg 73 section 3.6) the operation of charge conjugation reverses the sign of the charge and the magnetic moment of a particle. Does this mean the spin also flips? But according to Griffiths, the spin is untouched by charge conjugation. What...
  29. K

    Change of energy under charge conjugation

    I was going through an article on antiparticles: http://www.statemaster.com/encyclopedia/Antiparticles The article mentions that energy is unchanged under charge conjugation among the CPT operations. I do not understand this. Shouldn't a charged particle in an electric field have a change...
  30. S

    Help About charge conjugation of Dirac spinor

    The following formula appears in P J Mulders's lecture notes http://www.nat.vu.nl/~mulders/QFT-0E.pdf {\cal C}~b(k,\lambda)~{\cal C}^{-1}~=~d(k,{\bar \lambda}) (8.18) where {\cal C} is charge conjugation operator. \lambda is helicity. I don't know why there is {\bar {\lambda}} on the...
  31. wolram

    Charge Conjugation Invariance of the Vacuum

    http://arxiv.org/abs/hep-th/0507020 Title: Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem Authors: J. W. Moffat Comments: 14 pages, Latex file, No figures We propose a method of field quantization which uses an indefinite metric in a Hilbert space of...
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