Questions tagged [charge-conjugation]

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Is there a systematic way to construct the parity and charge conjugation operator for any Poincaré irreducible representation?

I am currently taking an undergraduate introductory QFT course. However, the proceeding will be about classical field theory, the results of which I assume will carry over mutatis mutandis into ...
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Charge conjugation is a symmetry for the quantized free Dirac action?

I am self-studying QFT on "A modern introduction to quantum filed theory" by Maggiore, and on page 95 he states: "For the free Dirac action, one immediately sees that C,P and T are ...
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Dirac field charge conjugation

I struggled a bit to understand the proof of the relation $C\overline\psi\psi C=\overline\psi\psi$ in Peskin's and Schroeder's book An Introduction to Quantum Field Theory (page 70, formula 3.147): $$...
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Dirac Lagrangian under charge conjugation

I am trying to understand why the Dirac Lagrangian is invariant under charge conjugation. The Dirac Lagrangian is: $$\mathcal{L} = i\bar{\psi}\gamma^\mu \partial_\mu\psi - m \bar{\psi}\psi $$ I know ...
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Charge conjugated Dirac equation

I would very much like to understand the motivation behind the correlation between: $(i\partial\!\!/-eA\!\!/-m)\psi=0$ and $(i\partial\!\!/+eA\!\!/-m)\psi_c=0$ when dealing with the derivation of the ...
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Do the WI coupling constants change sign under $C$?

I am trying to understand discrete symmetries in the SM, and I have some troubles in understanding why the CC interaction violates CP. In my (badly written) notes it's said that, taken two fermonic ...
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Euler-Lagrange for Dirac Lagrangian - is $\bar \psi$ independent of $\psi$?

In Peskin and Schroeder (3.34) they write the Dirac Lagrangian: $$ L_{Dirac} = \bar \psi (i \gamma^\mu \partial_\mu - m ) \psi $$ where $\bar \psi = \psi^\dagger \gamma^0$. Then, they write: "The ...
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Where does this charge conjugation coefficient come from? Wong's Introductory Nuclear Theory

I'm following Wong's Introductory Nuclear Physics, 2e. In section 2-4 there's a discussion of charge conjugation I don't fully follow. Something simple is escaping me. The excerpt is produced below, ...
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Are Hamiltonians CPT invariant?

I'm confused by the CPT theorem. It states (more or less) that a Lorentz invariant quantum field theory needs to be CPT invariant. But what does it actually mean for a QFT to be CPT invariant? It ...
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Charge congjuation and Transition form factors

Let us consider the transition form factor of proton to Delta (see reference of https://doi.org/10.1103/PhysRevD.100.034001): $\gamma^{\ast}p \to \Delta$. Then we should also have the timelike ...
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Why not put the anti-quarks in the conjugate representation?

The isospin doublet consisting of $u$ and $d$-quark is defined as $$ \begin{pmatrix} u\\ d \end{pmatrix}. \tag{1} $$ But the isospin doublet consisting of the antiquarks, $\bar{u}$ and $\bar{d}$, is ...
Solidification's user avatar
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Broken symmetry and three-photon vertex

I know that loop-level three-photon vertex in QED is zero since the contribution from fermion and antifermion cancel each other. Also, from what I know this has something to do with gauge invariance ...
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$C$-violation in SM Lagrangian?

It's usually said that SM Lagrangian violates charge conjugation, and should be obvious from the fact that "only left handed fermions are charged under $SU(2)_{L}$ but left and right handed ...
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Noether's Theorem application [duplicate]

So I know that Noether's theorem has a symmetry that corresponds to a conservation law. I was wondering what quantity is conserved in charge conjugation symmetry.
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Is the charge-conjugation symmetry in cond-mat physics different from that in QFT?

In condensed matter physics, the terms "particle-hole symmetry" and "charge-conjugation symmetry" are often used interchangeably. As far as I understand, they refer to the ...
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Charge conjugation of Fourier modes

Considering the charge conjugation operator acting on a complex scalar field: $$ \mathcal{C} \phi(x) \mathcal{C}^{-1} = \alpha \phi^{\dagger}(x) $$ By doing a Fourier expansion of the complex scalar ...
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Charge conjugation operator effect on electromagnetic potential

The charge conjugation operator acts on a complex scalar field as follows: $$ \mathcal{C} \phi(x) \mathcal{C}^{-1} = \alpha \phi(x)^{\dagger}$$ and by assuming that the interaction of the field with ...
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Charge+Parity operator lead left-handed to right-handed

So i need to show that the, if $\psi$ is left-handed, $$C\gamma^0\psi^*$$ Is right-handed. So, we know that, for any $\psi$, $P_L \psi$ is left handed. Also, for any $\omega$, is right-handed, $P_R \...
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The transformation of Gamma matrices under charge cojugation

Consider the Dirac field theory. In this theory the transformation of charge conjugation on a Dirac field is given by, $U(C) \psi(x) U(C)^{-1} = \eta_c C \psi^*(x)$, please note the $C$ give on RHS is ...
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Why the long lived Kaon can not decay into two pions?

The short-lived and long-lived states of kaon $|K_1>$ and $|K_2>$ respectively have the following compositions if they are the eigen states of CP parity: $|K_1> = \frac{|K^0>\:-\:|\bar{K^0}...
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If the protons in a nucleus were replaced by antiprotons and the electrons by positrons what fundamental change would be introduced into the universe?

Exactly what the question says; If all the protons and electrons in every single atom in the universe were swapped for their anti-particles, what would essentially change?
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Does Furry's Theorem for QED hold in lower dimensions as well?

In $1+3$ dimensional QED, it is well-known that an amplitude for a process described by a Feynman diagram with odd number of vertices is zero. This is Furry's Theorem. I wonder if this theorem holds ...
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Check of the Majorana condition in Srednicki's book

I wonder how it is possible to reach at the equation (37.18) also called the Majorana condition: $$\bar{\Psi} = \Psi^T {\cal{C}}\tag{37.18} $$ of Srednicki's book from (37.16), (37.17) and (37.19). We ...
Frederic Thomas's user avatar
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Charge Conjugation

For my calculations I need to know how charge conjugation acts on the Spin 3/2 propagator. The charge conjugation operator $C$ is calculated as $C= i\gamma^2\gamma^0$. The Spin 3/2 propagator is $$ S_{...
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How charge conjugation operator flips chirality

I am trying to understand the charge conjugation operator by reading several references online. Until I come to a point which mention that using the anticommutation properties of the Dirac-$\gamma$ ...
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Charge Conjugation of Dirac equation

In contituation of this question In answers of this question people mentioned charged conjugation and formula below $\bar{\psi}\gamma^\mu\psi=u^2-v^2$ With $u$ for particles and $v$ for antiparticles ...
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Regarding the action of Time reversal on Dirac spinors

I'm inquring about the difference between notions of time reversal found in Streater & Wightman's "PCT, Spin and Statistics, and All That", and this accepted answer from Chiral Anomaly. ...
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Time reversal or complex conjugate of Dirac spinor in Peskin & Schroeder QFT book

I have a naive question on the complex conjugate of Dirac spinor in Peskin & Schroeder QFT book (Introduction to quantum field theory), from the part below Eq.(3.137) of the book, $$ u(\tilde{p}, -...
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How is C-symmetry violated?

I see how P-symmetry and CP-symmetry are violated, but no one is talking about experiments related to C-symmetry. How did people prove that C-symmetry is violated?
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If protons were negative and electrons were positive, would Coulomb's Law change?

Coulomb's Law is $$F=k\frac{q_1 q_2}{r^2}$$ where $F$ is the force, $k$ is the Coulomb's universal constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between the two charges.
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Switching particles for antiparticles in Feynman diagrams

While studying, I found a problem involving $e^-\nu_e$ and $e^-\bar{\nu}_e$ scattering, though this could also apply to $e^- e^-$ and $e^- e^+$ scattering if we wanted to keep everything within QED. ...
ChemiCalChems's user avatar
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$C$-parity in $\pi^0\pi^+\pi^-$ system

I'm studying the conservation of the quantum number in the decay $\omega^0\rightarrow\pi^0\pi^+\pi^-$. Since $P(\omega^0)=-1$ and $P(\pi^0\pi^+\pi^-)=P(\pi^0)P(\pi^+)P(\pi^-)(-1)^{L_{+-}}(-1)^{L_{(+-)...
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Covariant derivative of Charge conjugation matrix

I'm thinking about the Clifford algebra in arbitrary dimensions, and following "Supergravity" from Freedman and Van Proeyen. Specifically I am working on problem 22.15 therein. The charge ...
Stardust9922's user avatar
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Does electrons keeps on removing from conductor under this setup? [duplicate]

Let say we bring a conductor near a high static positively charged surface and connect earth to the side of conductor facing the positively charged surface. Then due to positively charged surface, let ...
Aniket Kumar's user avatar
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Why does $C$-parity forbid odd number of photons in pion decay, but not in positronium decay? (Martin-Shaw)

I'm reading Martin and Shaw's "Particle Physics." In Section 5.4.1 they show how $C$-parity restricts the number of photons in pion decay to an even number of photons: $$ \pi^0=u\bar u\...
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Is CPT a unitary symmetry or an antiunitary symmetry?

Is CPT a unitary symmetry or an antiunitary symmetry, such as the free Dirac theory of fermion $\psi$ in Chapter 3 of Peskin's QFT book? Since T is antiunitary symmetry, P is unitary symmetry, C is ...
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Complex conjugation in time-reversal $T$ symmetry v.s. in charge conjugation $C$ symmetry

How is the complex conjugation $K$ of time-reversal symmetry $T$ differed by the complex conjugation of charge conjugation $C$? How are they differed from each other? For instance, take the Dirac ...
Марина Marina S's user avatar
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Complex conjugation of negative energy solutions of the Klein-Gordon-equation

In the university (of Cambridge) script "Gauge Field Theory" of Ben Gripaios on p.11 the positive and negative energy (or if you prefer positive & negative frequency) solutions of the ...
Frederic Thomas's user avatar
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Charge Conjugation to Analyze CPT Invariance

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/cpt.html#:~:text=Charge%20conjugation(C)%3A%20reversing,like%20momentum%20and%20angular%20momentum. In the image below, reaction (1) shows ...
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Define $C,P,T$ symmetry transformation in even dimensional $d$ spacetime on a relativistic Weyl fermion theory

According to https://physics.stackexchange.com/a/488388/42982 we can define $C,P,T$ discrete symmetry transformation in even dimensional spacetime. How could we write $C,P,T$ symmetry transformation ...
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What is the correct relation between Dirac matrices and Charge conjugation?

Setup Let $C$ be the charge conjugation operator for spinors and $\gamma$ a Dirac matrix. From this post we conclude that the critical relation between the operator and the Dirac matrices is $$-C(\...
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Charge conjugation Operator for non-abelian group of a fermion

For deriving the Charge conjugation operator one (the Schwartz book) takes the complex conjugate of the Dirac equation like the following, where $\psi_c=C\psi^*$: $$(i\partial_\mu \gamma^\mu-eA_\mu\...
krabby patty's user avatar
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How do charge conjugate fields transform under $SU(2)$ and $SU(3)$?

I am trying to derive the gauge transformation for the charge conjugate field of a quark doublet (left handed quark) such that its field $Q$ transforms under $SU(2)$ and $SU(3)$ as: $SU(2):$ $Q \...
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Charge conjugation on spinors: Am I missing a (-1)? [duplicate]

I'm trying to prove the transformation rules for Dirac Bilinears under charge conjugation as given in "Fundamentals of neutrino physics and astrohysics" by Carlo Giunti et.al. According to ...
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Complex conjugate of the Dirac equation

(Following the calculations done in 'Quantum Field Theory in a Nutshell' [Second Edition] by Zee, Page 101) The Dirac equation in the presence of an electromagnetic field is given by: $$ [i \gamma^{\...
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$C$-conjugation of a gluon

In some explanations about the OZI rule ( for example at page 38 here), I found that gluons have definite eigenvalue of the charge conjugation operator $C$. The eigenvalue is $-1$. How can this result ...
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Charge conjugation of fields

This page on Wikipedia says, "In the language of quantum field theory, charge conjugation transforms as - $\psi \Rightarrow -i\big(\bar{\psi} \gamma ^0 \gamma ^2 \big)^T $ $\bar{\psi} \...
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In this example, how can we have CP conservation with C violation?

Consider a simple two-body decay process $X\to Y+Z$ where $X$ is a boson, and $Y,Z$ are fermions. If $C$ is violated, $$\Gamma(X\to Y+Z)\neq \bar{\Gamma}(\bar{X}\to\bar{Y}+\bar{Z}).\tag{1}$$ However, ...
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C, P and T transformations of $\phi$ that preserves symmetry

I have a series of exercises regarding C, P and T symmetry but I am not really sure how to start with the problems. If anyone could help me with one of the problems, or show me a few example problems ...
a20's user avatar
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Does the $U(1)$ charge of a scalar particle flip under charge conjugation?

Consider a complex scalar particle $\phi$ coupled to an electromagnetic field. The Lagrangian is given by $$ \mathcal{L} =(D_\mu \phi)^* D^\mu \phi - m^2 \phi^2 - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$...
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