Questions tagged [charge-conjugation]
The charge-conjugation tag has no usage guidance.
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Action of charge conjugation on bispinors
I'm following an introductory course to particle physics. We have introduced Klein-Gordon's equation for spinless particles and Dirac's equation for spin $1/2$ particles. Klein-Gordon's equation works ...
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$CP$-transformation for fermionic bilinears
I am trying to derive the transformation of the fermionic bilinear $\bar{\psi}\psi$ under $CP$ transformation.
I know that $P$ acts as:
$$\psi(t, \vec{x}) \xrightarrow{P} \gamma^0 \psi(t, -\vec{x})$$
...
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$C$-number ignored in charge conjugation
In Weinberg’s QFT V1, under equation 5.5.58, he says that an anticommutator ($c$-number) can be ignored when we exchange spinors, $\psi$ and $\bar{\psi}$. I cannot fully appreciate why we can ignore ...
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Why is charge parity (eigenvalue of $\hat{C}$) conserved?
Looking at processes with neutral initial and final state, for example
$$e^+e^- \rightarrow \gamma \gamma$$
we know that charge parity (eigenvalue of charge conjugation operator $\hat{C}$) is ...
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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 $$
where $\bar \psi = \psi^\dagger \gamma^0$.
Then, they write: "The ...
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Where does this charge conjugation coefficient come from? Wong's Introductory Nuclear Theory
I'm following Wong's Introductory Nuclear Physics, 2e. In section 2-4 there's a discussion of charge conjugation I don't fully follow. Something simple is escaping me. The excerpt is produced below, ...
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Are Hamiltonians CPT invariant?
I'm confused by the CPT theorem. It states (more or less) that a Lorentz invariant quantum field theory needs to be CPT invariant. But what does it actually mean for a QFT to be CPT invariant? It ...
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Charge conjugation and Transition form factors
Let us consider the transition form factor of proton to Delta (see reference of https://doi.org/10.1103/PhysRevD.100.034001):
$\gamma^{\ast}p \to \Delta$.
Then we should also have the timelike ...
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Why not put the anti-quarks in the conjugate representation?
The isospin doublet consisting of $u$ and $d$-quark is defined as
$$
\begin{pmatrix}
u\\
d
\end{pmatrix}.
\tag{1}
$$
But the isospin doublet consisting of the antiquarks, $\bar{u}$ and $\bar{d}$, is ...
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Broken symmetry and three-photon vertex
I know that loop-level three-photon vertex in QED is zero since the contribution from fermion and antifermion cancel each other.
Also, from what I know this has something to do with gauge invariance ...
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$C$-violation in SM Lagrangian?
It's usually said that SM Lagrangian violates charge conjugation, and should be obvious from the fact that "only left handed fermions are charged under $SU(2)_{L}$ but left and right handed ...
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Noether's Theorem application [duplicate]
So I know that Noether's theorem has a symmetry that corresponds to a conservation law.
I was wondering what quantity is conserved in charge conjugation symmetry.
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Is the charge-conjugation symmetry in cond-mat physics different from that in QFT?
In condensed matter physics, the terms "particle-hole symmetry" and "charge-conjugation symmetry" are often used interchangeably. As far as I understand, they refer to the ...
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Charge conjugation of Fourier modes
Considering the charge conjugation operator acting on a complex scalar field:
$$ \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} $$
of Srednicki's book from (37.16), (37.17) and (37.19).
We ...
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Charge Conjugation
For my calculations I need to know how charge conjugation acts on the Spin 3/2 propagator. The charge conjugation operator $C$ is calculated as $C= i\gamma^2\gamma^0$. The Spin 3/2 propagator is
$$
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}$$
where $F$ is the force, $k$ is the Coulomb's universal constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between the two charges.
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Switching particles for antiparticles in Feynman diagrams
While studying, I found a problem involving $e^-\nu_e$ and $e^-\bar{\nu}_e$ scattering, though this could also apply to $e^- e^-$ and $e^- e^+$ scattering if we wanted to keep everything within QED.
...
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$C$-parity in $\pi^0\pi^+\pi^-$ system
I'm studying the conservation of the quantum number in the decay $\omega^0\rightarrow\pi^0\pi^+\pi^-$. Since
$P(\omega^0)=-1$
and
$P(\pi^0\pi^+\pi^-)=P(\pi^0)P(\pi^+)P(\pi^-)(-1)^{L_{+-}}(-1)^{L_{(+-)...
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Covariant derivative of Charge conjugation matrix
I'm thinking about the Clifford algebra in arbitrary dimensions, and following "Supergravity" from Freedman and Van Proeyen. Specifically I am working on problem 22.15 therein.
The charge ...
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Does electrons keeps on removing from conductor under this setup? [duplicate]
Let say we bring a conductor near a high static positively charged surface and connect earth to the side of conductor facing the positively charged surface. Then due to positively charged surface, let ...
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Why does $C$-parity forbid odd number of photons in pion decay, but not in positronium decay? (Martin-Shaw)
I'm reading Martin and Shaw's "Particle Physics."
In Section 5.4.1 they show how $C$-parity restricts the number of photons in pion decay to an even number of photons:
$$ \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 ...
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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 ...
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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\...
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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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