Questions tagged [charge-conjugation]
The charge-conjugation tag has no usage guidance.
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Charge conjugation of the Dirac action
I'm following David Tong's convention on charge conjugation,
$$
\psi^c = C \psi^* \ , \qquad C^\dagger C = 1, \qquad C^{-1}\gamma^\mu C = - (\gamma^\mu)^* \ ,
$$
where $\gamma^0$ is hermitian, while $\...
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Unitary operator corresponding to charge conjugation
I understood that at the level of classical fields, the charge conjugation $C$ on a fermion field acts as follows:
$$\psi(x) \rightarrow \psi^c(x)=i \gamma^2 \gamma ^0 \overline{\psi(x)}^T$$
At the ...
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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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What causes the degrees of freedom to be halved for Majorana fermions?
In many textbooks and on this site (nanophys answer here) it is stated that 'Majorana Spinors have half the degrees of freedom of a typical Dirac spinor'. A generic spinor in 3+1D has 8 degrees of ...
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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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Charge conjugation matrix in terms of rank-2 antisymmetric tensors
I am having trouble with the sign when computing the charge conjugation matrix in the Weyl representation, namely I am yielding an additional minus sign.
Let me start with some of the conventions I ...
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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 of a pseudoscalar current
A pseudoscalar current $i\bar\psi \gamma^5 \psi$ is invariant under the charge conjugation $\psi \rightarrow \psi^c = -i\gamma_2\psi^*$. In particular, it is trivial if we consider a Majorana fermion $...
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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:
$$
[i \gamma^{\...
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$C$-conjugation of a gluon
In some explanations about the OZI rule ( for example at page 38 here), I found that gluons have definite eigenvalue of the charge conjugation operator $C$. The eigenvalue is $-1$. How can this result ...
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Charge conjugation of fields
This page on Wikipedia says, "In the language of quantum field theory, charge conjugation transforms as -
$\psi \Rightarrow -i\big(\bar{\psi} \gamma ^0 \gamma ^2 \big)^T $
$\bar{\psi} \...
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In this example, how can we have CP conservation with C violation?
Consider a simple two-body decay process $X\to Y+Z$ where $X$ is a boson, and $Y,Z$ are fermions. If $C$ is violated, $$\Gamma(X\to Y+Z)\neq \bar{\Gamma}(\bar{X}\to\bar{Y}+\bar{Z}).\tag{1}$$
However, ...
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C, P and T transformations of $\phi$ that preserves symmetry
I have a series of exercises regarding C, P and T symmetry but I am not really sure how to start with the problems. If anyone could help me with one of the problems, or show me a few example problems ...
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Does the $U(1)$ charge of a scalar particle flip under charge conjugation?
Consider a complex scalar particle $\phi$ coupled to an electromagnetic field. The Lagrangian is given by
$$ \mathcal{L} =(D_\mu \phi)^* D^\mu \phi - m^2 \phi^2 - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$...
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Why do we need two gluons for the decay $ϕ \to 2K$?
The Feynman diagram for the decay $\phi \to K^+K^-$ usually depicts two gluons. (This can be seen e.g. on Wikipedia).
Why do we need two gluons, instead of just one?
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Charge conjugation symmetry operation on single-particle Hamiltonian
How can I show that given the second-quantized Hamiltonian of a system of non interacting fermions
$\hat{\mathcal{H}}=\sum_{\alpha, \beta}\hat{\Psi}_{\alpha}^{\dagger}H_{\alpha\beta}\hat{\Psi}_{\...
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Is the $U(1)_A$ axial vector current even under charge conjugation?
The axial current of a Dirac spinor is given by $j_A^\mu = \bar{\psi} \gamma^5 \gamma^\mu \psi$. In this book, in the paragraph under equation (2.18) it is stated that the current is even under charge ...
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Does the $U(1)$ vector current flip under charge conjugation?
The conserved $U(1)$ current of the Dirac Lagrangian is given by $j^\mu = \bar{\psi} \gamma^\mu \psi$, where $\bar{\psi} = \psi^\dagger \gamma^0$. As this is interpreted as electric current I would ...
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QED $PC$ conservation
I'm trying to prove that the QED Lagrangian
$$\mathscr{L}=\bar{\psi}(i\!\!\not{\!\partial}-m)\psi - \frac{1}{4}F^{\mu\nu}F_{\mu\nu} - J^\mu A_\mu$$
Is invariant under P and C. The two fields transform ...
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What does it mean when a particle is an eigenstate of the charge conjugation operator?
I have limited background in Quantum Physics and am trying to understand some Particle Physics material.
I was reading about Charge Conjugation and it reads that "Most particles in nature are not ...
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What do you mean by in the mirror world?
I was trying an attempt to replicate Wu experiment mentally when I heard the term mirror world kept popping ups, why should we care what happens inside the mirror world? Is it a math thing?
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Confusion with the meanings of fermion fields $\hat{\Psi},\hat{\overline{\Psi}},\hat{\Psi}^C$
If $\hat{\Psi}$ is a field that annihilates an electron and creates a positron, $\hat{\overline{\Psi}}$ is a field that annihilates a positron and creates an electron. This takes all possibilities ...
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Commutations relations of C,P,T transformations with Lorentz group
Almost any QFT textbook discusses the C,P,T symmetry operators which are charge conjugation, parity transformation, time reversal respectively.
I failed so far to find any discussion of the ...
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$CP$-transformation for spinor field. $C$ and $P$ do not commute?
I am bothered by an exercise about CP transformations where I get the result that CP acting on a Dirac spinor field is not the same as the PC transformation. The exercise states the following ...
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Does charge conjugation symmetry sit in the Lorentz group?
We know the Lorentz group is $O(3,1)$ in 4 dimensional spacetime.
We know that there are 4 disconnected components in Lorentz group $O(3,1)$, and https://math.stackexchange.com/q/2204349/
$$\pi_0(\...
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Complex conjugation between particle/ anti-particle?
I am just a first year undergrad so I don't really know much about particle physics or the underlying mathematics. So I'm very sorry if the following question may be just stupid :D
So I noticed that ...
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Algebra of Time Reversal and Particle Hole Symmetry in 10-fold Classification of Topological Insulator/superconductor
In the ten fold classification of TI/TSC, when time reversal symmetry $\mathcal{T}$ and particle hole symmetry $\mathcal{P}$ are both present, i.e., in the symmetry classes BDI, DIII, CII, CI, for all ...
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Weak interaction and charge conjugation $C$
Does the weak interaction always change the charge of all participating particles?
And in this context, what does $C$-violation do then?
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Why does the majorana equation preserve handedness?
In the "QFT Nutshell" by A. Zee, it is stated that
The Majorana equation is
$$i\not\partial\psi=m\psi_c$$
where $\psi_c$ is the charge conjugated spinor $\psi_c = \left(C\gamma^0\right)\psi^*$....
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Why does the charge conjugation of the spinor transform as a spinor?
I have come across (in QFT Nutshell, A. Zee) how the charge conjugation of the spinor, $\psi_c \equiv \gamma^2 \psi^*$, transform (where $\gamma^2=\sigma^2\otimes i\tau^2$ is the component of the ...
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Detail on C vs. CP violation
In the answer given by knzhou to the post What distinguishes the behaviour of particle from its antiparticle: C violation or CP violation? it is said that
"but the reaction $i \rightarrow f$ will ...
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Why is charge conjugation $\hat C | \alpha \psi \rangle = C_\alpha |\alpha\psi \rangle$?
Charge conjugation replaces all particles by antiparticles in the same state, so that momenta, positions, etc are unchanged. It can be represented by
$$\hat C | \alpha \psi \rangle = C_\alpha |\alpha\...
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Feynman Rules from Lagrangian with charge conjugation matrix
I'm dealing with a doubly charged scalar singlet that interacts only with the
right-handed muon as follows,
$$\mathcal{L} = \lambda \psi_{R}C\psi_{R} \phi^{++},$$
where $\lambda$ is the coupling, $\...
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Why is the Higgs $CP$ even?
Why was it always assumed that the Higgs boson is a CP even particle?
I understand that experimentally, it just is so but I am under the impression that before its discovery people took it to be CP ...
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