Questions tagged [charge-conjugation]

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Charge conjugation and chirality

while I was reading about charge conjugation I found some (apparently) contradictory facts. For example Itzykson & Zuber says (page 153) "Up to a phase, $\cal C$ interchanges particles and ...
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189 views

Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?

In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity $$ \overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}. $$ Here, I am using 4 ...
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136 views

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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257 views

Charge conjugation operator in second quantization

How can we write charge conjugation operator's action in second quantization's formalism? I don't know if I am explaining it correctly or not but I am interested in finding how can we write fermionic ...
3
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0answers
485 views

For fermion, is charge conjugate operator $C$ an anti-unitary operator?

In condensed matter theory, $C$ is called "particle-hole inversion", such that $C^2=-1$, for fermionic state. In high energy physics, just like most of the QFT textbooks, $C$ is introduced from Dirac ...
2
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64 views

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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503 views

Charge conjugation in chiral representation

I'm reading Maggiore's book and I got to the part of charge conjugation symmetry for Dirac spinor. I get that the definition of charge conjugation is representation-dependent, however I couldn't find ...
2
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0answers
313 views

Are Lifshitz and Berestetskii right in this case?

In the Quantum electrodynamics book (look at the problem) its authors Lifshitz and Berestetskei claim that operator of charge conjugation $\hat {C} = -\alpha_{2}$ in Majorana basis transforms as $\hat ...
1
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19 views

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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1answer
56 views

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 \...
1
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1answer
118 views

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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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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115 views

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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193 views

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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328 views

Antiparticle solution of the Dirac Equation

I'm really confused by the antiparticle solution of the Dirac equation. I follow Chapter 11 of Schwartz's book "Quantum Field Theory and the Standard Model" and find a couple of problems. In ...
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80 views

Questions about Five Dimensional SUSY Gauge Theories

I am studying the paper "Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces" by Intriligator, Morrison and Seiberg (arXiv:hep-th/9702198), and have a few questions ...
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36 views

CP-violating coupling

In this paper, after equation (38), there is the statement that the term $$\bar{t}\sigma^{\mu\nu}q_\nu\gamma_5tZ_\mu$$ is CP-violating. How exactly do we see this? Can anyone make explicit how we ...
1
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1answer
259 views

Charge conjugation of $|b\bar b\rangle$ states?

I know that for a state of a boson and its anti boson $|b\bar b\rangle$ the charge conjugation is $(-1)^{L+S}$ but I don't understand how this value is arrived at. Wikipedia says that is to do with ...
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104 views

Confused about anti-fermion notation

Classically anti-fields are obtained by charge conjugation, right? But sometimes authors label hermitian conjugated fields as anti-particles (or barred fields in Dirac language). But h.c. and charge ...
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1answer
29 views

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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30 views

How does theta term in non-abelian violate CP symmetry?

I am trying to show that theta-term violates P and CP symmetries, $$\theta \frac{g^2}{32\pi^2} G^a_{\mu\nu}\tilde{G}^a_{\mu\nu}$$ In the case of QED I could show that this term violates P and CP ...
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33 views

Do $C$-parity eigenstates have to have well defined exchange symmetry?

Obviously for C-parity eigenstates of a particle and itself (which is its own antiparticle) this is a wavefunction of identical particles and will thus have well defined exchange symmetry. I also ...
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32 views

Time reversal and charge conjugation for scalar electrodynamics

What happens to positive electric charge when the time direction is reversed? my intuition is this will not effect the type of electric charge (positive or negative) but how can I show it rigorously ...
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323 views

Invariance under charge conjugation… Or not?

I have read some paper which says that the electroweak Lagrangian includes these terms like $\bar{\psi} \gamma_a\gamma_5\psi$ and $\bar{\psi} \gamma_a \psi$. They violate charge conjugation symmetry. ...