Questions tagged [charge-conjugation]

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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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24 views

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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59 views

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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1answer
162 views

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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22 views

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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3answers
154 views

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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26 views

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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1answer
53 views

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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1answer
116 views

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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42 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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55 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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25 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
108 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 \...
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1answer
70 views

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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40 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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1answer
281 views

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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35 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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1answer
160 views

$C$-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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1answer
244 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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1answer
94 views

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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97 views

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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2answers
140 views

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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1answer
76 views

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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1answer
85 views

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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1answer
278 views

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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2answers
205 views

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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0answers
87 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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1answer
502 views

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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3answers
187 views

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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1answer
72 views

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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1answer
51 views

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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1answer
216 views

$CP$-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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1answer
232 views

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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47 views

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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2answers
258 views

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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134 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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1answer
470 views

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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222 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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1answer
52 views

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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1answer
590 views

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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2answers
505 views

Invariance of Yang-Mills Lagrangian under charge conjugation

The Yang-Mills Lagrangian gauge invariant under an $SU(N)$ tranformation can be written as $${\cal L} = -\frac{1}{4}F_{\mu\nu}^i F^{i\ \mu\nu} \tag1$$ (Sum over $i$ implicit) This Lagrangian ...
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1answer
423 views

The Majorana condition and C violation

Is the Majorana condition $$ \psi = \psi^c = C \overline{\psi}^T, $$ general? The point is often made that Majorana particles should be defined by CPT symmetry and not C as generally theories do not ...
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2answers
861 views

$SU(2)$ Invariant Lagrangian

Consider two arbitrary scalar multiplets $\Phi$ and $\Psi$ invariant under $SU(2)\times U(1)$. When writing the potential for this model, in addition to usual terms like $\Phi^\dagger \Phi + (\Phi^\...
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1answer
605 views

C and T Symmetry of Free Dirac Lagrangian

I want to show the $C$ and $T$ symmetry of the free Dirac Lagrangian $$\mathcal{L}=\overline{\psi}\left(i\gamma^\mu\partial_\mu-m\right)\psi.$$ Following the notation of Peskin, Schroeder, we have ...
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1answer
449 views

Is $CP$ instead of $C$ responsible for changing a particle to its antiparticle?

The charge conjugation operator $C$ reverses the charge of a state. But it may or may not convert a particle to its antiparticle. For example, consider a neutrino which is charge-neutral and left-...
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1answer
454 views

How to show that the charge conjugation reverses the charge of a state?

How to show that the charge conjugation operator reverses the charge(s) of a (fermionic or bosonic) state? Let us consider a spin-$\frac{1}{2}$ fermionic state of momentum $\textbf{k}$ and spin ...
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2answers
750 views

What are the assumptions that $C$, $P$, and $T$ must satisfy?

I am not asking for a proof of the $CPT$ theorem. I am asking how the $CPT$ theorem can even be defined. As matrices in $O(1,3)$, $T$ and $P$ are just $$ T = \begin{pmatrix} -1 & 0 & 0 & ...
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1answer
751 views

Charge conjugation transformation of complex scalar field

This is a quick and simple question. I'm studynig about a charge conjugation tranformation over a complex scalar field, $\psi\left(x\right)$, $$ \psi\left(x\right)\rightarrow C\psi\left(x\right)C^{-1}...
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1answer
217 views

What distinguishes the behaviour of particle from its antiparticle: C violation or CP violation?

It is said that a CP violation would mean that the behaviour of the particle is different from the behaviour of antiparticle. Why is C violation not good/enough?