Questions tagged [charge-conjugation]

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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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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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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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52 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
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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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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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87 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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31 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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102 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
104 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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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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96 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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68 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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70 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
161 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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131 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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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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331 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
131 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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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
44 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
143 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
138 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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41 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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210 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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112 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
335 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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191 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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51 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
447 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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409 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
343 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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657 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
470 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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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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342 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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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
637 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
195 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?
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Difference in symmetries of Second quantized and First quantized Hamiltonian [duplicate]

The following is stated in (among others) the articles Topological insulators and superconductors: ten-fold way and dimensional hierarchy - Shinsei Ryu, Andreas Schnyder, Akira Furusaki, Andreas ...
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739 views

What is the definition of the charge conjugation?

I seem to have troubles finding definitions of the charge conjugation operator that are independant of the theory considered. Weinberg defined it as the operator mapping particle types to ...
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485 views

Majorana Flip Relations

In the Supergravity book of Freedman et.al, which uses the signature $(+,-,\dots,-)$, we have defined the charge conjugation matrix for general Clifford Algebra as $(C\Gamma^{(r)})^T = -t_rC \Gamma^{(...
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Physically, what is a pseudoreal representation?

There are three kinds of representations: real, complex, and pseudoreal. A complex representation is not equivalent to its conjugate, and a real one is, which is pretty straightforward. A pseudoreal ...
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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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2answers
528 views

How are parity and charge conjugation eigenvalues related to angular momentum?

I have seen many equations where $P$ and $C$ (eigenvalues of parity and charge conjugation, resp.) are related to $J$, $L$, $S$ and $I$ (eigenvalues of total angular momentum, angular momentum, spin, ...
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1answer
374 views

Spin state of two distinguishable bosons

I was reading about the $C$-parity of a particle-antiparticle pair. Since charge conjugation has the effect of swapping the particle and antiparticle, the $C$-parity can be found from the symmetry of ...
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Why is $|\bar{K}^0\rangle=\mathscr{CP}|K^0\rangle$ and not $|\bar{K}^0\rangle=\mathscr{C}|K^0\rangle$?

If the charge conjugation operator $\mathscr{C}$ changes a particle state into the corresponding anti-particle state then we must write $|\bar{K}^0\rangle=\mathscr{C}|K^0\rangle$. But instead, we ...
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498 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 ...