Questions tagged [charge-conjugation]
The charge-conjugation tag has no usage guidance.
86
questions
2
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1answer
61 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, ...
3
votes
1answer
87 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 ...
3
votes
2answers
73 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
$$ \mathcal{L} =(D_\mu \phi)^* D^\mu \phi - m^2 \phi^2 - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$...
1
vote
1answer
66 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?
1
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1answer
41 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}_{\...
1
vote
1answer
59 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 ...
3
votes
2answers
81 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 ...
2
votes
0answers
49 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 ...
0
votes
1answer
149 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 ...
1
vote
3answers
91 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?
4
votes
1answer
63 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 ...
1
vote
1answer
34 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 ...
0
votes
0answers
36 views
Mass term with charge conjugation and fermion transposition
I am trying to convince myself that a $G_{ab}[\overline{(\psi^c_a)_R}(\psi^c_b)_L-\overline{\psi_{aR}}\psi_{bL}]$, where $G_{ab}$ is antissymetric, is just as good a mass term as $-\bar{\psi}\psi$ (...
1
vote
1answer
99 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 ...
1
vote
1answer
91 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/
$$\pi_0(\...
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0answers
36 views
Algebra of Time Reversal and Particle Hole Symmetry in 10-fold Classification of Topological Insulator/superconductor
In the ten fold classification of TI/TSC, when time reversal symmetry $\mathcal{T}$ and particle hole symmetry $\mathcal{P}$ are both present, i.e., in the symmetry classes BDI, DIII, CII, CI, for all ...
1
vote
2answers
126 views
Weak interaction and charge conjugation $C$
Does the weak interaction always change the charge of all participating particles?
And in this context, what does $C$-violation do then?
1
vote
0answers
69 views
Why does the majorana equation preserve handedness?
In the "QFT Nutshell" by A. Zee, it is stated that
The Majorana equation is
$$i\not\partial\psi=m\psi_c$$
where $\psi_c$ is the charge conjugated spinor $\psi_c = \left(C\gamma^0\right)\psi^*$....
2
votes
1answer
174 views
Why does the charge conjugation of the spinor transform as a spinor?
I have come across (in QFT Nutshell, A. Zee) how the charge conjugation of the spinor, $\psi_c \equiv \gamma^2 \psi^*$, transform (where $\gamma^2=\sigma^2\otimes i\tau^2$ is the component of the ...
1
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0answers
162 views
Detail on C vs. CP violation
In the answer given by knzhou to the post What distinguishes the behaviour of particle from its antiparticle: C violation or CP violation? it is said that
"but the reaction $i \rightarrow f$ will ...
0
votes
1answer
46 views
Why is charge conjugation $\hat C | \alpha \psi \rangle = C_\alpha |\alpha\psi \rangle$?
Charge conjugation replaces all particles by antiparticles in the same state, so that momenta, positions, etc are unchanged. It can be represented by
$$\hat C | \alpha \psi \rangle = C_\alpha |\alpha\...
3
votes
0answers
114 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, $\...
0
votes
1answer
284 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 ...
2
votes
2answers
278 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 ...
2
votes
1answer
268 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 ...
2
votes
2answers
501 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^\...
0
votes
1answer
332 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 ...
6
votes
1answer
354 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-...
1
vote
1answer
244 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 ...
12
votes
2answers
584 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
$$
T = \begin{pmatrix} -1 & 0 & 0 & ...
1
vote
1answer
496 views
Charge conjugation transformation of complex scalar field
This is a quick and simple question. I'm studynig about a charge conjugation
tranformation over a complex scalar field, $\psi\left(x\right)$,
$$
\psi\left(x\right)\rightarrow C\psi\left(x\right)C^{-1}...
3
votes
1answer
180 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?
3
votes
0answers
129 views
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 ...
5
votes
2answers
592 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 ...
2
votes
2answers
365 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^{(...
8
votes
1answer
662 views
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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0answers
289 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 ...
1
vote
2answers
429 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, ...
1
vote
1answer
303 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 ...
3
votes
1answer
198 views
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 ...
2
votes
0answers
424 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
votes
0answers
229 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 ...
0
votes
2answers
1k views
Property of Charge Conjugation Operator
In class, we have defined the Charge Conjugation Operator ($C$) such that:
\begin{equation}
C \left(\gamma^\mu\right)^T C^{-1} = - \gamma ^\mu ,
\end{equation}
\begin{equation}
\psi^C \equiv C\,\...
17
votes
3answers
6k views
If electrons were positive and protons were negative, would life be different? [duplicate]
This was a question on a worksheet during my first week in a class on Electromagnetism. The answer is essentially:
No. Life would be no different if electrons were positively charged and protons ...
1
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0answers
73 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 ...
1
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0answers
35 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 ...
2
votes
1answer
380 views
Charge Conjugation of massive Dirac spinor in 3 dimensions with Euclidean signature
In 2+1 dimensional massive Dirac equation (Minkowski signature), we can define the charge conjugation operator so that the equation can be symmetric under it. However, the charge conjugation does not ...
4
votes
2answers
362 views
Is $N_R$ a Majorana field in the Seesaw Lagrangian?
Consider the Lagrangian for the type-I seesaw given by
$$-\mathcal{L}=\bar{\nu}_{L}m_DN_{R}+\frac{1}{2}\overline{(N_{R})^c}M_R N_{R}+\text{h.c.}.$$
$\bullet$ In this Lagrangian, what is the nature ...
4
votes
2answers
462 views
Can a Majorana field $\psi$ be charged under some $U(1)$ with a charge other than zero?
I know Majorana particles have to be electrically neutral because electric charged is conserved.
My question, however, is whether at all a Majorana field $\psi$ be charged under any $U(1)$ (other ...
2
votes
1answer
2k views
Charge conjugation operator and gamma matrices
The gamma matrices are defined by their anticommutation relations, which are symmetrical in permutations of $\gamma_1, \gamma_2, \gamma_3$. Given this symmetry, why is the change conjugation operator $...
