Questions tagged [charge-conjugation]
The charge-conjugation tag has no usage guidance.
80
questions
0
votes
1answer
69 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
76 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
60 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
25 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
24 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
63 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
72 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/
$$\pi_0(\...
0
votes
0answers
32 views
Particle Hole symmetry in Interacting superconductor
For noninteracting superconductors (fermion hopping plus fermion pairing), there is a particle hole (PH) symmetry which is a redundancy. The redundancy says that the BdG Hamiltonian satisfies the ...
1
vote
0answers
29 views
Algebra of Time Reversal and Particle Hole Symmetry in 10-fold Classification of Topological Insulator/superconductor
In the ten fold classification of TI/TSC, when time reversal symmetry $\mathcal{T}$ and particle hole symmetry $\mathcal{P}$ are both present, i.e., in the symmetry classes BDI, DIII, CII, CI, for all ...
1
vote
2answers
82 views
Weak interaction and charge conjugation $C$
Does the weak interaction always change the charge of all participating particles?
And in this context, what does $C$-violation do then?
0
votes
0answers
42 views
Why does the majorana equation preserve handedness?
In the "QFT Nutshell" by A. Zee, it is stated that
The Majorana equation is
$$i\not\partial\psi=m\psi_c$$
where $\psi_c$ is the charge conjugated spinor $\psi_c = \left(C\gamma^0\right)\psi^*$....
1
vote
1answer
85 views
Why does the charge conjugation of the spinor transform as a spinor?
I have come across (in QFT Nutshell, A. Zee) how the charge conjugation of the spinor, $\psi_c \equiv \gamma^2 \psi^*$, transform (where $\gamma^2=\sigma^2\otimes i\tau^2$ is the component of the ...
1
vote
0answers
130 views
Detail on C vs. CP violation
In the answer given by knzhou to the post What distinguishes the behaviour of particle from its antiparticle: C violation or CP violation? it is said that
"but the reaction $i \rightarrow f$ will ...
0
votes
1answer
42 views
Why is charge conjugation $\hat C | \alpha \psi \rangle = C_\alpha |\alpha\psi \rangle$?
Charge conjugation replaces all particles by antiparticles in the same state, so that momenta, positions, etc are unchanged. It can be represented by
$$\hat C | \alpha \psi \rangle = C_\alpha |\alpha\...
3
votes
0answers
94 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
216 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
229 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
187 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
376 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
251 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
313 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
193 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
520 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
$$
T = \begin{pmatrix} -1 & 0 & 0 & ...
1
vote
1answer
415 views
Charge conjugation transformation of complex scalar field
This is a quick and simple question. I'm studynig about a charge conjugation
tranformation over a complex scalar field, $\psi\left(x\right)$,
$$
\psi\left(x\right)\rightarrow C\psi\left(x\right)C^{-1}...
3
votes
1answer
153 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
111 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
469 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 ...
1
vote
2answers
287 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
464 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 ...
1
vote
0answers
255 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
384 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, ...
0
votes
1answer
268 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
197 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
356 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
208 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
772 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
vote
0answers
68 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
vote
0answers
33 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
240 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
337 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
397 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
1k 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 $...
2
votes
2answers
277 views
What property (besides charge) of antimatter is different than matter?
There must be a property that is different other than charge. When two oppositely charged matter particles interact, they do not annihilate. I'm told that two neutrally charged matter/antimatter ...
1
vote
1answer
209 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 ...
asked Apr 20 '17 at 19:20
Quantum spaghettification
5,5117 gold badges32 silver badges104 bronze badges
4
votes
2answers
285 views
How do we know the number of photons in a decay?
How can we determine the exact number of photons produced in a decay or other event? This has puzzled me because photons can have arbitrarily low energy and momentum, so how do we tell if two photons ...
3
votes
1answer
364 views
Charge conjugation in arbitrary basis
Consider the matrix $C = \gamma^{0}\gamma^{2}$.
It is easy to prove the relations
$$C^{2}=1$$
$$C\gamma^{\mu}C = -(\gamma^{\mu})^{T}$$
in the chiral basis of the gamma matrices.
Do the two ...
6
votes
1answer
291 views
Can real scalar fields break charge conjugation symmetry?
Is it possible to have a Hermitian term in a Lagrangian that breaks $C$ symmetry and is made up of only real scalar fields? I thought that real scalar fields would always have to be even under $C$ ...
2
votes
0answers
437 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 ...
13
votes
1answer
453 views
What feature of QFT requires the C in the CPT theorem?
Classical tensor field theories have a PT theorem, so what changes in a QFT to require charge conjugation to be a part of the theorem? Charge conjugation seems a bit unrelated to space-time, but is an ...
