Questions tagged [charge-conjugation]
The charge-conjugation tag has no usage guidance.
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Charge conjugation opearation in odd dimension
In my problem, I use the following set of $\gamma$-matrices (in (2+1) spacetime):
$$\gamma^0=\sigma^1;\quad \gamma^{1}=i\sigma^2;\quad \gamma^{2}=i\sigma^{3},$$
where $\sigma^{(i)}$ are usual Pauli ...
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0answers
71 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
32 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
$$\hat C | \alpha \psi \rangle = C_\alpha |\alpha\...
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0answers
25 views
What is the 4x4 matrix for the charge inversion operator and how do you construct it?
I have a 4x4 Hamiltonian describing a part of my system. To get a holistic view of the situation I need to do a charge inversion on the matrix. What is the 4x4 charge inversion operator? And what is ...
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0answers
45 views
Feynman Rules from Lagrangian with charge conjugation matrix
I'm dealing with a doubly charged scalar singlet that interacts only with the
right-handed muon as follows,
$$\mathcal{L} = \lambda \psi_{R}C\psi_{R} \phi^{++},$$
where $\lambda$ is the coupling, $\...
0
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1answer
59 views
Why is the Higgs $CP$ even?
Why was it always assumed that the Higgs boson is a CP even particle?
I understand that experimentally, it just is so but I am under the impression that before its discovery people took it to be CP ...
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1answer
129 views
Invariance of Yang-Mills Lagrangian under charge conjugation
The Yang-Mills Lagrangian gauge invariant under an $SU(N)$ tranformation can be written as
$${\cal L} = -\frac{1}{4}F_{\mu\nu}^i F^{i\ \mu\nu} \tag1$$
(Sum over $i$ implicit)
This Lagrangian ...
2
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1answer
73 views
The Majorana condition and C violation
Is the Majorana condition
$$
\psi = \psi^c = C \overline{\psi}^T,
$$
general?
The point is often made that Majorana particles should be defined by CPT symmetry and not C as generally theories do not ...
2
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2answers
137 views
$SU(2)$ Invariant Lagrangian
Consider two arbitrary scalar multiplets $\Phi$ and $\Psi$ invariant under $SU(2)\times U(1)$. When writing the potential for this model, in addition to usual terms like $\Phi^\dagger \Phi + (\Phi^\...
0
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1answer
63 views
C and T Symmetry of Free Dirac Lagrangian
I want to show the $C$ and $T$ symmetry of the free Dirac Lagrangian
$$\mathcal{L}=\overline{\psi}\left(i\gamma^\mu\partial_\mu-m\right)\psi.$$
Following the notation of Peskin, Schroeder, we have ...
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1answer
187 views
So is it not $CP$ instead of $C$ that is responsible for changing a particle to its antiparticle?
The charge conjugation operator $C$ reverses the charge of a state. But it may or may not convert a particle to its antiparticle. For example, consider a neutrino which is charge-neutral and left-...
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1answer
63 views
How to show that the charge conjugation reverses the charge of a state?
How to show that the charge conjugation operator reverses the charge(s) of a (fermionic or bosonic) state?
Let us consider a spin-$\frac{1}{2}$ fermionic state of momentum $\textbf{k}$ and spin ...
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2answers
397 views
What are the assumptions that $C$, $P$, and $T$ must satisfy?
I am not asking for a proof of the $CPT$ theorem. I am asking how the $CPT$ theorem can even be defined.
As matrices in $O(1,3)$, $T$ and $P$ are just
$$
T = \begin{pmatrix} -1 & 0 & 0 & ...
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1answer
245 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
100 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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0answers
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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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2answers
240 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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2answers
119 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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1answer
197 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
204 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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2answers
232 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
185 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
189 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 ...
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0answers
257 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
148 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 ...
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2answers
356 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\,\...
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3answers
5k 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 ...
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0answers
53 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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0answers
32 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$$
is CP-violating.
How exactly do we see this? Can anyone make explicit how we ...
2
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1answer
188 views
Charge Conjugation of massive Dirac spinor in 3 dimensions with Euclidean signature
In 2+1 dimensional massive Dirac equation (Minkowski signature), we can define the charge conjugation operator so that the equation can be symmetric under it. However, the charge conjugation does not ...
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2answers
298 views
Is $N_R$ a Majorana field in the Seesaw Lagrangian?
Consider the Lagrangian for the type-I seesaw given by
$$-\mathcal{L}=\bar{\nu}_{L}m_DN_{R}+\frac{1}{2}\overline{(N_{R})^c}M_R N_{R}+\text{h.c.}.$$
$\bullet$ In this Lagrangian, what is the nature ...
4
votes
2answers
291 views
Can a Majorana field $\psi$ be charged under some $U(1)$ with a charge other than zero?
I know Majorana particles have to be electrically neutral because electric charged is conserved.
My question, however, is whether at all a Majorana field $\psi$ be charged under any $U(1)$ (other ...
2
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1answer
976 views
Charge conjugation operator and gamma matrices
The gamma matrices are defined by their anticommutation relations, which are symmetrical in permutations of $\gamma_1, \gamma_2, \gamma_3$. Given this symmetry, why is the change conjugation operator $...
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2answers
228 views
What property (besides charge) of antimatter is different than matter?
There must be a property that is different other than charge. When two oppositely charged matter particles interact, they do not annihilate. I'm told that two neutrally charged matter/antimatter ...
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1answer
135 views
Charge conjugation of $|b\bar b\rangle$ states?
I know that for a state of a boson and its anti boson $|b\bar b\rangle$ the charge conjugation is $(-1)^{L+S}$ but I don't understand how this value is arrived at. Wikipedia says that is to do with ...
2
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1answer
153 views
How do we know the number of photons in a decay?
How can we determine the exact number of photons produced in a decay or other event? This has puzzled me because photons can have arbitrarily low energy and momentum, so how do we tell if two photons ...
3
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1answer
240 views
Charge conjugation in arbitrary basis
Consider the matrix $C = \gamma^{0}\gamma^{2}$.
It is easy to prove the relations
$$C^{2}=1$$
$$C\gamma^{\mu}C = -(\gamma^{\mu})^{T}$$
in the chiral basis of the gamma matrices.
Do the two ...
6
votes
1answer
253 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
353 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 ...
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1answer
402 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 ...
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1answer
544 views
How to treat charge conjugation and time reversal operators for Dirac Field in representation invariant way?
Since manipulations with charge conjugation and time reversal operators involve taking complex conjugate of bispinors, most formulas are not invariant under change of representation of $\gamma$ ...
2
votes
1answer
461 views
C-parity violation evidence
I know about the CP-violation experiments from the 60's and the P-violation from the 50's. But, is there a similar experiment which displays (perhaps historically in the same way as the experiements ...
0
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1answer
296 views
Schroedinger and Klein-Gordon equation and their complex conjugate
Let's consider the Schroedinger equation
\begin{equation}
i\hbar\frac{\partial}{\partial t}\psi=-\frac{\hbar}{2m}\nabla^2\psi
\end{equation}
If I have a wavefunction $\psi$ as a solution, then its ...
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1answer
469 views
Is Charge Conjugation Representation Dependent?
I'm having a problem understanding section 7 of this paper:
http://arxiv.org/abs/1006.1718
The author defines the commonly know $\Psi^c$ as $\textit{C}\Psi \textit{C}^{-1}=\eta \hat{\Psi}$ in ...
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1answer
281 views
Conservation of $C$-Parity and $P$-parity
Under what situations are $C$-Parity $C=(-1)^{L+S}$ and/or $P$-parity $P=-(-1)^L$ conserved? ( $L$ here is the relative angular momentum and S is the total intrinsic spin).
It would make sense that ...
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1answer
443 views
Symmetry properties of gamma matrices
While reading a paper on supersymmetry i faced the following problem. Its about the symmetry property of charge conjugation matrix in different space time dimension. The charge conjugation matrix is ...
3
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1answer
932 views
How to determine if interaction is allowed?
I'm trying to determine if the reaction
$$n\rightarrow p + \pi^-$$
is allowed. First of, this doesn't list this as one of the decay modes of the neutron, so I suspect that it should not be allowed. ...
1
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0answers
98 views
Confused about anti-fermion notation
Classically anti-fields are obtained by charge conjugation, right? But sometimes authors label hermitian conjugated fields as anti-particles (or barred fields in Dirac language). But h.c. and charge ...
2
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1answer
259 views
Charge Conjugation for $SU(N)$?
For $SU(2)$ the charge conjugation operator $C$ reads explicitly
$$ C \Psi = i \sigma_2 \Psi^\star ,$$
where $\sigma_2$ is a Pauli matrix. What is the generalized charge conjugation for $SU(N)$?
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Why do we assume that particles and their antiparticles have the same half-life?
Has it been proven experimentally? What would the consequences be if their half-lives were different?
