# Questions tagged [parity]

Parity inversion P amounts to the sign flip of an odd number of coordinates (reflection). A parity-symmetric theory conserves P; since P²=I, the eigenvalues of P are 1 or -1. May be also used for formally analogous global, discrete, Z₂ symmetries, such as R- or G-parity.

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### Parity transformation of the $\pi^{0}\rightarrow\gamma\gamma$ process

I want to prove that the amplitude $$\mathcal{M}^{\mu\nu}=\epsilon^{\mu\nu\alpha\beta}q_{1\alpha}q_{2\beta}$$ is violating parity. Here $q_{i=1,2}$ are the external momenta of the photons. The total ...
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### $\pi^0\to \gamma\gamma$ parity conservation

Let's consider the decay process $\pi^0\to \gamma \gamma$. After we spontaneously broke the chiral symmetry of QCD coupled to an abelian gauge field $A^\mu$, we end up with the Goldstone boson ...
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### Can the Parity Operator in polar coordinates be defined as $\hat\Pi\psi(r,\theta,\phi) = \psi(r,\theta+\pi,\phi).$?

I was reading about Symmetries & Conservation Laws from Introduction to Quantum Mechanics, David J. Griffiths when I came across this question about the parity operator in three dimensions: ...
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### Parity violation via symmetry breaking?

(Apologies in advance for a poorly formulated question.) In Physics, if something can be equally well found in state A or state B, but for whatever reason is in state A, we sometimes observe the ...
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### $CP$-transformation for fermionic bilinears

I am trying to derive the transformation of the fermionic bilinear $\bar{\psi}\psi$ under $CP$ transformation. I know that $P$ acts as: $$\psi(t, \vec{x}) \xrightarrow{P} \gamma^0 \psi(t, -\vec{x})$$ ...
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### Magnetic parity and electric parity parts of solutions?

I'm currently reading the paper Conserved charges of the extended Bondi-Metzner-Sachs algebra by Flanagan and Nichols. In equation (2.15), the solution $$Y^A = D^A\chi + \epsilon^{AB}D_B\kappa$$ is ...
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### Do GUT's really explain parity violation?

Every book on the Standard Model introduces early on the concept of left and right-handed quantum fields, defined as \begin{align} (\psi_L)_{\alpha} = \left(\frac{1-\gamma_5}{2}\right)_{\alpha \beta}\...
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### Why is charge parity (eigenvalue of $\hat{C}$) conserved?

Looking at processes with neutral initial and final state, for example $$e^+e^- \rightarrow \gamma \gamma$$ we know that charge parity (eigenvalue of charge conjugation operator $\hat{C}$) is ...
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### Is there a systematic way to construct the parity and charge conjugation operator for any Poincaré irreducible representation?

I am currently taking an undergraduate introductory QFT course. However, the proceeding will be about classical field theory, the results of which I assume will carry over mutatis mutandis into ...
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### Parity of a bound state determined by potential

Some time ago in my QM class, we were working with an infinite well potential, and my professor told us we could know beforehand the bound states we were going to obtain for said potential would have ...
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### Possible typo in Weinberg's QFT parity for massless particles (p78)

A massless particle state with the standard momentum $k^\mu=(\kappa,0,0,\kappa)$ and helicity $\sigma$ is denoted by $\Psi_{k,\sigma}$, Weinberg defines the parity phase $\eta_\sigma$ for the parity ...
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### Is the intrinsic parity necessarily $\pm 1$?

Intrinsic parities of various particles we know are $\pm 1$. My question is, can it be a more general phase? It seems it's sometimes argued (like page 140 in "Introduction to elementary particles&...
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### Why the spatial inversion operation $P$ in two space dimensions is $(x, y)→(−x, y)$, whereas in three space dimensions it is $(x, y, z)→(−x,−y,−z)$?

The parity operation in quantum mechanics and quantum field theory is $\hat P|\vec r\rangle=|-\vec r\rangle$, which we can check from the Fourier transform. Why the spatial inversion operation $P$ in ...
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### Explain this step (related to gamma matrices and parity operator)

I am having hard time reproducing a step from the textbook "Lecture Notes on Quantum Field Theory", by Ashok Das. On page 429 ( above equation 11.72), the author is talking about the parity ...
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### Is really hermiticity necessary to be a physical observable? What about larger class of operators like PT invariant operators or pseudo hermitian one?

It's really necessary for an observable represented by an operator acting in a Hilbert space to be hermitian? It's known that not only hermitian operators have real eigenvalues and that also normal ...
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### What is the correct inversion symmetry in a two-band model

Consider a simple two-band tight-binding model $$H(k)=\sin{k_x}\,\sigma_x+\sin{k_y}\,\sigma_y + \left(\sum_{i=x,y,z}\cos{k_i}-2\right)\sigma_z.$$ Let's assume $H$ is for real spins. It breaks the time-...
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### Parity symmetry complete/detailed definition and the group elements

I am trying to write down a complete/detailed definition for the parity symmetry. Symmetry as a concept is different in mathematics and in physics. There are also many other concepts which differ in ...
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### How is parity of the deuteron measured experimentally?

I'm reading Wong 'Introductory Nuclear Physics' and in chapter 3-1 he writes that "For the deuteron, it is known that the parity is positive. Let us see what we can learn from this piece of ...
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### How many degrees of freedom does a photon have in 2+1D?

Wigner's classification of particles implies that the internal degrees of freedom of a particle transform under unitary representations of the subgroup of the Lorentz group that leaves its momentum ...
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### Gamma Ray Emission in the Wu Experiment

In the classic Wu experiment (https://doi.org/10.1103/PhysRev.105.1413) parity violation was discovered in the weak interaction through the asymmetry in the distribution of electrons in the beta decay ...
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### How does parity conservation follow from the Wu experiment?

The Wu experiment shows how parity symmetry does not hold for the weak force. However, how does this proof that parity conservation also doesn't hold? If my understanding is correct, the absence of ...
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### Classical conservation laws and anomalies in QFT

At the beginning of chapter 4 of the book "Anomalies in quantum field theory" Reinhold Bertlmann, on page 178, the book says: symmetries: conservation laws are connected with symmetries, ...
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### Intrinsic Parity of the $𝐾^+$ Meson

Why it is not possible to determine intrinsic parity of the $𝐾^+$ mesons from the $𝐾^+ → 𝜋^+ 𝜋^0$ decay?
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### Charge+Parity operator lead left-handed to right-handed

So i need to show that the, if $\psi$ is left-handed, $$C\gamma^0\psi^*$$ Is right-handed. So, we know that, for any $\psi$, $P_L \psi$ is left handed. Also, for any $\omega$, is right-handed, \$P_R \...
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