# 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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### Why are vectors considered to have odd/negative/- parity while pseudovectors are even/positive/+ in parity?

Most places I read say that true/polar vectors are of odd or - parity, while axial/pseudovectors are of even + parity. But, pseudovectors gain an 'extra' sign flip after a reflection/parity ...
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### QFT: Vacuum invariant, but vacuum correlations aren't

Consider a free scalar field theory. My struggle is that vacuum correlation functions of fields are only Lorentz invariant under a subgroup of Lorentz transformations, despite the invariance of the ...
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### How to search for an atom electric dipole moment

I read some papers about searching for induced atomic EDM. Finding such an EDM would imply a violation of the P and T-invariance (and hence CP). The way the derivation works (very roughly) is by ...
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### How to use only parity arguments to derive selection rules for $X$ and $P$ operators?

Derive rules of selection between matrix elements of eigkets $|{l,m}\rangle$ and $|{l',m'}\rangle$ for the operator $\hat{X}$ and $\hat{P}$. Use only parity arguments. I now that that the elements of ...
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### Homework: Probability to get spin aligned in delta decay [closed]

During my subatomic physics course, we get homework with no particular explanation. This time one of the questions really got us lost. The question is: The ∆+(1920) resonance decays into pρ0. What is ...
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### Calculation of Parity in Quantum Field Theory

In the book "Relativistic Quantum Mechanics An Introduction To Relativistic Quantum Fields" by Luciano Maiani Omar Benhar, page 174, the picture of that page is provided below. I don't ...
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### Prove that the parity operator is Hermitian

We know that an operator is Hermitian when: $\langle f|\hat{O}g\rangle$ = $\langle \hat{O} f|g\rangle$ Parity operator in 1D is simply defined as: $\hat{\Pi} f(x) = f(-x)$ I don't know anything about ...
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### Orthogonal eigenfunctions [closed]

I have to show that two eigenfunctions of an electron in a 1 dimensional infinite square well with different parity and different quantum numbers are orthogonal. I am attempting this by integrating ...
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### Mirror/Parity symmetry

I am trying to solve a problem of Griffiths' book. $\hat{\Pi} \psi(\vec{r}) = \psi(-\vec{r})$ where $\vec{r}$= (x,y,z), eq. (1) $\hat{\Pi}$ is the parity operator. The problem says to show that ...
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### Why is $PT$ transformation not observable?

In the Preskill's notes, QFT 1 page 70, he said: Unlike charge conjugation $U_C$ and parity $U_P$, $U_{PT}$ is not an observable. For example \begin{align} U_{PT}\,e^{i\theta} \psi=e^{-i\theta}\,U_{PT}...
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### Are active and passive parity transformation different?

As per this Phys.SE post, an active parity transformation is when a particle at $(a,b,c)$ is reflected about origin to move it to $(-a,-b,-c)$. A passive one is when the particle is still at the exact ...
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### Why does the subclassification of fields under parity require the quantum theory?

The fields of relativistic field theory (scalars, vectors, tensors, and spinors) are all defined via their transformation properties under the restricted Lorentz group (which excludes discrete ...
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### Parity of Particles

Like charge, spin,etc.. Parity is an intrinsic property of the particle. As I read in Grifith's introduction to elementary particles book , he states parity mathematically but I am not able to see it ...
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### What is a parity generator in physics?

In digital electronics and the application of gates, I came across a parity generator. By using a parity checker we can check the binary data transmitted over telephone lines or other communication ...
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### Parity of the eigenfunctions of Hamiltonian for a symmetrical potential

I have seen in different posts (like this one) that, in case the potential $V(x)$ of a quantum system is symmetrical, you can always find a basis of eigenstates of the Hamiltonian that have definite ...
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### Absorption of pi mesons on deuterium nuclei

In the process we have \begin{equation}\pi^{-}+d \longrightarrow n+n\end{equation} and by the parity conservation \begin{equation}\eta_{\pi} \eta_{d}(-1)^{\ell_{i}}=\eta_{n} \eta_{n}(-1)^{\ell_{f}}\...
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### Parity violation potential

I read in several papers (e.g. this one) that if we have 2 levels of fixed, opposite parities, which are the eigenstates of a $P$,$T$-even Hamiltonian, and we add a perturbing potential which is $P$-...
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### $\rm SO(10)$ grand unified model restores the parity symmetry lost in $\rm SU(5)$ model

It is said in Lie Algebras in Particle Physics 2ed - From Isospin to Unified Theories (Georgi, 1999) p.285, Georgi said that $\rm SO(10)$ grand unified model restores the parity symmetry that was ...
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### Variational method when the Hamiltonian commutes with the parity operator

Why can we apply the variational method to determine the first excited state of a system when the Hamiltonian commutes with the parity operator? Ignoring the information about the commutation, it ...
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### What are quantum numbers associated with inversion symmetry and time reversal symmetry?

It is well known that for each symmetry in the system there must be a conserved quantum number, I would like to know what are the conserved quantum numbers associated with inversion and time-reversal ...
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### What difference does it make if a molecule has odd or even parity?

I've been reading a lot about term symbols and spectroscopic notation, but I must have missed the part about WHY a molecule's evenness or oddness matters, in terms of spectroscopy or whatever...
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### Is the parity operator an observable?

I'm trying to justify whether the parity operator is an observable in quantum mechanics, and if so, why. I'm at a loss here, any advice on how to tackle this problem?
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### Triplet state with symmetric wavefunction?

In the $1s,2s$ electronic configuration, I've found that the possible states are 1S0 and 3S1. $L=0$ for both of these terms, so would the parity of the spatial wave function not be $(-1)^L=1$, and ...
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### Parity and degeneracy

We know that if Hamiltonian commutes with parity operator and energy eigen values are non-degenerate then the corresponding wave function has well defined parity. But my question is what about ...
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### Inversion symmetry on surface and spin

Let us assume you have a 3D bulk periodic crystal which has inversion symmetry e.g. $r\rightarrow -r$. Assume we are considering spinful operators with $S=1/2$. Now let us imagine cutting a surface ...