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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Parity of a Displaced Cat State [closed]

I am looking at the parity of a displaced cat state, where even and odd parity cat states are defined as $$ |\pm \rangle = \mathcal{N}_\pm \left(|\alpha\rangle + |-\alpha\rangle \right) $$ where $|\...
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Time-reversal and inversion operators commuting, topological insulators

See Eq. (1.26-1.27) in https://phy.ntnu.edu.tw/~changmc/Teach/Topo/latex/06.pdf, where it seems the parity and time-reversal operators commute. I was wondering how does this exactly come? Spins are ...
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How does cobalt-60 beta decay experiment also violate charge conjugation?

I understand why the cobalt-60 decay experiment shows that parity is violated in the weak interaction. However, my lecture notes also say that 'Note that the outcomes of this experiment can also be ...
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How does the parity eigenvalue change in cobalt-60 beta decay parity violating process?

All the explanations for why the beta decay of cobalt 60 seem to revolve around 'in a mirror flipped world the process is different', and while I understand the intrinsic relationship between ...
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Do $C$-parity eigenstates have to have well defined exchange symmetry?

Obviously for C-parity eigenstates of a particle and itself (which is its own antiparticle) this is a wavefunction of identical particles and will thus have well defined exchange symmetry. I also ...
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Parity transformations and Dirac Spinor

I'm reading "No-Nonsense quantum field theory" and I have some doubts about the transformation law for Dirac Spinors as explained by the author. In the book the left chiral spinors $\chi$ ...
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Parity and time reversal symmetries in QFT and the Standard Model

The parity transformation $\mathcal{P}$ and the time-reversal transformations $\mathcal{T}$ are defined as follows : \begin{equation} \mathcal{P}= \begin{bmatrix} 1 & & & \\ & -1 &...
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PT-Symmetry and the existence of a preferred reference frame

(I am new to quantum field theory and I am still learning about symmetries and gauge theories, so please forgive this question if it is naΓ―ve, the formulation is not entirely rigorous in a ...
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Parity Operator eigenstates in arbitrary basis

On page 298 of Shankar's 'Principles of Quantum Mechanics' the author makes the statement : ""In an arbitrary $\Omega$ basis, $\psi(\omega)$ need not be even or odd, even if $| \psi \rangle $...
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Lorentz group generators and its dimensionality

I am unsure about the generators of the Lorentz group and its dimensionality. I believe any Lorentz transformation can be written as the product of a proper, orthochronous Lorentz transformation with ...
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Using Wavefunction Parity to Simplify Integrals

I have seen that $\langle \phi_{200}|r| \phi_{100} \rangle =0$ due to parity. while on the other hand, $\langle \phi_{210}|r| \phi_{100} \rangle$ cannot be determined by the parity. Can anyone explain ...
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Two Questions on the nuclear spin

To those who are familiar with nuclear physics, I have two questions of understanding: Why does it happen that nuclei have a spin greater than 1 (e.g. I=8 at 90Nb)? How can we infer the parity of a ...
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Why To Care About Parity?

I was reading the following article on wikipedia :- Wu Experiment. The excerpt from that article is - "If a particular interaction respects parity symmetry, it means that if left and right were ...
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Why reflection is generator of Minkowski space, if we know that only CPT symmetry is true?

In particular, we know that $P$ symmetry (parity transformation, which is basically a reflection), is not the symmetry of the universe, a whole combination of $C$, $P$, and $T$ is. Because of this, it'...
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Questions on parity transformation

Is a parity transformation $$(π‘₯,𝑦,𝑧) β†’ (βˆ’π‘₯,𝑦,𝑧)$$ or $$(π‘₯,𝑦,𝑧) β†’ (βˆ’π‘₯,βˆ’π‘¦,βˆ’π‘§)$$ Which coordinates cancel out momentum? $(π‘₯,𝑦,𝑧)$ (clockwise directions) and $(βˆ’π‘₯,𝑦,𝑧)$ (counterclockwise ...
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Showing Parity of the Associated Legendre Function

We define the Associated Legendre Function as follows: $$ P_{\ell}^m (x) = (-1)^m (1-x^2)^{\frac{m}{2}} \left( \frac{d}{dx}\right)^m P_{\ell}(x)$$ How would we show that $P_{\ell}^m (-x) = (-1)^{\ell +...
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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 βˆ†+(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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Why is it OK to commute a quantum operator with the cross product?

I am going through lecture notes relating to the parity operator $\mathcal{P}$ My confusion relates to the derivation of the symmetry transformation of the orbital angular momentum $$\mathcal{P} \vec{...
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Does parity violation just mean particles are chiral? [closed]

Wu's experiment shows that the mirror image of a system doesn't necessarily act the same as the original system. But the experiment only mirrors the position of every particle, not the particles ...
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Is it legal to add two physical quantities that behave differently under time-reversal, parity etc to define a new that has no definite behaviour?

In physics, can we legally add two physical quantities that behave differently under time-reversal or parity? For example, let $\vec{a}$ and $\vec{b}$ are two observables. Let $\vec{a}$ flips sign ...
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Why symmetric potential has even bound ground state and does odd ground state exist?

I have read that symmetric potential has even bound ground state, but I don't know how to derive it? The only conclusion I can derive is for even potential I can take real wavefunction. I also want to ...
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How do I determine the zero elements of a Hamiltonian in a 4 ket space?

The Hamiltonian matrix of particle subject to a central potential is described by $$ H=\begin{pmatrix} H_{11} & H_{12} & H_{13} & H_{14}\\ H_{21} & H_{22} & H_{23} & H_{24}\\ ...
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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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Parity $P$ symmetry restored by 1 in the $1 \oplus \bar{5} \oplus 10$?

In Lie Algebras in Particle Physics 2ed - From Isospin to Unified Theories (Georgi, 1999) p.283 Georgi wrote: When we include the $1$ in the $\rm SU(5)$ Unified Theory model, we get the 16 $$ 1 \...
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PT transformation of a spinor

By demanding the the Dirac equation be invariant under general Lorentz transformations, we get an equation for the transformation matrix of a Dirac spinor, $$ S^{-1}(\Lambda) \gamma^\mu S(\Lambda) = {\...
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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 ...
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Question about perturbation theory and even and odd wavefunctions

I was solving a question about perturbation theory and I came across something my teacher didn't mention and I can't seem to understand it. In the question there is an external electric field on a H-...
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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 ...

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