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 conservation in second harmonic generation?

The second harmonic arises from susceptibility of third rank tensor $X^{(2)}$ which have (-1) parity. page 28 Let say two photons are absorbed and one is emitted, so the total change in parity is ...
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69 views

Parity operators and spin

Consider the following excerpt from Weinberg's Lectures on Quantum Mechanics: I follow everything up until the last statement in the excerpt. In fact, from other things I've read, it seems that one ...
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18 views

Why can $\chi_{c}$ states not decay leptonically?

I am trying to understand why the $\chi_{c}$ states of charmonium cannot decay to $l\overline{l}$ pairs. I believe it is because they have positive parity, but I'm unsure why this prevents the decay?
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33 views

How to check if a Hamiltonian is PT symmetric or not?

Consider the Hamiltonian $$H=p^2+ix^3+ix.$$ This paper by Carl M bender claims this is a $PT$ symmetric Hamiltonian. In this he describes $PT$ symmetry as parity $P$, whose effect is to make ...
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63 views

Parity transformations and massless Dirac spinors

I am having a bit of a trouble understanding how a parity transformation acts on Dirac spinors with a well-defined chirality and, in particular, the (intuitively correct, since chirality is related to ...
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11 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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16 views

Conjugation Operator General Question

I’m sitting here reading my particle physics book, and the Conjugation Operator is defined as: $C = -(-1)^{S+1}(-1)^{L}$, where $L = $ relative angular momentum for the $q\overline{q}$ pair for a ...
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74 views

Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
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Clarification regarding Eq. (2.6.21) Weinberg Vol. 1

While reading the action of time reversal operator for massless particles, I was going through the derivation for Eq. (2.6.21) from Weinberg Vol. 1 which proceeds as follows $$ \begin{aligned} ...
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Parity and Time reversal when the number of space or time dimensions is even

There's a side remark in the middle of section 2.6 of Weinberg I that I find a bit unclear. Suppose that $L(p)$ is a boost that carries the four momentum $k^\mu=(0,0,0,M)$ to $p^\mu$, and that ${\bf ...
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59 views

What does well defined parity mean

I'm reading a textbook (Physics of Quantum Mechanics by Binney) and it says that the ground state ket $\left\lvert 1 0 0 \right \rangle$ of the hydrogen atom has well defined (even) parity. What does ...
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34 views

Massive spin one pseudovector decay?

Suppose you have a massive spin one pseudo-vector particle. Is it allowed to decay into an electron-positron pair? I'm thinking it might be disallowed because of parity conservation. If it is ...
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105 views

What is polarisation, spin, helicity, chirality and parity?

Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what ...
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64 views

Why do three-scalar correlation functions vanish by parity?

We have the following Lagrangian: $$ \mathcal L = \frac12 (\partial_\mu \phi)^2 - \frac12 m^2 \psi^2 + \bar\psi(\mathrm i \gamma^\mu \partial_\mu -M) \psi - \mathrm i g \bar\psi \gamma^5 \psi \phi \,. ...
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66 views

How do we know that elementary particles possess definite parity?

As I was reading Griffiths' "Introduction to Elementary Particles" Wiley 2008, on chapter 4 "Symmetries", the question stroke me. The same as Parity operator (inversion in 3-dimensional space) we ...
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27 views

What are the actual conventions for the standard model particles' intrinsic parities?

It is known that by fixing the intrinsic parity of three particles with linearly independent quantum numbers B, L and Q, the other particles' parities are fixed by the request that parity be conserved ...
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73 views

Is $PT$ always a symmetry in (2+1)D?

Is the combination of parity $P: (x,y,t)\to (-x,y,t)$ (sometimes also called reflection $R$) and time reversal $T: (x,y,t)\to (x,y,-t)$ always a symmetry in (2+1)D theories with Lorentz or Galilean ...
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74 views

Definition of partity in quantized Dirac Theory.

I'm studying from the book "An Introduction to Quantum Field Theory" from Michael E. Peskin and Daniel V. Schroeder, and I read the following: "The operator P should reverse momentum of a particle ...
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43 views

Wu experiment beta decay

maybe it's a stupid question. But in Wu experiment she showed that parity in not conserved in beta decay. So how to say on general that this is true for any weak force interaction?
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46 views

Physical meaning of parity in nuclear decays

I think it has to do with asymmetry in direction during emission of decay products .also what is implied physically when we say parity is violated in beta decays? I cannot imagine 'l' having an odd ...
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149 views

Behavior of the Electric- and Magnetic-field under time reversal and parity

The behavior of the electric- $\mathbf{E}$ and the magnetic-field $\mathbf{B}$ und time reversal and parity can be calculated in different ways. My first solution is to study the transformation ...
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Parity operator eigenstates [closed]

I have a problem I cannot solve on my own. I have given two states $\psi_1$ and $\psi_2$ and an Operator $O$ such that $P \psi_1 = \epsilon_1 \psi_2$, $P \psi_2 = \epsilon_2 \psi_2$ and $POP^{-1} = ...
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66 views

Parity operator with other operators

I need to show the following: $$P x P^{-1} = -x, \ P p P^{-1} = -p, \ P L P^{-1} = L$$ where $P$ is the parity operator and $x$, $p$ and $L$ are the position, momentum and angular momentum ...
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68 views

How can parity be meaningful in an affine space?

I've recently begun a course in QFT (within a Physics Master's), and despite (admittedly limited) reading I can't get my head round the idea of parity. Here's what I think I understand: the Minkowski ...
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72 views

Demonstration that the $\langle f(x)\rangle$ of an odd function $f(x)=-f(-x)$ of position $x$ in a symmetric potential well $V(x)=V(-x)$ is null

Consider a potential infinite well, which borders are $x=-a$ and $x=a$. I pretend to demonstrate that the expected value of a odd function $f(x)$, i.e., $\langle f(x)\rangle$, is null. We have the ...
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86 views

Regarding parity conservation in the decay $\omega \to \pi^0 \,\pi^+\, \pi^-$

I'm somewhat confused by this decay. Associated vertex seem to be related to QCD residual terms contributing to the nuclear force, therefore they should manifest conservation of Isospin and Parity. ...
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82 views

“This operator is odd under parity”

In problem 8.10 of Schaum's Quantum Mechanics they say: "We see that under the parity operator $r \rightarrow r$, $\theta \rightarrow \pi - \theta$ and $\phi \rightarrow \pi + \phi$ .. since ...
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91 views

Intrinsic parity

When we apply parity on a field two times, we demand that we should get back the same field. This gives us, $P^{2} =1$, which implies, $ P \psi = e^{i \theta} \psi$ . This extra phase factor is ...
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74 views

Is the decay of the positive Kaon into 3 pions a weak processs or strong one?

The strangeness is not conserved in the decay of the positive Kaon into 3 pions. so this decay should be a weak process but on the other hand parity is conserved in this decay. Kaon has odd parity and ...
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28 views

Solutions to time-independent Schrödinger's equation with symmetrical (even) potential [duplicate]

A problem from Griffith's Introduction to Quantum Mechanics asks to prove the following: Given a symmetric potential $V(x)$ $(=V(-x))$, the solutions to the time-independent Schrödinger's equation ...
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70 views

Correct way to define parity of two parafermions

I am checking the literature on parafermions and it seems that people define the parity of two parafermions to be $\gamma_{a}^{-1}\gamma_{b}$. Is this definition always valid? How does one come up ...
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Does charge conjugation affect parity?

Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in ...
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103 views

Parity of $n$-photon system

The $C$-parity (charge conjugation) of an $n$-photon system is given by $(-1)^n$. If I'm not totally wrong, the intrinsic parity of a photon is $(-1)$. What is the parity $P$ of a system of $n$ ...
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458 views

What's the idea behind Wu's experiment?

Madame Wu discovered the parity violation in beta-decays. To do so, she took some Co-60 nuclei, which decay via beta-decay in Ni-60 with emission of electron, antineutrino and 2 gamma rays. She ...
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272 views

Spin, isospin, parity etc. in nuclear physics

I have one question regarding these quantum numbers. When I read through my textbook, it sometimes just says something like: "And this atoms ground state has $J^{\pi} = 0^+$ and isospin $+1$" - as an ...
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37 views

What are the parity of particles? [duplicate]

When looking to see if particle collisions/decays are possible and what force they act through, how do you know the parity of particles to know whether they act through weak force? Is there a grouping ...
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81 views

Are mass terms forbidden in the Lagrangian because of parity violation or because fermions live in a complex representation?

Normally one argues that we can't write down Lorentz AND gauge invariant mass terms, because of parity violation, i.e. l-chiral and r-chiral fields transform differently. This means that mass terms ...
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80 views

Is Witten's claim that gauge group representations get exchanged with its dual under parity correct?

I'm currently reading Physics and Geometry by Witten, which I really liked up to the point where he claimed that we exchange representations $R$ and $\tilde R$ under parity transformations, where $R$ ...
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101 views

How is $J^{PC}$ value experimentally determined for new types of particles?

How is $J^{PC}$ value experimentally determined for new types of particles? For example, this paper says ... Angular correlations in B+→X(3872)K+ decays, with X(3872)→ρ0J/ψ, ρ0→π+π− and J/ψ→μ+μ−, ...
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121 views

What's difference between C parity and charge?

I know C parity as an operator : $$ C\psi=\pm\psi $$ has two eigenvalues like parity operator P. But what I wonder is, i.e, is it true to say for a negative charged particle has (-) eigenvalue? If not ...
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252 views

Particle physics: Why is J^P called spin parity if J is the total angular momentum?

Here is the question I am working on: "The Ξ- has spin parity=½+. It decays through the weak interaction into a Λ0 and a π- meson. If the spin parity of the Λ0 particle is 1/2+ and the spin parity of ...
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102 views

Fujikawa's method for 2+1-dimensional parity anomaly?

Fujikawa's chiral rotation method is applied to calculate 3+1 dimensional chiral anomaly in many textbooks, but is there any counterpart of that method in deriving 2+1 dimensional parity anomaly, i.e. ...
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391 views

What is the definition of parity conservation?

I searched quite hard, and am still confused what is the exact definition of parity conservation? For example, we have quantum system with initial state $\Phi_i$, and after decaying it comes to final ...
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58 views

Parity transformation is proper orthochronous?

In 3+1 dimensional spacetime the parity transformation is $$P^\mu_{\;\,\nu}=\begin{pmatrix}+1&&&\\&-1&&\\&&-1&\\&&&-1\end{pmatrix}.$$ This is ...
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91 views

$\mathbb{Z}_2$ topological insulators which obey inversion symmetry as well

According to Fu & Kane (2006), systems with simultaneous time-reversal invariance and inversion symmetry have their $\mathbb{Z}_2$ topological invariant given by the product of the parity ...
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230 views

Spin, parity, etc. conservation in decays/reactions

I have a long list of short physics questions I'm reviewing, and there are several that ask about whether certain decays or reactions are allowed. Clearly these questions are testing my knowledge of ...
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1answer
67 views

Wigner's Theorem and discrete Symmetries

According to my skript: A pure state is a ray: $\quad$ $\{λψ\}$, where $ψ ∈ \mathcal H$, $||ψ|| =1$ fixed and $λ ∈ \mathbb C$, $|λ| = 1$. Pure states are uniquely given by 1-dimensional orthogonal ...
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100 views

Determining Parity of Decaying Quantum System

Show that a particle of spin $1$ cannot decay into two identical particles of spin $0$. The $\rho$-meson has spin $1$ and can decay into two spinless (spin-$0$) $\pi$-mesons, or pions, with ...
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149 views

Is the weak interaction Lagrangian invariant under parity transformations?

The weak interaction term in the Lagrangian reads $$ \bar \Psi \gamma_\mu P_L \Psi W^\mu. $$ Under parity transformations, because of $\Psi \rightarrow \gamma_0 \Psi$ and $\gamma_5 \rightarrow ...
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Is Parity really violated? (Even though neutrinos are massive)

The weak force couples only to left-chiral fields, which is expressed mathematically by a chiral projection operator $P_L = \frac{1-\gamma_5}{2}$ in the corresponding coupling terms in the Lagrangian. ...