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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Conceptual interpretation of the left- and right-handed spinor representations of the Lorentz group

I understand mathematically that the Lorentz group's Lie algrebra $\mathfrak{so(3,1)}$ (given by eqns. (33.11)-(33.13) in Srednicki's QFT book) is isomorphic to $\mathfrak{su(2) \times su(2)}$ (given ...
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27 views

Where do the intrinsic parities of particles come from?

It is known that some particles have negative intrinsic parity - for example pion $\pi$. I was wondering if this parity can be understood. I read somewhere that parity of quarks is defined to be ...
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1answer
22 views

Parity tranformation on Lagrangian of free fields

Free lagrangians of scalar, Dirac field and vector fields are always invariant under Parity. I am able to get this result mathematically, but I want to know if there is any obvious reason for it. ...
3
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67 views

Does this physical situation distinguish whether you are viewing it a mirror?

The weak interaction's lack of $P$-symmetry is often explained by saying that "the amplitudes for processes involving the weak interaction are different from the amplitudes for the same processes ...
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1answer
33 views

Does an odd potential commute with parity operator?

I can prove when a Hamiltonian commute with the partity operator if the potential is even. But what about an odd potential? my understanding is that the parity operator mirrors the coordinate system, ...
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1answer
30 views

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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81 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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20 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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1answer
37 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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1answer
68 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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1answer
12 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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1answer
79 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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56 views

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} U^{-1}(...
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29 views

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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2answers
68 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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1answer
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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1answer
137 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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71 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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1answer
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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28 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 ...
3
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75 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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1answer
46 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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1answer
55 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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1answer
167 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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1answer
43 views

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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1answer
72 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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1answer
69 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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1answer
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 ...
3
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1answer
94 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. ...
2
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1answer
83 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 $\frac{d}...
3
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104 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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1answer
79 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 ...
4
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0answers
71 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 ...
2
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2answers
156 views

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 the ...
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0answers
113 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 $n$ ...
1
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1answer
511 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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2answers
303 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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0answers
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 ...
2
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0answers
84 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 ...
3
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0answers
82 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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1answer
102 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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1answer
126 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 ...
2
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1answer
270 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 ...
3
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112 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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1answer
416 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 ...
2
votes
1answer
59 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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98 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 ...