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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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Parity operator action on quantized Dirac field

I am stuck on equation 3.124 on p.65 in Peskin and Schroeder quantum field theory book. There they are claiming that: $$P\psi(x)P=\displaystyle\int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_{\bf p}}}\...
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What does $f(x)$ satisfies the given equation means?

In problem 2.1 part c of Introduction to Quantum Mechanics, 3rd ed. by Griffiths and Schroeter, they ask the reader to prove that if the potential is an even function of $x$, then if $\psi(x)$ ...
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What is parity of charge?

In the book Field Theories of Condensed Matter Physics by Fradkin: When discussing the gauge-invariant operators of $Z_2$ lattice gauge theory in Page 299, the author says Owing to the $Z_2$ symmetry,...
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Is the proper antichronous transformation a global transformation?

Is the proper antichronous transformation (PT-transformation) a global or local transformation? P stands for parity and T for time transformations. If global, why does General Relativity not have ...
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What is intrinsic parity? Why is negative intrinsic parity possible?

What is intrinsic parity? It seems that it is a concept only for relativistic quantum physics. Why is it not relevant for non-relativistic quantum mechanics?
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Dipole moments of elementary particles

Reading T violation from Perkins High Energy Physics, 4th ed, pp 82. Here I don't understand the definition of last 4 quantities, magnetic and electric dipole moments, longitudinal and transverse ...
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Parity of Photons

In nuclear physics, while studying gamma decay (Nuclear physics, Roy and Nigam, 1st ed, pp 450) I have read that the parity of photons depends on the type of multipole radiation they represent. Means ...
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Do the WI coupling constants change sign under $C$?

I am trying to understand discrete symmetries in the SM, and I have some troubles in understanding why the CC interaction violates CP. In my (badly written) notes it's said that, taken two fermonic ...
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Why do Dirac basis spinors stay invariant under the action of the parity operator

In Chapter 3.6, the Peskin & Schroeder define the action of the parity operator $P$ on the creation and annihilation operators as follows: $Pa^s_\mathbf{p}P = a^s_{-\mathbf{p}}$. The action of $P$ ...
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Understanding orthochronous, proper and improper Lorentz transformations

The Lorentz group has four connected components that can be characterized as follows: $\det A = 1$ $\det A = -1$ $A^0_0 = 1$ $A^0_0 = -1$. I think I understand the third and fourth components well, ...
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Action invariant under Parity in Yukawa theory

The Lagrangian density for the scalar Yukawa theory is given by \begin{equation} L=\frac12(\partial_\mu\phi)(\partial_\nu\phi)\eta^{\mu\nu}-\frac{m^2}{2}\phi^2+\overline\psi(i\gamma_\nu\partial^\...
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Why is the vacuum state $|0\rangle$ invariant under parity?

I was studying the leptonic pion decay $\pi\rightarrow l\nu_{l}$, and usually the amplitude is computed by $$\mathcal{M}(\pi\rightarrow l\nu_{l})=-i\frac{G_{F}}{\sqrt{2}}V^{*}_{ud}\langle0|\bar{d}\...
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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 ...
Panopticon's user avatar
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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 ...
QuantumQuasar's user avatar
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Showing that measurement of spin parity does not conserve total angular momentum

So I've been sitting on the following question for days now and I really gave my best, but I just can't seem to get the right solution. The initial problem was that we have a singlet-triplet qubit $$ |...
DisposableGuy's user avatar
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Primary operators in $d=3$ (bosonic free) conformal field theory

Consider the free bosonic conformal field theory (CFT) in spacetime dimension $d=3$. I would like to explicitly construct a primary operator of spin $l=4$, with four scalar fields $\phi$ and five ...
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How the parity violation was shown in Experimental Test of Parity Conservation in Beta Decay?

I read that in Experimental Test of Parity Conservation in Beta Decay by C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson, Phys. Rev. 105, 1413 – Published 15 February 1957 the ...
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Parity transformation on fermionic bilinears

In the Fermi weak theory we have the fermion bilinears which look like $$ V_\mu = \bar{\psi} \gamma_\mu\psi $$ $$ A_\mu = \bar{\psi} \gamma_\mu \gamma_5 \psi $$ Under a parity transformation $$ x = (...
god_operator's user avatar
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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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3-point 1PI vertex function in pseudoscalar Yukawa theory

Consider pseudoscalar Yukawa theory in 4D: $$ S =\int d^4x\ \frac{1}{2}(\partial\phi)^2 - \frac{1}{2}m_\phi^2\phi^2 +\bar\psi(i\gamma^\mu\partial_\mu-m_e)\psi - ig\bar\psi\gamma^5\psi\phi -\frac{\...
BVquantization's user avatar
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How can scalar mesons have even parity?

From my understanding a pseudo-scalar meson has: $$J^P=0^-$$ That makes sense since the total spin $S=0$ and $l$ must be $l=0$ which makes the parity: $$ P=(-1)^{l+1}=-1 $$ uneven. Now, for scalar ...
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Consistency of One-Pion Exchange with Selection Rules for NN Pion Production (in Chiral EFT, e.g.)

Hope you're ready for a long question, but I think quite an interesting one! One-pion exchange is an established nucleon-nucleon potential which is well-defined for any joint angular momentum state of ...
Graham Van Goffrier's user avatar
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Does particle parity play any role in matter anti-matter annihilation?

If a left handed electron and a right handed antimatter electron were to meet, would they still annihilate? In the same way, if a left handed electron and a left handed antimatter electron meet, will ...
NonPartisanObservor's user avatar
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Why the eigenstate of an even observable is an eigenstate of the parity operator?

Definition of an even observable: $B_+=\Pi B_+\Pi$, where $\Pi$ is the parity operator. Consider an arbitrary even observable $B_+|\psi_b\rangle=b|\psi_b\rangle$, then $|\psi_b\rangle$ is an ...
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Why the long lived Kaon can not decay into two pions?

The short-lived and long-lived states of kaon $|K_1>$ and $|K_2>$ respectively have the following compositions if they are the eigen states of CP parity: $|K_1> = \frac{|K^0>\:-\:|\bar{K^0}...
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The implications of symmetry + uniqueness in electromagnetism

I have tried to follow "Symmetry, Uniqueness, and the Coulomb Law of Force" by Shaw (1965) in both asking and solving this question, but to no avail. Some of the mathematical arguments there ...
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How to implement projection as potential?

Consider the quantum mechanics of a single particle in $d$ dimensions, which is governed by the Hamiltonian $$ H = P^2+V(X)\,$$ with $P$ being the momentum operator and $X$ being the position operator,...
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Fermion parity vs gauge symmetry

Take for instance a 4d gauge theory with a fermion $\psi$ in some representation of the gauge group $G$ and say that I want to study the fate of the "non ABJ-anomalous" part of the axial ...
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Why do we have this divergent graph as odd diagrams are excluded?

I got a follow-up question to my earlier post. Suppose we have the pseudoscalar Yukawa Lagrangian: $$ L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\bar\psi(i\not\partial-m)\psi-...
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