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 does the parity of a meson have a “+1” in it?

The parity of a meson is defined as $ P = (-1)^{L+1} $ where $L$ is the angular momentum. What does the "1" in the exponent represent?
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Symmetry reason why magnetic dipole transitions are suppressed

In the theory of light-matter interaction, electric dipole transitions between two atomic states of same parity are forbidden. This is because the Hamiltonian conserves parity. Is there a symmetry ...
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Generator for parity?

The unitary translation operator, $\hat{T}(\lambda) = e^{i\hat{p}\lambda/\hbar}$, is generated from the Hermitian operator $\hat{p}$. The unitary rotation operator, $\hat{R}_z(\alpha)=e^{-i\hat{L_z}\...
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Does time evolution preserve parity?

Let $\psi(t_0, \cdot)$ be the state of a quantum system corresponding to a Hamiltonian $H$ in the position representation at time $t_0$. Assume $\psi(t_0, -x) = \psi(t_0,x)$, that is $\psi(t_0, \cdot)$...
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Schrodinger equation: If $V(x)=V(-x)$ then prove that $\psi(x)=\psi(-x) $ or $\psi(x)=-\psi(-x)$ [duplicate]

The title explains itself. If the potential is an even function then prove that wave function is either odd or even. I set $-x$ in Schrodinger equation and find out that $\psi(-x)$ is also a solution ...
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Pseudotensors for describing physical quantities

I have been reading about tensors from Mathematical methods for Physics and Engineering, by K.F. Riley, M.P. Hobson and S.J. Bence. And there are a couple of things i am not getting. On page 949 (...
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Confused about the anapole (toroidal) moment

I am a bit confused about the existence of the anapole moment. As far as I understand, in order to fully describe a charge-current distribution, one needs, beside the normal electric and magnetic ...
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Parity operator expression in relativistic quantum mechanics

I was reading Schwabl's Advanced quantum mechanics. In that book it is written in the Spatial reflection part that the parity operator is $P=e^{i\phi}\gamma^0$.But after some lines it is written as $P=...
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Particle interactions simulator

I'm an A-Level student trying to write a program that will take in two particles (like a proton and electron) and output the new particles. I'm planning to implement the conservation laws so that the ...
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qm problem with spin,angular momentum and parity

there is a particle A in the state $|J,M\rangle=|1,1\rangle$ where $J$ is the total angular momentum and $M$ the $z$ component, and has parity $=-1$. It decays in 2 particles B and C. B has spin $=1/2$...
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Spacial Wavefunction Symmetries and Identical particles

I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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Why is field action not a pseduo-scalar in 4D?

If the Lagrangian density is a scalar and the 4-volume is a pseudo-scalar (w.r. to proper orthochronous LT), how is then action not a pseudo-scalar? If it is a pseudo-scalar (i.e. the above reasoning ...
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Why does electron-positron annihilation conserve parity?

I think I'm missing something quite basic here but consider the process: $$ e^- + e^+ \rightarrow 2\gamma$$ Fermions have opposite parity to antifermions so the parity quantum number before the ...
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Possible spins and parities of $^{38}_{17}Cl$

In my introductory nuclear physics course, the following question came up: Consider the odd-odd nucleus $^{38}_{17}Cl$, which has 17 protons and 21 neutrons. Its 17th proton sits in the $1d_{3/2}$ ...
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Why is the decay $\rho ^+ \rightarrow \rho ^0 \pi^+$ allowed by parity conservation and angular momentum conservation?

In the following decay: $$\rho ^+ \rightarrow \rho ^0 \pi^+$$ where $\rho^+$ and $\rho^0$has $J^P = 1^-$ and $\pi^+$ has $J^P = 0^-$ The parity conservation $P$ entails that $L$ (orbital angular ...
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What is an optical supermode?

What is an optical supermode? Is it related to a specific type of symmetry? Am studying a paper, Parity anomaly laser. D.A. Smirnova et al. Opt. Lett. 44, 1120 (2019), arXiv:1811.06300 that ...
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Why in QFT what really matters is $\exp(\mathfrak{so}(1,3))$ instead of $O(1,3)$?

In QFT fields are classified according to representations of the Lorentz group $O(1,3)$. Now, most books when getting into this say that in order to understand the representations of $O(1,3)$ we need ...
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Non-Abelian Gauge Field and Fermions Under Parity?

Under a discrete parity transformation, how does a non-abelian gauge field $A^a_{\mu}(x)$ transform? Is it possible to get mixing between the colors? How about the fermion $\psi_n(x)$ which is coupled ...
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Parity in $\rho^0 \rightarrow \pi^0+\gamma$ decay

I am doing a homework question for $\rho^0 \rightarrow \pi^0+\gamma$ decay. It is given the $J^{PC}=1^{--}$ for the $\rho^0$ meson and that parity is conserved for this process. To calculate the ...
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Detail on C vs. CP violation

In the answer given by knzhou to the post What distinguishes the behaviour of particle from its antiparticle: C violation or CP violation? it is said that "but the reaction $i \rightarrow f$ will ...
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Why parity required symmetry?

I'm studying parity for the first time but there is something I don't understand. I read that a system conserves parity if every experiment is the same in a mirror that is also $180^{\circ}$ flipped. ...
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How does one find the parity trasformation matrix of spinors for non-free field theory?

In many QFT textbook, for example, the book of Srednicki, they use free field theory to derive the transformation matrix of the Spinors: $$P^{-1}\Psi(x)P=D(P)\Psi(P^{-1}x)$$ Then we have a relation: ...
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Connected components of conformal group $ {\rm Conf}(p,q)$ containing $P$, $T$ and conformal inversion are same or different?

As we known (see this post), the global conformal group for $\mathbb{R}^{p,q}$ is $$ {\rm Conf}(p,q)~\cong~O(p\!+\!1,q\!+\!1)/\{\pm {\bf 1} \}$$ The global conformal group ${\rm Conf}(p,q)$ has 4 ...
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Identically null Einstein equations in Schwarzschild spacetime

In deriving Schwarzschild solution one assumes many constraints on the metric, in particular parity invariance (invariance of $g _{\mu \nu}$ under $t \rightarrow-t, \phi \rightarrow-\phi, \theta \...
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What is $\mathbb{Z}_2$ Parity?

While reading about exotic decays of Higgs boson one of the simplest interaction that we come up with which leads to BSM decays is: $$\Delta L = \frac{\zeta}{2}s^{2}|H|^{2}.$$ This is the ...
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Maximal Parity violation in Weak interactions

In 1956 Lee and Yang proposed parity violation of the weak interactions to explain the $\theta-\tau$ puzzle. The following year, 1957, Madam Wu and collaborators found that in the $\beta$ decay of ...
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Parity transformation and mirror reflection

I have some trouble understanding what exactly is parity transformation. The definition of parity transformation is a flip in the sign of all three spatial coordinates, ie $$(x,y,z) \rightarrow (-x,-...
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Parity of Harmonic oscillator in 2 and 3 dimensions: the case of $l_z$

From doing exercises and trying to understand their solutions, i figured in two dimensions, not all values of $l_z$ can be taken by the particles (this is to conserve parity). For example, for n=0, ...
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How do we see that the axion is a pseudoscalar?

The axion is the pseudo-Goldstone boson associated to the breaking of the conjectured Peccei-Quinn Abelian symmetry. The axion couples to the SM gauge fields in a CP-invariant manner (e.g. $aF\tilde F ...
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Covariant Maxwell equations invariant under parity transformation

I tried to proof that the Maxwell equations are invariant under parity transformations. Therefore I used the covariant formulation of the Maxwell equations \begin{align} \partial_{\nu}F^{\nu\mu} &...
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Are pseudospinors valid or useful?

We all know that in addition to scalars and vectors, there are pseudoscalars and pseudovectors, which have an additional sign flip under parity. These are useful and necessary when constructing ...
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Why is the Higgs $CP$ even?

Why was it always assumed that the Higgs boson is a CP even particle? I understand that experimentally, it just is so but I am under the impression that before its discovery people took it to be CP ...
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How to perform parity tranformation in a Lagrangian?

In this forum https://www.physicsforums.com/threads/how-to-check-if-lagrangian-is-parity-invariant.333562/ appears a discussion about the performing of the parity transformation in the Dirac ...
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parity oscillation in trapped ions

I am trying to understand this trapped ion paper. More specifically, I am trying to understand what they are exactly varying, when they are varying 'the phase'to obtain the oscillation of the parity....
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Spectrum of two particles system hamiltonian

Consider the following hamiltonian describing a system of two identical spin 1/2 particles in one dimension: $$H = H_1 +H_2 - \lambda \vec {s_1} . \vec {s_2}$$ Where $H_i$ is the Hamiltonian of an ...
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Which direction does “the mirror” in the Wu experiment flip?

I have seen two different setups for the Wu experiment: One where the "imaginary" mirror flips the experiment along a plane parallel to the magnetic field and one where the mirror is aligned ...
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Question about fundamental states on an finite well

My question is the following, when we search for the bound states a finite well potential we have solutions symmetric and antisymmetric so we get two families of solutions. In this case, the ...
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Parity Violation in Feynman diagrams

I'm trying to understand how parity violation in a lagrangian traduces to changes in Feynman's rules/diagrams. To illustrate, consider the following self-interaction case for fermions which contains P ...
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Parity Anomaly and Gauge Invariance

In Fermionic Path Integral and Topological Phases, Witten shows that in $2+1$ dimensions, the free massless Dirac fermion suffers from parity anomaly. To be specific, he shows that it is impossible to ...
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Parity Transformation on Classical Fields

I've been confused by this parity transformation in classical field theory for a long time. Let $\phi(t,\vec{x})$ be a scalar field. Then, up to some constant phase factor, it transforms to $\phi^{\...
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Why is the parity of the spatial wavefunction $(-1)^{\ell}$?

Consider a composite particle state $|\psi\rangle$ (like a hadron or a meson) that is an eigenstate of some Hamiltonian (e.g. the QCD Hamiltonian). Since the Hamiltonian is invariant under rotations ...
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Permanent electric dipole moment parity violation

In particle physics we deal with parity transformations and in particular when we regard weak interactions. While learning this subject I found something that needs more clarification for me. Namely, ...
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Weak interaction, parity violation, and the observer-dependence of helicity

It is said that the Weak Interaction only couples to left-handed particles which a negative spin (left-handed). However some sources say that spin or helicity is dependent on the observer's position ...
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Orbital parity of simple bound states in atomic and particle physics

The parity operator commutes with the Hydrogen atom Hamiltonian. The energy eigenfunctions are parity eigenstates with orbital parity $(-1)^\ell$ which follows from the fact that $Y_{\ell m}(\theta,\...
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Why Parity Anomaly in Odd Dimensions?

In section 13.6 of Nakahara, the parity anomaly is in odd dimensional spacetime. From the paper Fermionic Path Integral And Topological Phases by Witten, the problem appears as one cannot define the ...
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What about the (1, 1/2), or (3/2, 1/2) representations of the Lorentz group?

All irreducible finite dimensional complex representations of the Lorentz group can be specified by two positive half-integers, i.e. $(j_1, j_2)$. The $(0,0)$ representation is the trivial scalar ...
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Parity conserving QFT

I was reading Peskin's QFT text and in Chapter 6 (Radiative Corrections), there is a line in section 6.2, page 185 which I am quoting below. The passage is about the $\Gamma^{\mu}(p^{'},p)$ and its ...
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What are the assumptions that $C$, $P$, and $T$ must satisfy?

I am not asking for a proof of the $CPT$ theorem. I am asking how the $CPT$ theorem can even be defined. As matrices in $O(1,3)$, $T$ and $P$ are just $$ T = \begin{pmatrix} -1 & 0 & 0 & ...
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Parity conservation in electromagnetic decays

When a $\pi^0$ decays into photons, the only possible number of photons to which it can decay is 2$\times n$, with $n$ a natural number. This is because in electromagnetic decays charge conjugation is ...
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What does parity operation mean on a vector represented in polar form

Recently i studied vector's mathematical meaning (i.e the vectors transforms the same way as co- ordinate system) and our teacher introduced us to parity operation and how vectors transforms under it. ...