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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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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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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 and Parity violation

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. ...
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Expectation values of odd operators in case of even potentials are zero? [duplicate]

Taking, for example, position operator (which is an odd operator), and then proceeding : Assuming the eigenvalue of position operator $\hat x$ equal to $k$, can I not write: $$\begin{align} \langle\...
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Expectation values of the position operator is equal to zero in case of even potentials?

Assuming the eigenvalue of position operator $\hat x$ equal to $k$, can I not write: $$\begin{align} \langle\psi_n|x|\psi_m\rangle &= \langle x\psi_n|\psi_m\rangle \\ &=\langle k\psi_n|\psi_m\...
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Is it possible to couple an odd number of Dirac fermions, at finite density, to a massless gauge field in 2+1d?

In a beautiful paper by A. N. Redlich (PRL $\bf{52}$, 18 (1984)) on the parity anomaly, the author indicates that an odd number of Dirac fermions can never be coupled to a massless gauge field in 2+1d ...
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Are broken time reversal symmetry and inversion symmetry forbidden in a Weyl semimetal?

In much of the literature floating around, it is commonly implied that an important part of obtaining a Weyl semimetal phase is to break either time reversal symmetry or inversion symmetry. However, ...
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What does it mean for a quantum state to have even parity?

Parity is a spacial reflection of coordinates. I understand that much. When it comes to quantum states though I'm a bit confused. Can someone explain it to me in layman's terms?
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Parity violating cows

I am preparing an outreach talk about CP violation. I can vaguely remember that there is a (famous?) nature paper about parity violating cows (direction of chewing rotation is not evenly distributed.) ...
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Parity of Bloch states at TRIM points

There is an argument presented in Fu and Kane's paper on inversion symmetric topological insulator which I have not yet convinced myself. Just below Eq.(3.6), the authors said that because of ...
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Is the intrinsic parity the only contribution to parity for single-particle systems?

In the book A Introductory Course Of Particle Physics by Palash B. Pal, the author claims the following (on page 167, section 6.4.3) For single-particle systems, intrinsic parity is the only ...
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Parity transformation property of $\epsilon^{\mu\nu\sigma\rho}$ and $F_{\mu\nu}$ (and $G_{\mu\nu}^a$)

The Lorentz invariant term $\epsilon^{\mu\nu\sigma\rho}F_{\mu\nu}F_{\sigma\rho}$ is not parity invariant. To show this one needs to find the parity transformation property of $F_{\mu\nu}=\partial_\mu ...
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Spin and orbital angular momentum parity transformation in 2D

under parity transformation in 1D and 3D, we know that a parity transformation takes $\vec{r}\mapsto-\vec{r}$ and $\vec{p}\mapsto-\vec{p}$. For the 3D case, the above means that the orbital angular ...
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Parity in Madame Wu experiment

To see the effects of parity violation it's necessary to consider an observable that is non-invariant under parity, was chosen the projection of the electron momentum ($p_e$) on the polarization ...
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Is spin invariant under Parity operator or not?

If I take spin as an angular momentum, which defined as $\overrightarrow{r}\times\overrightarrow{p}$, then it is invariant under parity operation. On my lecture slide, it is also written that spin is ...
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Implications of parity violation for molecular biology

In biology, the concept of parity emerges in the context of chiral molecules, where two molecules exist with the same structure but opposite parity. Interestingly, one enantiomer often strongly ...
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Inversion symmetry restrictions to the Berry curvature in 2D

It is said that if a lattice has inversion symmetry, then the Berry curvature, $\vec{\Omega}(\vec{k})$ is even in $\vec{k}$, i.e. $$\vec{\Omega}(\vec{k})=\vec{\Omega}(-\vec{k})$$ I have also derived ...
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Parity for Dirac lagrangian in 2 + 1 dimensions

I have a problem in defining the parity operator that leaves the kinetic term of Dirac lagrangian invariant. The problem is: given the parity operator as being $\Lambda_p$ = diag{1 , 1, -1} I have to ...
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weak interaction are not parity invariant

I'm having some hard time trying to see why the left-handed lagrangian for fermions $\psi$, $$\mathcal{L} := G\overline{\psi}_{1L}\gamma^\mu\psi_{2L}\overline{\psi}_{3L}\gamma_\mu\psi_{4L}$$ is not ...
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Parity violation

I've been reading on wikipedia about parity violation in the weak force and the conclusion is: This implies that parity is not a symmetry of our universe, unless a hidden mirror sector exists in ...