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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QED breaking of parity invariance

QED is invariant under P,T,C for the Lagrangian containing operators of dimension equal or smaller than 4. I was wondering, what are the possible parity-breaking terms in QED with dimension smaller or ...
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Position expectation values in quantum harmonic oscillator

I have read that $<x^n> $ is zero for all odd values of $n$ in any state of quantum harmonic oscillator. What is the reason behind this? I can imagine for $n=1$ ( because wavefunction is ...
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How to comprehend the fact that parity is an improper rotation in the odd dimension, but not in the even dimension, physically?

Some "clarification" To begin with, I'm not even talking about relativity so, in the following, rotations always act on the Euclidean space or only the space subpart of the Minkowski space. ...
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Why parity conserves in fermi transition?

Beta decay is a weak interaction process and in weak interaction parity doesnot conserve , then why in fermi transition initial and final parties of the nucleus is conserved ?
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Parity in Effective Lagrangians

Given the following Lagrangian $$\mathscr{L} = c\frac{g}{m}\bar{\psi}_A\Gamma_5\gamma^\mu\psi_B (i\partial_\mu)\phi$$ where $\Gamma_5 \in \{\gamma_5, 1\}$, for two spin one-half particles $A$ and $B$ ...
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Parity and intrinsic parity definitions

The action of parity operator on wavefunctions is defined as a reflection in the origin $$\hat{P}\Psi(\boldsymbol{r},t)=\Psi(\boldsymbol{-r},t)$$ In particle physics, though some books define its ...
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Question about the parity violation of weak interaction Lagrangian

In the textbook of A. Zee, Quantum Field Theory in a Nutshell, the author states that the following Lagrangian: $$ \mathcal{L} = G (\overline{\psi}_{1L} \gamma^\mu \psi_{2L})(\overline{\psi}_{3L} \...
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How does parity work for the electric field and electric dipole and electric quadrapole transitions?

It is known that the electric field is a (polar) vector and is odd under parity. Likewise, when an atom undergoes a dipole transition its parity must flip because the dipole electric field acts like ...
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What is parity useful for in physics?

What do we gain by defining the parity of different objects in physics? I can learn that $L$ (angular momentum) has the opposite parity as $p$ (linear momentum) or $B$ (magnetic field) hass opposite ...
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What is a rigorous and general definition of the parity operator?

Is there a rigorous definition of the parity operator? I see parity come up in the context of angular momentum, magnetic fields, quantum spin/particles. It is also related to the Levi-Civita symbol vs ...
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Matrix elements of vector current in $\pi^-$ decay

In positive pion decay $\pi^- \rightarrow \mu^- + \overline{\nu}_\mu$, the matrix element contains the following factor: $$<0|\overline{u}(0)\gamma^\mu d(0)|\pi^-(p)>$$ On the book by Nachtmann, ...
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When defining a coordinate system, does it matter if it is right- or left-handed?

When you are defining a coordinate system when solving a problem, do the coordinates need to be right-handed to obtain a correct solution? I feel like the answer is no because the directions of ...
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Electric field under time reversal using the field tensor

The problem I stumbled upon is the same as in this question. Namely, I tried to find transformations of $\vec{E}$ and $\vec{B}$ under parity and time reversal by transforming the field tensor $F^{\mu\...
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Unitary Transformation Taking a 4$\pi$ Periodic Wave Function to 2$\pi$ Periodic Wave Function

I am reading the following paper, which discusses Majorana fermions in Josephson junction arrays. Initially, the paper starts with a model such that the wavefunctions are $4\pi$ periodic. These ...
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Parity of the vector spherical harmonics?

The vector spherical harmonics can be defined as $$\textbf{Y}_{j, \ell, 1}^m(\theta, \phi) = \sum_{m_{\ell}=-\ell}^{+\ell} \sum_{m_s=-1}^{+1}C_{\ell, m_{\ell}, 1, m_s}^{j, m_j} Y_{\ell, m_{\ell}}(\...
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How is the parity transformation defined? Especially for vector or tensor fields?

If I have a scalar field \begin{align} f: \mathbb{R}^3 &\rightarrow \mathbb{C}\\ (x, y, z) &\mapsto f(x, y, z) \end{align} We can define an operator $P$ that takes a function like $f$ and ...
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Missing parity of free particle [duplicate]

in this Definite Parity of Solutions to a Schrödinger Equation with even Potential? post in David Z's answer it's stated that the eigenfunctions have parity if the potential has parity/if $[H,P]=...
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Regarding the action of Time reversal on Dirac spinors

I'm inquring about the difference between notions of time reversal found in Streater & Wightman's "PCT, Spin and Statistics, and All That", and this accepted answer from Chiral Anomaly. ...
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On intrinsic parity of the photon

I'm trying to figure out an intuitive way to calculate the intrinsic parity of the photon, without just blowing out the result as if it was a postulate. Apparently, it has odd parity: $$ P|\gamma\...
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Parity of object made up of Dirac spinors and gamma matrices

I am reading Introduction to Elementary Particles by Griffiths, specifically the chapter on Dirac equation. Griffiths states without proof, that the expression $\bar{\psi}\gamma^\mu\gamma^5\psi$ is a ...
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How to apply potential operator $V(\hat{x})$?

I want some clarification on the potential operator $V(\hat{x})$. Can you please help me Is the action of $V(\hat{x})$ defined by its action on the position kets as $\hat{V}(x)|x\rangle=V(x)|x\...
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Time independent Schrodinger equation and sign of $x$

Say I have a wavefunction and a potential energy function that satisfy the time-independent schrodinger equation. I now change $x$ to $-x$ in both functions, does the time-independent schrodinger ...
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Mirror Matter Gravitation Interactions

I was reading the Wikipedia page on Mirror matter and I was puzzled by one of the statements in the article: Mirror matter, if it exists, would need to use the weak force to interact with ordinary ...
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How does parity opeartor act on the integral measurel term $dp$?

Suppose we have a function $f(x)$ and its fourier transformation $$f(x)=\int_{-\infty}^{\infty}dpf(p)e^{-ipx}.$$ And let's define $\hat{P}$ as space inversion opeartor that maps $x \rightarrow-x$ and ...
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Why does inversion symmetry disallow valence band maximum (VBM) to conduction band minimum (CBM) electronic transitions?

I have somewhere read that due to inversion symmetry in the crystal structure the electronic transition occurs from some bands below VBM and therefore optical band gap comes into the picture with a ...
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I was solving some Parity Question then, I came across that is magnetic field is parity invariant?

Magnetic field is given by Biot-Savart's Law : $$\vec{dB} = \frac{\mu_o}{4\pi}\int \frac{I (\vec{dl}\times \hat r)}{r^2}$$ If $P$ denotes the Parity Operator then : $$P :B\to \,\,\, ?$$
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"Proof" that time-reversal symmetry is impossible

I know the proof goes wrong. Where does it go wrong? I obviously took inspiration from parity reversal. Parity reversal takes $X$ to $-X$ and consequently $P$ to $-P$. If the transformation leaves $H$ ...
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Kaon decay parity if pion parity is redefined as +1

I am reading in Neeman’s book, The particle hunter, second edition, page 169, about the “theta-tau riddle.” He writes that You might suggest that we define the parity of the pion as $+1$, but this ...
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What are hadron parity partners?

I am studying Lattice QCD and there are many papers mentioning "Parity partners". What does this term mean?
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$C$-parity in $\pi^0\pi^+\pi^-$ system

I'm studying the conservation of the quantum number in the decay $\omega^0\rightarrow\pi^0\pi^+\pi^-$. Since $P(\omega^0)=-1$ and $P(\pi^0\pi^+\pi^-)=P(\pi^0)P(\pi^+)P(\pi^-)(-1)^{L_{+-}}(-1)^{L_{(+-)...
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Derivation of symmetry properties of Clebsch-Gordan coefficients

According to wikipedia and some books, Clebsch-Gordan coefficients follow certain symmetry relations listed below (from Wikipedia) I am interested in proving (or at least know the method for deriving)...
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Why does the time component of a pseudovector reverse under parity?

Under parity, a four-vector $V^{\mu}=(V^0,\boldsymbol{V})$ transforms as $$(V^0,\boldsymbol{V})\rightarrow(V^0,-\boldsymbol{V})$$ which makes sense as parity only reverses the spatial components. ...
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Is QCD parity conserving also non-perturbatively?

Since QCD is fundamentally non-perturbative at low energies one may ask if QCD is still Parity conserving. In the path-integral formalism using the Faddeev–Popov ghosts as gauge fixing terms the ...
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Parity and chirality [closed]

I don't exactly understand how parity is related to chirality. On wikipedia it says that the parity transformation can be thought of as a test for chirality of a physical phenomenon. How those two ...
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Why do we care about chirality?

I'm trying to figure out what's the importance of chirality in QFT. To me it seems just something mathematical (the eigenvalue of the $\gamma^{5}$ operator ) without any physical insight in it. So my ...
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Parity transformation on the adjoint spinor

In eq. (3.128) of page 66 of "An Introduction to QFT", by Peskin & Schroeder, a step involves: $$P\,\overline{\psi}\left(t,\textbf{x}\right)P^{-1}=P\,\psi^{\dagger}\left(t,\textbf{x}\...
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Defining the parity group action

I am currently reading Schwartz's 'Quantum Field Theory and the Standard Model' book. When defining the action on a complex scalar field, its clear that we need the operator to take the general form $$...
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How will Hamiltonian Operator $H = q\vec{E}\cdot \vec{r}$ be affected by rotational operator [closed]

I have a question about how will Hamiltonian Operator H = qE.r be affected by rotational operator. Not sure where to start and what happens if the direction of time is reversed ( t -> -t(T) )
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Does $dx$, $dt$ change under $P$ or $T$ symmetry?

For example, under time reversal symmetry $T$, $\partial_\mu$ will be changed to $-\partial_\mu$. But does $dx$, $dt$ changes under such symmetry transformation also? Then, how about d$\phi$ in the ...
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Are chiral fermions and chiral bosons equivalent in a chiral Lagrangian?

Is it equivalent to talk about a chiral theory in terms of 1. chiral fermions which are differently coupled to the gauge field or 2. fermions coupled to a "vector minus axial" gauge boson? ...
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How is this Hamiltonian diagonalized? [closed]

In this paper, they have a Hamiltonian of the form \begin{equation} H=\begin{pmatrix} z\frac{\mathrm{d}}{\mathrm{d}z}+g(z+\frac{\mathrm{d}}{\mathrm{d}z}) & \gamma z\frac{\mathrm{d}}{\mathrm{d}z}+\...
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Uniqueness of Maxwell Lagrangian from first principles

In Quantum field theory by M. Srednicki, we find on p. 337 the statement regarding the Maxwell Lagrangian The action we seek should be Lorentz invariant, gauge invariant, parity and time-reversal ...
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Do wave functions of scattering states of a symmetric potential exhibit definite parity?

My question is quite simple. Suppose we are given a potential such as a potential barrier (potential $V = V_0, -a \leq x \leq a$ and 0 otherwise). Will scattering states which are solutions to this ...
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Space-orderings for the space-like, light-like and time-like vector can be altered

My question concerns the space-ordering for the space-like vector between two space-time points in the Lorentz invariant theory: $$ (t_1,\vec{x_1}) \text{ and } (t_2,\vec{x_2})$$ Is it correct to ...
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What measurable quantity is associated with parity?

In quantum mechanics, we learn that for any Hamiltonian with a symmetry, there exists a unitary operator associated with that symmetry. Consider the parity operator which is defined by its operation ...
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Parity transformation: mistake or puzzle in Sakurai's "Modern Quantum Mechanics"?

In Sakurai's Modern Quantum Mechanics, p.270, he wrote an equation the parity transformation $\pi$ (where $\pi = \pi^\dagger = \pi^{-1}$) as $$\pi \left(1- \frac{i p \cdot d x'}{\hbar}\right) \pi^\...
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Is a magnet and bouncy balls a case of parity violation?

This may well be a very odd question; however, I'm currently studying parity violation and it came to mind that, if a Cobalt-60 atom decaying by the weak force and emitting more electrons opposite the ...
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Confusion over Feynman’s description of the Wu experiment for parity violation

In his lecture on symmetry in physical law, Feynman said: Using a very strong magnet at a very low temperature, it turns out that a certain isotope of cobalt, which disintegrates by emitting an ...
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Why are right-hand rules not changed to left-hand rules under a parity operator?

Right-hand rules are, of course, merely convention; however, if we are to decide upon using a right-hand rule to obtain directions in one coordinate space, then why should we not use the left-hand ...
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Confusion over change of sign during parity transformations

In his lecture on symmetry in physical law, https://www.feynmanlectures.caltech.edu/I_52.html, (under the polar and axial vectors sub-section), Feynman writes: “ Now if the law of reflection symmetry ...
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