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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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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35 views

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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Proof $\langle p\rangle=0$ if and only if potential is symmetric

I came across a statement where $\langle p\rangle=0$ if and only if the potential in a Hamiltonian is symmetric, i.e. $V(-x)=V(x)$. It made some sort of sense to me comparing with the particle in a ...
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Express $P$ as a function of $H$ for quantum harmonic oscillator [closed]

Let $H = \frac{1}{2}(p^2+x^2) $ and $P$ is the inversion or parity operator, $P\psi(x) = \psi(-x)$. I have already proven that $P$ is unitary and Hermitian, that $P$ and $H$ commute, and thus since $i\...
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How to define chirality for massive particles on the level of the states and not fields?

Textbooks often define chirality on the level of the fields but not on the level of the states. How does one define chirality on the level of one-particle states? It is clear how one can define ...
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Time evolution of a system [closed]

I am confused on how they get the evolved state of system. Can someone explain this to me please? Problem: A quantum system has only two eigenstates, $|1\rangle$, $|2\rangle$, corresponding to the ...
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Why are the parity quantum numbers of low lying hadrons what they are?

So you can get the flavour and angular momentum from the $SU(3)_F$ symmetry and rotational symmetry respectively but I haven't seen how these models predict the parity of these states (and similarly ...
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Parity Transformations on Molecular Orbitals

I've been looking into the quantum mechanics of MO Theory and I stumbled across parity symmetries of atomic and molecular wavefunctions. In short, I understand how the parity operator $\hat{\mathcal{P}...
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Parity transformation in quantum mechanics

It was written in a book that if parity commutes with Hamiltonian and for some operator $\hat O$ if $P\hat O P^{-1} = -\hat O$ then $\langle\hat O\rangle = 0$. I know how to show $\langle\hat O\rangle ...
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Proof that the solution to Rayleigh stability fluid equation has defined parity when base flow is symmetrical?

I have the following exercise: Prove that if $U(z)$, the base flow, is symmetrical around $z=0$, then $\varphi(z)$ is either symmetrical or anti-symmetrical around $z=0$. The Rayleigh stability ...
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Finding $J^{PC}$ for multiparticle final state

Funnily enough, I have a question about an assertion made in one of my own papers (it was made by one of my collaborators, not me). At the bottom of pg. 8 it is stated that ... [T]he final state ...
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How can the strong nuclear force (QCD) be considered to violate chirality, but not parity?

Chirality is related to parity, correct? It is a form of 'parity'? So, How can the strong force violate chirality symmetry, but only the weak force violates parity symmetry? I am confused about the ...
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First non-unique beta decay transition (parity of the nucleus is changes)

What is the difference in the cross-section of the allowed and 1st non-unique forbidden beta decay transition? In other words, how does the change in parity of the daughter nucleus influence the cross-...
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Is the parity transformation dependent on the choice of origin?

In quantum field theory, the parity-transformation takes a scalar $\phi(t, x)$ and sends it to $\phi(t, -x)$. (For example, Peskin and Schroeder, eq. $3.129$). This transformation seems highly ...
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Unitary Equivalence of Parity Operator

I recently read a statement that 'parity operator is defined only up to unitary equivalence' in a paper about PT symmetric quantum mechanics. But I didn't understand the meaning of it. It was ...
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Define $C,P,T$ symmetry transformation in even dimensional $d$ spacetime on a relativistic Weyl fermion theory

According to https://physics.stackexchange.com/a/488388/42982 we can define $C,P,T$ discrete symmetry transformation in even dimensional spacetime. How could we write $C,P,T$ symmetry transformation ...
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Parity of electronic interaction operator

Context is for the case of the Helium Hamiltonian. For the interaction part, in atomic units, we have $$V_{12} = \frac{1}{|\boldsymbol{r}_1 - \boldsymbol{r}_2|},$$ and I'm wondering the parity of this ...
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Parity symmetry breaking implies time symmetry breaking in General Relativity?

I've recently been interested in parity violating Lagrangians in general relativity. One can obtain them using the totally antisymmetric tensor $\epsilon_{\alpha\beta\mu\nu}$. For instance the ...
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Active vs passive transformation in right handed particle

People often says that active transformation is equivalent to passive transformation. Suppose that we have a right handed particle that is, the spin and the momentum are pointing in the same direction,...
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Active vs passive transformation in parity violation

I am no familiar with electroweak force so I will pose this scenario. Suppose we have a positive charge at rest and an electric field pointing to the right than the particle would accelerate ...
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How do we know that parity is conserved in electromagnetism?

Theoretically it is well established that parity is conserved in electromagnetism, that is the lagrangian is invariant under parity operation. What I would like to know is what experiments enforce ...
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How does theta term in non-abelian violate CP symmetry?

I am trying to show that theta-term violates P and CP symmetries, $$\theta \frac{g^2}{32\pi^2} G^a_{\mu\nu}\tilde{G}^a_{\mu\nu}$$ In the case of QED I could show that this term violates P and CP ...
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A potential well with 3-fold reflection symmetry

When we are talking about Bloch's theorem and also the tight-binding approximation, we can use them to help finding eigenstates of a system. However, I am so confused how to apply it in this case (...
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Supersymmetry with two independent supercharges, $\mathcal N=4$, or $\mathcal N=(2,2)$, and physical significance?

My question is about a specific example of supersymmetry in quantum mechanics. I am not an expert on SUSY, and I would like to have some insights on this. Imagine you have a non-Hermitian supercharge $...
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Proton and anti-proton decay

I am trying to understand parity in more detail. Looking at a system with an anti-proton and proton $$\bar p p$$ For a two paricle system $P=P_1 P_2 (-1)^L$ So in this case $P = (-1)(1)(-1)^{L}$ If ...
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Parity of a fermion bilinear

I'm assuming that the parity transformation of a 4-vector field is: $$x^\mu = (t,\mathbf{x}) \rightarrow x'^\mu = (t',\mathbf{x'}) = (t,-\mathbf{x})$$ $$V^\mu(t,\mathbf{x}) = (V^0(t,\mathbf{x}), V^i(t,...
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Classifying Reactions

I am trying to determine whether some reactions are either strong, weak, electromagnetic, or forbidden. I understand the way to check charge, lepton, and baryon number conservation. Parity ...

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