The Stack Overflow podcast is back! Listen to an interview with our new CEO.

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.

265 questions
Filter by
Sorted by
Tagged with
38 views

$CP$-transformation for spinor field. $C$ and $P$ do not commute?

I am bothered by an exercise about CP transformations where I get the result that CP acting on a Dirac spinor field is not the same as the PC transformation. The exercise states the following ...
27 views

How do time reversal and parity inversion act on a Majorana spinor in QFT?

Dirac particles are not the same Majorana particles. However, in the simple Lorentz group (boost and rotations, but no parity or time flips), they transform the same way. Particles in QFT were defined ...
44 views

Quantum harmonic oscillator hamiltonian in terms of the parity operator

Can you write the quantum harmonic oscillator hamiltonian $$H = -\dfrac{\hbar^2}{2m}\dfrac{d^2}{dx^2}+\dfrac{1}{2}m\omega^2x^2$$ in terms of the parity operator $P$?
15 views

Time ordering identities in integration over gluon fields

My question arised when trying to compute the Wilson Loop of a hybrid meson. When calculating the loop one has to keep in mind the path ordering and time ordering respectively. I have the following ...
24 views

47 views

Fermion parity operator

Fermion parity operator is defined as $$\hat{\mathcal{Q}}=\exp(i\pi\sum_j \hat{n}_j) = (-1)^{\sum_j \hat{n}_j}$$ And also if $\sum_j \hat{n}_j = \sum_j c^{\dagger}_{j}c_j=N$ is constant then it ...
41 views

What happens to the charge density under parity?

A question came to me when I tried to think about the parity prperties of the Maxwell's equations. The charge density $\rho(\vec{r})$ actually stands for a scalar quantity $\rho(x,y,z)$. Since the ...
48 views

Odd potentials in TISE

When we have an even potential we say that it has an even and odd parity wavefunctions, cf. e.g. this & this Phys.SE posts. What about an odd potential? For example, two delta functions centered ...
57 views

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?
73 views

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 ...
893 views

34 views

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 ...
36 views

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 $=1/2$...
51 views

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 ...
30 views

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 ...
106 views

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 ...
54 views

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 $1d_{3/2}$ ...
49 views

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 ...
65 views

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 ...
246 views

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 ...
53 views

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 ...
110 views

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 ...
107 views

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 ...
76 views

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. ...
32 views

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: ...
57 views

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 ...
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 ...