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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Explain this step (related to gamma matrices and parity operator)
I am having hard time reproducing a step from the textbook "Lecture Notes on Quantum Field Theory", by Ashok Das. On page 429 ( above equation 11.72), the author is talking about the parity ...
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A question about space inversion symmetry of parity in a rotated disk
In a rotated disk (say, Faraday disk), is the space inversion symmetry of parity still preserved?
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Is really hermiticity necessary to be a physical observable? What about larger class of operators like PT invariant operators or pseudo hermitian one?
It's really necessary for an observable represented by an operator acting in a Hilbert space to be hermitian?
It's known that not only hermitian operators have real eigenvalues and that also normal ...
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What is the correct inversion symmetry in a two-band model
Consider a simple two-band tight-binding model
$$H(k)=\sin{k_x}\,\sigma_x+\sin{k_y}\,\sigma_y + \left(\sum_{i=x,y,z}\cos{k_i}-2\right)\sigma_z.$$
Let's assume $H$ is for real spins. It breaks the time-...
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Parity symmetry complete/detailed definition and the group elements
I am trying to write down a complete/detailed definition for the parity symmetry. Symmetry as a concept is different in mathematics and in physics. There are also many other concepts which differ in ...
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How is parity measured experimentally?
I'm reading Wong 'Introductory Nuclear Physics' and in chapter 3-1 he writes that "For the deuteron, it is known that the parity is positive. Let us see what we can learn from this piece of ...
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How many degrees of freedom does a photon have in 2+1D?
Wigner's classification of particles implies that the internal degrees of freedom of a particle transform under unitary representations of the subgroup of the Lorentz group that leaves its momentum ...
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Gamma Ray Emission in the Wu Experiment
In the classic Wu experiment (https://doi.org/10.1103/PhysRev.105.1413) parity violation was discovered in the weak interaction through the asymmetry in the distribution of electrons in the beta decay ...
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How does parity conservation follow from the Wu experiment?
The Wu experiment shows how parity symmetry does not hold for the weak force. However, how does this proof that parity conservation also doesn't hold?
If my understanding is correct, the absence of ...
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Showing that measurement of spin parity does not conserve total angular momentum
So I've been sitting on the following question for days now and I really gave my best, but I just can't seem to get the right solution.
The initial problem was that we have a singlet-triplet qubit
$$ |...
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Primary operators in $d=3$ (bosonic free) conformal field theory
Consider the free bosonic conformal field theory (CFT) in spacetime dimension $d=3$. I would like to explicitly construct a primary operator of spin $l=4$, with four scalar fields $\phi$ and five ...
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Non-Hermitian Hamiltonians with just $\mathcal{T}$ symmetry
I apologise in advance if this is a trivial or nonsensical question. I am not very familiar with this area.
In the introduction to non-Hermitian Hamiltonians here, on page 7 (equations 8 and 9), the ...
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How the parity violation was shown in Experimental Test of Parity Conservation in Beta Decay?
I read that in Experimental Test of Parity Conservation in Beta Decay by C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson, Phys. Rev. 105, 1413 – Published 15 February 1957 the ...
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Connection between parity/time transformations, conformal-style dilation, and spin statistics
The operator $\left(2 \pi i t + \Delta\right)x^\mu \partial_\mu$ generates, for half-integer $t$, a combined parity and time-reversal and a dilation:
$$
\mathrm{e}^{\left(2 \pi i t + \Delta\right)x^\...
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Parity transformation on fermionic bilinears
In the Fermi weak theory we have the fermion bilinears which look like
$$
V_\mu = \bar{\psi} \gamma_\mu\psi
$$
$$
A_\mu = \bar{\psi} \gamma_\mu \gamma_5 \psi
$$
Under a parity transformation
$$
x = (...
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Transformation rules for CP conjugated spinors?
For a spinor in the chiral basis, we have the following transformation under an arbitrary Lorentz transform:
\begin{equation}
\left( \begin{array}{c}
\psi^\prime _L \\
\psi^\prime _R
\end{array}...
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Classical conservation laws and anomalies in QFT
At the beginning of chapter 4 of the book "Anomalies in quantum field theory" Reinhold Bertlmann, on page 178, the book says:
symmetries: conservation laws are connected with symmetries, ...
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Parity Violation In The Weak Force
I am having some trouble understanding parity violation in the weak interaction. Specifically, I have been reading about the 1956 Wu Experiment. From what I understand, it is the anisotropic ...
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Intrinsic Parity of the $𝐾^+$ Meson
Why it is not possible to determine intrinsic parity of the $𝐾^+$ mesons from the $𝐾^+ → 𝜋^+ 𝜋^0$ decay?
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Charge+Parity operator lead left-handed to right-handed
So i need to show that the, if $\psi$ is left-handed,
$$C\gamma^0\psi^*$$
Is right-handed.
So, we know that, for any $\psi$, $P_L \psi$ is left handed.
Also, for any $\omega$, is right-handed, $P_R \...
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3-point 1PI vertex function in pseudoscalar Yukawa theory
Consider pseudoscalar Yukawa theory in 4D:
$$ S =\int d^4x\ \frac{1}{2}(\partial\phi)^2 - \frac{1}{2}m_\phi^2\phi^2 +\bar\psi(i\gamma^\mu\partial_\mu-m_e)\psi - ig\bar\psi\gamma^5\psi\phi -\frac{\...
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How can scalar mesons have even parity?
From my understanding a pseudo-scalar meson has:
$$J^P=0^-$$
That makes sense since the total spin $S=0$ and $l$ must be $l=0$ which makes the parity:
$$ P=(-1)^{l+1}=-1 $$
uneven. Now, for scalar ...
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Consistency of One-Pion Exchange with Selection Rules for NN Pion Production (in Chiral EFT, e.g.)
Hope you're ready for a long question, but I think quite an interesting one!
One-pion exchange is an established nucleon-nucleon potential which is well-defined for any joint angular momentum state of ...
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Does particle parity play any role in matter anti-matter annihilation?
If a left handed electron and a right handed antimatter electron were to meet, would they still annihilate?
In the same way, if a left handed electron and a left handed antimatter electron meet, will ...
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Why the eigenstate of an even observable is an eigenstate of the parity operator?
Definition of an even observable: $B_+=\Pi B_+\Pi$, where $\Pi$ is the parity operator.
Consider an arbitrary even observable $B_+|\psi_b\rangle=b|\psi_b\rangle$, then
$|\psi_b\rangle$ is an ...
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Why the long lived Kaon can not decay into two pions?
The short-lived and long-lived states of kaon $|K_1>$ and $|K_2>$ respectively have the following compositions if they are the eigen states of CP parity:
$|K_1> = \frac{|K^0>\:-\:|\bar{K^0}...
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What simplifications of a spacetime metric can be made with the assumption of coordinate reflection symmetries?
I am interested in the role that the assumption of coordinate reflection symmetries (i.e. $x\rightarrow-x$) play in the potential simplification of the metric tensor for a spacetime. In particular, I ...
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The implications of symmetry + uniqueness in electromagnetism
I have tried to follow "Symmetry, Uniqueness, and the Coulomb Law of Force" by Shaw (1965) in both asking and solving this question, but to no avail. Some of the mathematical arguments there ...
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How to implement projection as potential?
Consider the quantum mechanics of a single particle in $d$ dimensions, which is governed by the Hamiltonian $$ H = P^2+V(X)\,$$ with $P$ being the momentum operator and $X$ being the position operator,...
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Fermion parity vs gauge symmetry
Take for instance a 4d gauge theory with a fermion $\psi$ in some representation of the gauge group $G$ and say that I want to study the fate of the "non ABJ-anomalous" part of the axial ...
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Why do we have this divergent graph as odd diagrams are excluded?
I got a follow-up question to my earlier post.
Suppose we have the pseudoscalar Yukawa Lagrangian:
$$
L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\bar\psi(i\not\partial-m)\psi-...
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How does parity operator act on a complex free scalar field, and how to understand the parity transformation from the invariance of Lagrangian?
At a fixed time (set $t = 0$), we can write the free complex scalar field as
\begin{equation*}
\begin{split}
\phi(x) &= \int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_p}}
\left[b_{-p}^\dagger+a_p\...
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Dirac Lagrangian not Parity Invariant?
I am following the book 'Quantum Field Theory and the Standard Model(2014)' by Matthew D. Schwartz, and I have some incertitude with regards to some subtleties that I have come across while reading ...
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Parity invariance of Dirac action
The Dirac action is
$$S=\int d^4 x \mathcal{L}(x)$$
where the $\mathcal{L}(x)$ is the Lagrangian density given by
$$\mathcal{L}(x)=\bar{\psi}(x)(i\gamma^\mu\partial_\mu-m)\psi(x).$$
In proving the ...
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"Alice Through the Looking Glass" (charge parity)
Everyone knows the old novel "Alice Through the Looking Glass".
The parity is reversed - mirror transformation in x axis correspond to the parity reversal + 180deg rotation in yz plane.
The ...
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Showing the effect of $C$, $P$ and $T$ operators for the Dirac fermion
I have the mode expansion for a Dirac fermion
\begin{equation}
\psi(x) = \int\frac{d^3k}{(2\pi)^3}\frac{1}{2\omega_k}\sum_\lambda \bigg(b(k, \lambda) u(k, \lambda)\exp(-i k\cdot x) + d^\dagger(k, \...
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Any system with $\rm SO(3)$ but not $\rm O(3)$ symmetry?
If we have a spherical symmetry potential, the single-particle Hamiltonian has not just $SO(3)$ symmetry but even $O(3)$ symmetry. That is, besides being rotationally invariant, it is automatically ...
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Why quantum mechanical degeneracy is unwanted?
Degeneracy arises when two or more distinguishable quantum states share something same, like energy or angular momentum.
Why physics always find for ways to remove this degeneracy?
Like external ...
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Correct law to use? Parity Conservation or Pauli Exclusion?
Consider two identical fermions in a state such that their positions are given as follows:
Say P1 is located at (x,y,z) then P2 would be located at (-x, -y, -z). In such a scenario say the state is ...
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Check if Hamiltonian is $PT$ symmetric
If an Operator is $PT$ symmetric, then its Eigenvalues are real and the time evolution is unitary, just like hermitian Operators. This is described in many books and papers, but I'm not sure how to ...
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Why the product of two pseudotensor would be a tensor?
I’m reading The Classical Theory of Fields by landau, and I’m quite confused about pseudotensor in the book, which indicates that the product of two pseudotensor would be a tensor. A example is that $...
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The effect of the world sheet parity reversal
(D Branes Clifford V. Johnson Page 105)
The action of world sheet parity reversal is to exchange $X^\mu(z)$ and $X^\mu(\bar z)$.
However, I don't quite follow what kind of parity reversal it was. Is ...
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Parity transformation of spinor helicity brackets
I'm trying to figure out why a parity transformation $P: (E, \textbf{p} ) \rightarrow (E, - \textbf{p})$ implies $\langle i \ j \rangle \rightarrow - [i \ j]$ and $[i \ j]\rightarrow - \langle i \ j \...
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If in principle all processes are $TPC$ symmetric then what causes the direction of time?
Let's assume all processes are TPC symmetric. Be it the breaking of an egg (just reverse all momenta of all particles involved), the evolution or collapse of the wavefunction (a big if but let's ...
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Parity operator for a general $N\times N$ Hamiltonian
Assume I've a $N\times N$ tight-binding Hamiltonian that depends on spatial coordinates $k=(k_x, k_y)$; it holds
$$ H(k)|\psi_k\rangle = E_k |\psi_k\rangle \quad .$$
Now I want to find the parity ...
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On the eigenvalues of parity operator
Parity operator $P : \psi(\mathbf{x}, t)\mapsto\psi(-\mathbf{x}, t)$ is an example of unitary, self-adjoint involution. As such, its eigenvalues can only be $\pm 1$. And yet, citing Wikipedia:
To see ...
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Parity-Odd Term in the Lagrangian
I'm currently reading chapter 94 of Srednicki's book, where he calculates the pion contribution to the nEDM (neutron electric dipole moment), after Eq. 94.22 he writes the following
I'm having a hard ...
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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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