Questions tagged [symmetry]

We say that something is symmetric if there is some transformation we can perform on that object that leaves some property unchanged. The set of symmetry transformations of an object form a group, and the name of this group is used as the name of the symmetry of the object.

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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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Symmetry implies Ward identity

I am thinking about symmetries and that their "quantum" consequences are Ward identities of the form $$<\beta|[Q,S]|\alpha>=0,$$ where $Q$ is the conserved charge associated with the ...
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Symmetry relations of a Hamiltonian (Mirror, Chiral, Inversion, Rotation)

I'm reading a paper https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.235136. Regarding Eq. (4)~(6), I have the following questions: (A) Eq. (5) shows a mirror symmetry relation $M_z H \left( ...
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Given a representation of $su(3)$ labelled by $(p, q)$, is there a way to construct its state of greatest weight?

My current understanding of the representations of $\mathfrak{su}(3)$ is as follows: We can construct 3 $\mathfrak{su}(2)$ subalgebras with step operators $I_\pm, U_\pm, V_\pm$. These maybe be ...
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How are anomalies possible?

From Matthew D. Shwartz Quantum Field Theory textbook, he writes: "Most of the time, a symmetry of a classical theory is also a symmetry of the quantum theory based on the same Lagrangian. When ...
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Problem 6 of Sheet 1 - Quantum field theory David Tong - Variation of Lagrangian density

The Problem reads: Consider the infinitesimal form of the Lorentz transformation derived in the previous question: $x^\mu \rightarrow x^\mu +\omega^{\mu}_\nu x^\nu$. Show that the scalar field ...
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Finding $\Sigma$ wavefunctions from proton wavefunction. Any operator which can achieve this?

Knowing the isospin part of the wavefunction of the proton, it is possible to find that of the neutron by applying the isospin lowering operator $I_-$ which sits horizontally to the left of the proton ...
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Noether current associated with transformation $\delta \psi=i\alpha \psi$

I'm doing problem 3 from sheet 2 of David Tong's lecture notes. We have given the complex field $\psi(x)$ which is governed by the Lagrangian $$\mathcal{L}=\partial_\mu \psi^*\partial^\mu \psi -m^2\...
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From the point of view of physics, why is it useful to know the irreps of rotation group?

In 3D, the rank two tensorial physical quantities, for example, the electric susceptibility, the conductivity, the stress tensor etc, are in general, not irreducible representations i.e. neither ...
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Why is the gravitational potential inside a hollow sphere same as that of the gravitational potential on the surface of the hollow sphere? [duplicate]

Gravitational potential inside a hollow sphere is given by $$V(r)=\frac{-Gm}{R}$$ Why is it the same as the gravitational potential on the surface of the hollow sphere, which is given by $\frac{-Gm}{R}...
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Chiral symmetry of the Dirac Lagrangian

I need to show that in the mass to zero limit the lagrangian density: $$\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi$$ is invariant under the transformations: $$\psi'=e^{i\alpha\gamma^5} \psi$...
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Are these two Feynman diagrams different?

I am a little confused about the symmetry of Feynman diagrams. As far as I understand, Feynman diagrams are not symmetric with respect to exchange of external points or momentums if the diagrams are ...
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The mathematics of different particle rotations

So, in general (if I understand this correctly): Force particles behave differently than matter particles under rotation The matter particles need a 720° rotation to put them back into their initial ...
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Geodesic deviation and Lie dragging

Suppose that $𝑥_\mu(\lambda,𝑠)$ represents a family of curves. Let $𝑣_𝜇$ represents the the tangent vector to a curve $𝑥_𝜇(\lambda,𝑠_0)$ with $𝑠_0$fixed that is $𝑣_𝜇=∂𝑥_𝜇/∂\lambda$ and ...
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Quantum Time Crystals

I am not sure I appreciate the implication made by Wilczek here: I definitely see how the expectation value for $\dot\phi$ becomes zero for an energy eigenstate $\Psi_E$ but I do not see what he is ...
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Killing field with a time dependent metric (including $g_{00}$)

Let's suppose that (in cartesian coordinates) $$g_{\mu\nu}=diag(-f(t)^2, g(t)^2, g(t)^2, g(t)^2).$$ So that all of the components of the metric are dependent on coordinate time. If we produce a ...
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Noether current for self-dual Yang-Mills theory

The Lagrangian for self-dual Yang-Mills theory, in spinorial notations is given by $$\mathcal{L}= B^{a\, AB} (\partial_{A}{}^{A'} A^a_{A'B} + f^{abc} A^b_{A}{}^{A'} A^c_{A'B})$$ where $B^{a\,AB}$ is a ...
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Representation of symmetry operators in second quantuzation

Hamiltonian invariant under a symmetry- The action of a group $G$ on the set of Bloch momentum is given by a linear representation $T_g: k \to T_g k \equiv k_g $. Now say that a fermionic Bloch ...
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Rotation and Killing vectors in Minkowski spacetime

There are $3$ Killing vectors in the Minkowski spacetime related to the conservation of angular momentum. Sometimes it is mentioned that it is related to the rotational symmetry of the spacetime. But ...
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I'm confused about the number of Killing vectors in Schwarzschild metric

I'm trying to perform a calculation to derive the Killing vectors of a spherically symmetric metric (so I use the Schwarzschild metric without loss of generality because the Birkhoff theorem tells me ...
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What makes energy "the" conserved quantity associated with temporal translation symmetry?

This kind of relates to my prior question about the non-triviality of temporal translation symmetry and will use some of the same concepts: How is energy conservation & Noether's theorem a non-...
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Are there non time-symmetric systems that increase total energy over time?

According to Noether's theorem, systems that are not time-symmetric have $\frac{\mathrm{d}E}{\mathrm{d}t}\neq0$. I have essentially two questions, then: Are there any real systems (discovered or ...
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Why can't spherical nuclei rotate?

When studying nuclei it is said that spherical nuclei do not rotate, instead rotations are considered for deformed nuclei only. I do not understand why is that. If one can write the hamiltonian of ...
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Symmetry Factors in $n$-point one-loop function for QCD

I am calculating (the divergent part) of the gluon 3-point function and gluon 4-point function in the QCD Lagrangian. So I have found here what I believe to be all the 1PI Feynman diagrams at one-loop....
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Symmetries of Riemann tensor

Is there a way to show that the symmetries of Riemann tensor are preserved even if the indices are raised or lowered in general. I know how to do it individually for each symmetry but am not sure how ...
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Can conservation of phase space volume be viewed as a consequence of some symmetry via Noether's theorem? [duplicate]

Liouville's theorem says that for the Hamiltonian evolution of a system, the flow of points on the phase space with time is like that of an incompressible fluid i.e. the phase space density is ...
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Could the Lorentz symmetry be theoretically broken in vacuum?

In this paper 1 which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says: "We now introduce a Higgs sector into the Lagrangian density such that the ...
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Preservation of symmetries of Tensors under lowering and raising indices

How do you go about showing that symmetry properties of tensors are preserved during lowering and raising indices in a metric space? I know how do do it for individual tensors with given symmetries ...
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Translation invariance for scalar field [closed]

How can I see that for a scalar field $$\phi(x)=e^{i\hat{p}\cdot x}\phi(0)e^{-i\hat{p}\cdot x}$$ if we have translation invariance?
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Why don't we chose $\det(H)$ in winding number density?

Hello i have a short question on the winding number in chiral systems. If we have a chiral system described by a hamiltonian like this $$ H = \left [ \begin{array}{cc} 0 & K \\ K^{\dagger} & 0 ...
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3 answers
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Lagrangian first integral

I want to extremize $$\int dt \frac{\sqrt{\dot x ^2 + \dot y ^2}}{y}.$$ I have thought that, since the Lagrangian $L(y, \dot y, \dot x)$ is $t$ dependent only implicitly, that i could use the fact ...
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Surface effect on non-symmorphic symmetries when applied to tensors

I am curious about the effect that a surface has on a non-symmorphic symmetry. To be concrete, assume that we have a crystal with symmetry-group $G$, which contains non-symmorphic elements $\{R|\tau_R\...
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How does 'symmetry' of a circuit allow us to find currents when a junction splits into 2 different resistors?

The book says what the picture shows. There's no parallel or series resistors and I could solve it with 4 different currents (if the top blue arrow is i3 and bottom green is i4) but that's a 4 ...
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5 votes
2 answers
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Symmetry factors in two interacting fields

Red and blue colored lines represent the two different fields. At 1st order, by the exchange of the blue legs and red legs we get $\frac{1}{4}$ factor and in one of the 2nd order term drawn above, ...
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Selection rules for electronic transitions when noble gas atoms collide

The selection rules of atoms that are alone are useful for determining whether there can be certain radiative transitions, or which transitions are more likely than others. For example, for small ...
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Particle number conservation in matrix product state

I've been trying to understand how particle number conservation is enforced in matrix product state algorithms. As far as I understand, if the Hamiltonian commutes with the number operator, you can ...
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Symmetry of two-electron wave function under electron exchange

Consider two electrons in some potential. The typical reasoning for the wave function having to be (anti)symmetric goes like this - The Hamiltonian remains unchanged under electron exchange. ...
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Conservation of symmetrization in quantum mechanics

I recently read about the symmetrization requirement, which my book states is axiomatic of quantum mechanics: $$ \psi(\mathbf r_1, \mathbf r_2) = \pm \psi(\mathbf r_2, \mathbf r_1). \tag{*} $$ It ...
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How to stack two Haldane chains?

This questions is a follow up to a pervious question of mine: Inverse of Haldane phase? Now that I know that Haldane phase is it's own inverse, I am having trouble is visualizing how could we stack ...
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Symmetry group of Haldane chain?

After having seen some videos and read some articles, I am having some confusion about the symmetry group G of spin 1 Haldane chain. Being composed of spin 1 sites, it seems natural to consider SO(3) ...
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Why do the electric field lines not originate from a positive charge in the following situation?

Consider two fixed positive point charges, each of magnitude $Q$ placed at a finite distance apart. Let point $O$ be the midpoint of the two charges. We can see that the electric field at $O$ is zero, ...
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Was asymptotic expansion also a form of symmetry?

Consider the infinitesimal expansion, which was used to describe the behavior of of the expression when taking the parameter to be small. The infinitesimal expansion was usually used to describe the ...
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Do we have any guarantee that the Noether current of continuous symmetry is non-zero? (Inspired by calculating $SO(2)$ charge of Majorana Fermion)

Let me first describe how I got to that problem. We know that Majorana Lagrangian (here I choose left-handed but for right-handed problem is analogue) $${\cal L}=\psi_{L}^{\dagger}i\bar{\sigma}^{\mu}\...
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2 answers
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Could somehow the fundamental laws and symmetries of physics change or be broken? [closed]

There are some theoretical processes (like vacuum decay in quantum field theory) that could change the physical constants of the universe. Similarly, in inflation theory, various models predict that ...
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Variation of the Lagrangian and the Noether current

In Schwartz’s book, QFT and Standard Model, section 8.3.1, he writes if we then let $\alpha$ be a function of $x$, the transformed $\mathcal L_0$ can only depend on $\partial_\mu \alpha$. Thus, for ...
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Poincaré Symmetry becoming Mobius Symmetry for Euclidean Theory on Riemann Sphere

I've just started reading some introductory notes by Goddard and Gaberdiel on CFTs. The authors start by considering a Euclidean signature meromorphic field theory on the Riemann sphere. They state ...
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Symmetry of Scalar Action Associated with (Conformal) Killing Tensor

Short version: Consider the action for a scalar field coupled to the Ricci scalar in $d$ spacetime dimensions: $$S = -\frac{1}{2}\int d^dx \, \left(\nabla_\mu \phi \nabla^\mu \phi + \xi R \phi^2\right)...
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What elements of my group am I missing and which group is it? [closed]

I am working on an exercise which is asking to find the elements of the symmetry group of the following figure given below: Note that the rectangular sides of the box all have the exact same pattern ...
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