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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Ruling out dependence of y and z coordinates in Lorentz transformation

Let us assume that motion is in the $x$ direction, axes of both coordinate systems are aligned and their origins meet at $t=t'=0$. The most general relation between $x$ and $x'$ then becomes (ruling ...
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Mesons wavefunction symmetry

Is it possible to write the valence quark wavefunction for mesons which is overall symmetric in nature? Because acc. to me, we can not say directly that flavor and color wavefunction is symmetric as ...
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Generality of Rotational transformation of Berry's Formula for Berry flux

In his paper, Michael Berry has given the general expression for the calculation of Berry flux for a particular level as: $$\vec{B}^{(n)}(R) = -\text{Im}\sum_{n'\neq n}\frac{\langle n(R)|\nabla H|n'(R)...
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What is the asymptotic charge for a two-form theory in Lorenz gauge?

I'm trying to derive the generating charge of the asymptotic symmetries for a two-form field in Lorenz gauge at future null infinity. I'm working in retarded Bondi coordinates $(u,r,x^A, x^B)$. First ...
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Time dependent Quantum Generators

We know a space-translation generator can be written as: \begin{equation} T(\textbf{r}_{0})|\alpha\rangle=e^{-i\frac{\textbf{p}\cdot\textbf{r} _{0}}{\hbar}}|\alpha\rangle=|\alpha'\rangle. \end{...
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Poincaré with spontaneously broken translations

What is the physical interpretation of Poincaré symmetries with spontaneously broken spatial and temporal translations? Is there an interesting low-energy effective model for it and what are its ...
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Continuum Mechanics: Equality of stresses on opposite sides [duplicate]

Introduction: According to the theory, the stress tensor should be symmetric. On This page, and on many others, the explanation is: Taking the rotational equilibrium around the center of this 2D ...
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Why did Noether use the Lagrangian for her conservation of energy theorem?

So I know that for Noether's conservation of energy theorem, the Lagrangian is used. However, I know that the Lagrangian doesn't always equal energy. So why did she use the Lagrangian and not other ...
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What is the Noether charge associated with screw symmetry?

I put my desk fan on top of a book, and noticed it was Neuenschwander's book about Noether's theorem. That got me thinking about the symmetries of the fan: while there is a periodic symmetry for each $...
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Gauss Law for finite linear conductor

Why can't Gauss Law be applied to a finite linear Conductor, while as the same can be applied to an infinite Conductor.
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How to show $SU(3)$ symmetry of the following hamiltonian?

I have a hamiltonian of the form: $H = \sum_i (\hat{U^+_i}\hat{U^-_{i+1}} + \hat{U^-_i}\hat{U^+_{i+1}}+\hat{V^+_i}\hat{V^-_{i+1}}+\hat{V^-_i}\hat{V^+_{i+1}}+\hat{T^+_i}\hat{T^-_{i+1}}+\hat{T^-_i}\hat{...
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Off-diagonal elements of the metric tensor and reversal symmetries

Given a metric that may be written as in some suitable coordinate system as $g_{\mu0}=\delta_{\mu0}$ and arbitrary other components, what properties of the spacetimes described by this kind of metric ...
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Gravitational potential energy inside of a solid sphere [duplicate]

I am self-studying classical mechanics. I came across a problem which required me to calculate the gravitational potential inside of a sphere. I found in one of my textbooks that the potential energy ...
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Selection rules in Stark Effect using parity in particular

In the context of the Stark effect as analyzed by perturbation theory with an electric field in the z-direction, we have to examine the matrix element $$\langle n',l',m'|z|n,l,m \rangle.$$ From ...
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Is there an infinite amount of conserved currents for a given finite symmetry?

Let's say we have a field $\phi(x)$ that gets transformed to $\phi(x, \epsilon)$ under some finite transformation. We also define $\phi(x,0)=\phi(x)$. If we Taylor expand our transformation we get: $$\...
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Is Newton’s third law of motion formed from Poincare symmetries?

So I know that Newton's third law states that every action has an equal reaction, making a symmetry. But just like how Poincare symmetries form conservation laws, do any Poincare symmetries form ...
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Can residual gauge symmetries have compact support

So, I have been reading this review about asymptotic symmetries, and one definition that is used is apparently due to Penrose : $$ G = \frac{\mbox{gauge symmetries preserving boundary conditions}}{\...
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Tensor symmetry: A symmetric mixed $(1,1)$ tensor is necessarily a multiple of the identity tensor

I found this observation in a book. "It is not possible to have an invariant definition of symmetry in one contravariant and one covariant index". That's all right, my problem is that to ...
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How is the Virasoro symmetry realised on $AdS_3$?

In the context of the Holographic correspondence, $AdS_{n}/CFT_{n-1}$, it is often cited as a "confirmation" that the two symmetry groups of the theories correspond. Indeed, in dimensions $n&...
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Gravitational potential at instant of collision

Two spheres colliding that are gravitationally attracted. I want to understand what the gravitational potential between the two is at the point of collision. Is it negative or positive or zero? This ...
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Derivation symmetrization canonical energy EM tensor

The Lagrangian for the electromagnetic field is $\mathcal{L}=-\frac{1}{4} F_{\mu\nu} F^{\mu \nu}$. Noether's theorem yields the following canonical stress-energy tensor: \begin{equation} T^{\mu \nu} = ...
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Representation of honeycomb lattice inversion symmetry operator acting on 2x2 Bloch Hamiltonian

I am considering a spinless nearest neighbor tight binding model of graphene, leading to a 2x2 Bloch Hamiltonian $$H(\vec{k}) = \vec{h}(\vec{k}) \cdot \vec{\sigma} = \begin{bmatrix} 0 & t(e^{-i\...
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Is it possible to elevate the electric-magnetic duality discrete symmetry to a continuous one?

I'm familiar with Electric-Magnetic duality, where in the absence of source fields one can exchange the $F_{\mu \nu}$ field with the dual field: $\tilde{F}_{\mu \nu}={\epsilon}_{\mu \nu \alpha \beta} ...
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In the event of a vacuum phase transition, could the universe be left into a state with no fundamental symmetries?

I was having a discussion with a physicist asking him whether there could be any process, compatible with our current knowledge of physics, where the universe would be left without any fundamental ...
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Are all asymptotic symmetries and their meaning known?

Beyond the Standard Model and the General relativity invariant groups, recently we have met (again) the BSM groups of asymptotic symmetries given by the Bondi-Metzner-Sachs (BMS) or the extended BSM ...
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Is the charge distribution of open shell atoms spherically symmetric?

I am confused about the symmetry of the electronic structure of open shell atoms, especially when it comes to calculating their response properties (polarizability, to name an example). Let's take the ...
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What's a Sewing Matrix?

I'm reading a paper on graphene that talks about these sewing matrices, but I don't understand their definition. Upon researching it on the internet, I've found the term in other papers, so I assume ...
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Lagrange multipliers (with indices) and symmetries of effective action

I feel a bit embarrassed asking this, but I am a bit confused with this atm. I will try to skip most details and hopefully provide the essence of my question with clarity. Suppose there is an action ...
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Effective field theory odd dimension operators

In the Standard Model Effective Field Theory, $$L_{EFT} = L_{SM} + \sum_{d=5}^{\infty}\sum_{i} \frac{c_i^{(d)}}{\Lambda_{i}^{d-4}} \mathcal{O}_i^{(d)},$$ typically, the odd dimension terms are omitted ...
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Wick's rotation, unitary transformation and symmetry

The Wick's rotation $W$ facilitates dealing with integrals in the Minkowski space by rotating time into the Euclidean space. As this rotation in time is performed within integrals, one can view that ...
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Axion quantum corrections

I've seen theories of multiple axions written down, e.g. $$ V(a,\phi) = \Lambda_{\rm QCD}^4\left(1 - \cos \frac{a}{f_a}\right) + \Lambda_{\rm ALP}^4\left(1 - \cos \left(\frac{a}{f_a} + \frac{\phi}{f}\...
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Hourglass fermions + going from glide symmetry eigenvalues to energy eigenvalues

In this paper, the authors describe how you'd get an hourglass fermion. The gist (page 2, second column) is that you have the operator $ \bar M_x$ consisting of a translation along z, $ t( c \hat z /...
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Does the commutator between the total derivative term of a symmetry generator and a quantum field always vanish?

I am trying to understand the following derivation in Schwartz section 28.2 as to how Noether Charges can be thought of as symmetry generators. We start with the definition of $Q$ (for simplicity let'...
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How to map a complex plane Mobius transformation to 1+1D Minkowski real plane?

So consider the $(x,t)$ plane endowed with the minkowski metric, namely: $$ds^2 = dx^2-dt^2.$$ It is well known that we can Wick rotate the time coordinate to get to the Euclidean metric. This can be ...
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Relation between Homogeneity and Isotropy of space?

As per my understanding so far, homogeneity of space doesn't require a special vantage point (all points in space are "equivalent" to each other) and is a universal statement in that sense; ...
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Noether Charges as symmetry generators: the boundary term

I am trying to understand the following derivation in Schwartz section 28.2 as to how Noether Charges can be thought of as symmetry generators. We start with the definition of $Q$ (for simplicity let'...
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Can the $SU(3)$ gauge field be put in geometric algebra terms?

According to this article on the spacetime algebra, we know the Dirac spinor can be thought of as an even element of the Clifford algebra over spacetime, which in turn can be thought of as a general ...
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What is a symmetry of the generating functional, and what is the significance?

I cannot find a definition for a symmetry of the generating functional in Quantum Field Theory: $$ Z[J] = \int \mathrm d \mu \, \exp\left\lbrace i S[J] \right\rbrace \, .$$ I know it's a simple ...
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In theory, could any of the theories about the end of the universe leave the universe with no symmetries?

There are several models about the end of the universe (https://en.wikipedia.org/wiki/Ultimate_fate_of_the_universe), the most popular ones are Big Freeze (or Big Chill), Big Rip, Big Crunch and Big ...
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D'Alembert operator interaction term in QFT Lagrangian

I'm trying to understand how to find the Feynman rules (and use them to calculate loop diagrams) for this Lagrangian (found on the Saclay lectures): $$\mathcal{L}=\mathcal{L}_\text{kin}-\frac{\tilde{...
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Why is it that in gauge theories the assumption "all fields decay sufficiently rapidly at infinity" not justified anymore?

I read that in gauge theories the assumption that "all fields decay sufficiently rapidly at infinity" is not justified anymore and therefore, one needs to consider boundary terms that ...
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Symmetry and corresponding operator

For a quantum symmetry, is the operator of symmetry necessary to be unitary?
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Can we find force of gravitation of irregular shape objects by assuming mass to be concentrated in its centre of mass (OUTSIDE THE OBJECT)? [closed]

I come across with a question, Asked in JEE MAINS 2014 Question stated below From a sphere of mass M and radius R, a smaller sphere of radius R/2 is carved out such that the cavity made in the ...
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Time reversal on the field operator

What I roughly know about time reversal operator T is, $$ T[a] = a^\dagger, T[a^\dagger] = a\\ T[i] = -i, T[t] = -t. $$ For the number operator $n=a^\dagger a$, I expect $T[n]=n$. Does that mean time ...
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Gravitational Force in a two hollow identical spheres? [closed]

Two identical hollow spheres of negligible thickness are placed in contact with each other. the force of gravitation between the spheres will be proportional to (r = radius of each sphere): R R² R⁴ R³...
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Is a stress tensor still symmetric when the object is rotating?

I am trying to simulate a spinning & flying deformable football with FEM method. It is always accelerating, instead of keeping static. Let an undeformed nodal position on this football $X \in \...
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Why do "good" quantum states remain stationary under perturbation?

I've been reading the degenerate perturbation theory section of Griffiths QM. He introduces the idea that, if we can find an operator $\hat A$ which commutes with $\hat H^0$ and $\hat H'$, then ...
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Galilean Symmetry of Newtonian Mechanics

So for the equations of motion to be symmetric about a transformation from $(t,x)$ to $(\tau, y)$, the following must be true (for Newtonian mechanics): $$m \frac{d^2 x}{dt^2} = f \left( x, \frac{dx}{...
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Electric potential generated by spherical symmetric charge density

I know this question is pretty basic but I found a supposedly wrong formula in my notes and I'm trying to understand where this is coming from. Suppose we have a spherically symmetric charge density $\...
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Does $CP$-violation mean $CP$-odd?

This might be a very simple question but I'm doing some reading into the Higgs boson and $CP$-symmetry breaking. I've seen the terms $CP$-even and $CP$-odd terms in the Hamiltonian floated around and ...
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