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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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Symmetry Argument of a Line Charge

I am been trying to make sense of my professor's lecture notes on where he talks about line charges; in general, I am lost when it comes to the symmetry argument in the case that $E_\phi=0$ on an ...
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Why impose invariance of the Lagrangian under infinitesimal coordinate transformations?

I am reading Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries by Sylvain Marsat. In section 2B the author imposes the invariance of the ...
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How is conservation of momentum a consequence of translational symmetry (translational invariance)? [on hold]

If conservation of momentum is a consequence of transnational symmetry, then why we have the condition of conservation of momentum with respect to time i.e. "momentum before collision is same as ...
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Why does $\Delta^+$ decay into $p$ and $\pi^0$? C P T symmetries

I am not very sure how to check if a decay (or other particle interaction) is possible. I know that one has to check that some quantities (as energy, electric charge, Baryon/Lepton number,...) are ...
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Does the homogeneity and isotropy of space imply that the expansion of the universe is uniform?

I have asked this question. Now I wonder what could happen if I take a step further. If space is assumed to be BOTH homogeneous AND isotropic, can I prove that the expansion of the universe is uniform?...
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Why is electric field constant over the charged solid Gaussian sphere?

I saw this example at griffiths. It’s a basic question about gauss’s law but I saw the electric field being treated as a constant and thus, it got outside of the integral. I couldn’t quite understand ...
63 views

What do we understand by a force being central?

Gravity is said to be a central force. But the resultant force field of multiple bodies is no longer central as it has many attraction points. My Doubts: Is the idea of a force being central ...
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Supertranslations, superrotations and beyond

Is there any other hidden asymptotic symmetry beyond supertranslations and superrotations? What about superboosts or alike? And super-special transformations analogue to special conformal ...
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Symmetry v.s. isometry of Minkowski and AdS or dS spacetime

We know some nice spacetime have a lot of symmetries. It is said that Minkowski spacetime has $$ISO(d-1,1)/SO(d-1,1),$$ de Sitter spacetime has $$SO(d,1)/SO(d-1,1)$$ and anti-de Sitter spacetime ...
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Rotational invariance of the conductivity tensor (Classical Hall Effect)

In classical Hall effect, the conductivity tensor is given as $\sigma = \frac{\sigma_{DC}}{1+\omega_B^2 \tau^2} \begin{pmatrix} 1 & -\omega_B \tau \\ \omega_B \tau & 1 \end{pmatrix}$ where ...
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Translation invariance of point particles as a field theory

The case of point particles, relativistic or not, can be treated as a field theory in general, ie for the $(1+1)$-dimensional case this is the theory of a field theory on the vector bundle \pi : \...
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How to show that translational invariance in $y$ of implies that it's an eigenstate of $p_y$?

Let us consider a particle on a plane with uniform magnetic field $B=B\hat{z}$, and hence with the Hamiltonian $H=\frac{1}{2m}(\vec{p}+e\vec{A})^2$. I am concerned with finding the energy eigenstates, ...
60 views

Gravity in an Earth-sized hole in “solid” outer space [duplicate]

I'm a math PhD student, and far from an expert on physics. If anything is ambiguous or uses the wrong terminology, please correct it or let me know. About a decade ago, a friend gave me a paradoxical ...
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Are special conformal transformations continuous?

My understanding of special conformal transformations (SCTs) is fairly limited, but I believe that they are composed of an inversion, a translation and another inversion. Since inversions are discrete ...
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Does isotropy depend on the location of the origin from where we see the medium?

Let us say we have a charged non-conducting sphere having a spherically symmetrical charge density $\rho (r)$ that decreases as $r$. Ignoring all other properties, If we positon ourselves in the ...
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Extended objects, bundle description and transformations

In the hope of trying to come up with a clear mental picture for what a transformation is in physics, I encounter some difficulties due to the variety of objects that appear in physics. While no ...
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How to check if a generating function produces an identity transformation without substituting the CT equations in the Hamiltonian?

In chapter 9, Goldstein ($3^{rd}$ ed.) includes a discussion and a few "trivial special cases" of Canonical Transformation which keeps the form of the Hamiltonian unchanged and named it Identity ...
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Solving resistance using symmetry

Recently I've been studying current electricity and I saw many books using symmetry to solve circuits. broadly categorised as left/right symmetry and up/down symmetry where we take current to be ...
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Is there a specific structure to the automorphism set of a field theory with respect to internal v. spacetime symmetries?

I'm trying to work out what it means exactly for a field to be transformed, without referring to gauges for now. As far as I can tell, from a rigorous perspective, a transformation of the field is an ...
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Are radial forces always conservative? [duplicate]

Well both gravity and coulombic electrostatic forces are radial forces (acting along the line joining the sources) and their potential energy is defined whereas magnetic force is not radial force and ...
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A fast and automated way to check if symmetry (space group) operations preserve a lattice

Consider the simple cubic lattice. There are symmetry operations which preserve the lattice symmetry such as translations and rotations around certain axes. There are also symmetry operations that do ...
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Simple/elementary explanation for $\mathbf{3} \otimes \mathbf{\bar{3}} = \mathbf{8} \oplus \mathbf{1}$? [duplicate]

I am preparing a talk on the Eightfold Way, and am attempting to explain the spectra of the light mesons/baryons via representation theory. It will be delivered to students who have never seen ...