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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Inversion symmetry in Kane-Mele model?

I am trying to understand how the famous Kane-Mele spin-dependent hopping term in Quantum Spin Hall state respects the parity symmetry. As far as I understand, the spin does not change sign under ...
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Birkhoff and shell theorem - key differences

Given a spherically symmetric mass distribution the shell theorem states that a test particle at radius $r$ experiences no net force from shells at a radius $R > r$; the Birkhoff theorem states ...
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Using symmetry in Gauss' Law

I have to find electric field at any inside point due to a uniformly charged solid sphere I do it in following steps $\to$ First I choose a spherical gaussian surface passing through required point ...
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Translating an operator (generator of a symmetry) acting on a field

The representation of Poincare symmetry on fields at the origin, $\Phi(0)$, induces a representation of Poincare symmetry on a field at any point $\Phi(x)$. For Lorentz transformations, we define a ...
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When will the equations for finding $x$- and $y$- coordinate of center of mass of a simple shape be the same? [closed]

I notice that the equations of finding $x$- and $y$- coordinate of the center of mass of a triangle are the same (at least look similar). Both are h(height or base of the triangle)/3. For the case of ...
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What measurable quantity is associated with parity?

In quantum mechanics, we learn that for any Hamiltonian with a symmetry, there exists a unitary operator associated with that symmetry. Consider the parity operator which is defined by its operation ...
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What are the symmetries in fermionic quantum mechanics?

Consider a $d=0+1$ theory of fermions, i.e., fermionic QM: $$ L=i\psi\partial_t\psi-V(\psi) $$ The Hamiltonian is just $H=V$. What is the definition of a symmetry here? I can construct transformations ...
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Symmetry in the solution of orbit equation in central force

In Goldstein's Classical Mechanics, following comment is made regarding the equation of orbit in central force: $\frac{d^2u}{d\theta^2}+u=-\frac{m}{l^2}\frac{d}{du}V\Big(\frac{1}{u}\Big)\tag{3.34}$ ...
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Permittivity-Permeability-Scale symmetry in Classical Electromagnetics

Is this statement true: "If we double the permittivity and the permeability of the entire universe, then shrink it down to half; we wouldn't be able to tell the difference (within classical ...
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Implementing symmetry in MRCI calculation

I am running Multi Reference Configuration Interaction calculations for Aluminium Flouride molecule in its A1Pi state interacting with Helium. For a complete Potential energy surface, i am doing the ...
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Is a charge between two rotating charged cylinders influenced by the magnetic field of the inner cylinder?

I have calculated the field, but I am unsure whether I would have to consider the magnetic field of the inner cylinder. Whether this influences the movement of the point charge. Is a charge between ...
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Mixing $SU(N)$ and $U(1)$ generators to form an unbroken $U(1)’$

I’m trying to understand some symmetry breaking patterns and have been reading David Tong’s Gauge Theory notes for an overview. I’m getting very confused about how one can mix $SU(N)$ and $U(1)$ ...
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Regarding the physical significance of the eigenvalues of the permutation operator

Is the permutation operator an observable? I know that it is Hermitian* and unitary. If yes, what is the physical quantity that corresponds to the eigenvalues of this operator? If we apply the ...
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Different derivations of first Noether's theorem [duplicate]

I'm my current studies in Noether's theorem, the two that I liked the most are joshphysics answer to this Phys SE. post, and the derivation in chapter $4$ of An Elementary Introduction to Classical ...
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What do we mean when we say that some Hamiltonian is invariant under rotations?

Before going on to examine some examples of spin precession, it is worthwhile commenting on the time dependence of the expectation values $(4.23),(4.28)$, and (4.30). First, note from (4.16) that $$ \...
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A footnote in Altland Simons

On page 212 footnote 18 says: Remember that, in a theory with complex or Grassmann fields, only contractions $\sim \langle \bar{\psi}\psi\rangle_0$ exist, i.e., there is a total of $n!$ distinct ...
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Proof that Wilsonian renormalization only generates terms consistent with the symmetry of the action

In the Wilsonian approach to renormalization it's easy to see that integrating out high momentum dofs in the path integral generates an infinite number of terms in the renormalized action. It's often ...
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How spontaneous symmetry breaking plays with the gauging of a finite Abelian higher-form global symmetry

My question is about a claim which I suspect is true in some generality, but that I have not seen stated anywhere in the literature, and for which I do not know of any counter-examples. Most of the ...
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How do the boundary conditions on lattice fields ensure that the particle has the correct symmetries in the perspective of CPT theorem?

Imagine for simplicity that we have scalar fields. Why don't we just impose on it the symmetries dictated by CPT theorem instead of using the boundary conditions as given in literature? A detailed ...
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Is this a valid way to derive the uncertainty principle?

In both Galilean and Special Relativity the laws of physics are the same in all reference frames, and similarly they are the same for all points in space. Not all objects have the same mass, so in ...
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What is the difference between objectivity and symmetry?

I encounter this question when reading a paper about continuum mechanics (Kumar and Parks, 2015, Proc.R.Soc.A. refer to eq.3.1 and eq.3.3) Speaking of the objectivity of strain energy density ${\psi}$,...
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Would this equation for electromagnetic four force be valid when the energy of electromagnetic radiation is negligible?

The first piece of information I used in my derivation is that, with respect to electric charge, anti-matter is mathematically equivalent to ordinary matter traveling backwards in time, which means ...
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How is energy conservation & Noether's theorem a non-trivial statement?

Noether's theorem says that energy conservation is a result of temporal translation symmetry of the laws of physics. This is implied to be - and I'm not saying it's not - a very non-trivial statement. ...
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What are some references on discrete symmetries (CMT)

I'm a condensed matter theorist, and find that others in the field are very literate in consequences of breaking discrete symmetries. For example, there are a number of statements which often float ...
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Confusion over change of sign during parity transformations

In his lecture on symmetry in physical law, https://www.feynmanlectures.caltech.edu/I_52.html, (under the polar and axial vectors sub-section), Feynman writes: “ Now if the law of reflection symmetry ...
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Principle of least action to prove that conservation of momentum results from translational symmetry

In an article that I am reading http://go.owu.edu/~physics/StudentResearch/2005/LauraBecker/SymmetrytoConservation.html - the author proves, firstly, why translational symmetry in space results from ...
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Why is the reciprocal vector with Miller indices orthogonal to the respective plane?

I always just see how the Miller indices are constructed, but nowhere an explanation why the reciprocal vector $\vec{G}=h\vec{b}_1+k\vec{b}_2+l\vec{b}_3$ with the reciprocal basis $\vec{b}_i$ is ...
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Newtonian vs Lagrangian symmetry

Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as: $$ ma = -mg $$ From here we can conclude that we have translational symmetry of the ...
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Identify symmettry in BdG hamltonian

I am confused about what symmetry is responsible for the $(E,-E)$ pairing of the energy levels in a superconducting hamiltonian. Consider the superconducting Hamiltonian $$ \mathcal{H} = \Psi^\dagger ...
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How can we show the Lorentz symmetry is not anomalous in $\phi^{4}$ theory?

how can I show in a lagrangian with scalar fields and $\phi^{4}$ interaction, the energy-momentum tensor isn't anomalous?
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SYK model and $SL(2,\mathbb{R})$

Two-point function in SYK model is given by $$\begin{align} G_{ij}(\tau,\tau')=\frac{b}{|\tau-\tau'|^{1/2}}{\rm sgn}(\tau-\tau')\delta_{ij} \end{align} \tag{1}$$ where $i$ and $j$ are the indices of ...
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Potential proof/disproof to preferential direction of the speed of light?

Imagine this, a spherical planet with a spherical moon which spherically orbits the planet every 24 hours. On this planet is a rail system with a camera attached which points perpendicular to the ...
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Equation of motion for scalar field

I am trying to derive the equation of motion for a scalar field in flat and homogenous space time where the metric is $g_{\mu \nu}=diag(-1,a^2(t),a^2(t),a^2(t))$ and the Lagrangian is given by $$\...
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Why was the supersymmetry super?

The Wikipedia page stated that In a supersymmetric theory the equations for force and the equations for matter are identical. And the supersymmetry was also stated to be the correspondence between ...
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Lagrangian density for flat space time

The lagrangian density of a classical scalar field is given as $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi -V(\phi).$$ For a flat and homogenous space time the FRW metric is $g_{\...
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Why is group theory important in General Relativity?

I came across the Poincaré group, and most importantly the Lorentz group while studying GR. What is the significance of these groups as well as any other groups used in GR? I mean, why should I care ...
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Calculation of commutation relations in the SYK model

I'm reading this paper (https://arxiv.org/abs/1604.07818). And I'm having trouble showing an equality. We consider the following $SL(2,R)$ generators. \begin{align} D=-t\partial_t-\frac{1}{4},\ P=\...
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Coordinate transforms in Birkhoff's theorem [duplicate]

In Sean Carroll's Introduction to General Relativity: Spacetime and Geometry, the section under Birkhoff's theorem in Chapter 5 attempts to remove cross terms of the form $(dtdr + drdt)$ in the metric ...
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Why geometrical symmetry breaks in planetary motion?

We all know a planet's orbit around a star (like our earth and sun) is an ellipse and not a circle and the sun locates in one of the focal points of the ellipse. When textbooks formulate this motion, ...
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Experimental evidence for the shape of a single electron's EM field?

I've read about how people have literally measured the gyromagnetic ratio of a single electron in a Penning trap. Naturally, I am frankly blown away by the exquisite precision of such an experiment. ...
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Must spacetime be homogeneous?

According to Einstein's equations of general relativity, space must be homogeneous. It can't have an edge or a centre. Is the same true of 4-dimensional spacetime – must it also be homogeneous?
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Bogoliubov spectrum of pair-density wave is not particle-hole symmetric

I am currently reading this review article about pair-density wave: https://doi.org/10.1146/annurev-conmatphys-031119-050711. There is a statement that I am not sure whether I understand. It is said ...
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Why are there three charges (all with the same form) with Pauli Matrices?

I am working on problem 2.2 Part d of Peskin and Schroeder's An Introduction to Quantum Field Theory. The authors claim that there are three charges based on the three Pauli Matrices and that that ...
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Global and gauge symmetries in AdS/CFT correspondence

Based on the AdS/CFT dictionary, global symmetries of the boundary theory are related to the gauge symmetries in the bulk theory, but I could not find a relation between gauge symmetries of the ...
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Symmetry of S-matrix in Weinberg QFT book

In volume 1 of Weinberg's QFT book, he discusses symmetry at length in chapter 2. Crucially, he defines a symmetry of a quantum system as a transformation on rays that preserves probabilities. A key ...
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Proof of Weinberg effective field theorem?

In the book Effective field theory at page 6 there is this Weinberg's theorem To any given order in perturbation theory, and for a given set of asymptotic states, the most general possible ...
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Symmetry in electrical circuits [closed]

I was able to solve the above question by assuming potentials( Nodal Analysis), but the solution was very lengthy as i had three variables and had to solve three equations. Is it possible to solve ...
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Noether current of the Dirac field under spacetime translation [closed]

My problem is that I don't get, how you can calculate the Noether current under spacetime translation of the Lagrangian density of the Dirac field. I know that in the end you get the energy and the ...
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Position operator in momentum space generator

Position operator in momentum space generator How to get the position operator in the momentum representation from knowing the momentum operator in the position representation? derived the position ...
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Why the isospin structure of the two-nucleon force falls into the four different classes?

According to this article Nuclear forces from chiral effective field theory the isospin structure of the two-nucleon force falls into the four different classes according to the $$ \begin{array}{ll} \...

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