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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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Relative reflection symmetry [on hold]

Please explain what is relative reflection symmetry in physics and how this apply to conservation law and conserved quantity. From this demonstration posted with title Time Coordinate Transformation ...
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Check if total angular momentum is well-defined for a particular photon wave function

I have an exotic state, which can be expressed in a way: $$\pmb{A}(\rho, \phi, z; t)= \hat{e}_{\pmb k, \sigma} A_0 e^{i (k_z z - m \phi +\omega t)}$$ where $A_0$ is a scalar amplitude of the EM-...
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What does a symmetry that changes the Lagrangian by a total derivative do to the Hamiltonian $H$?

A tiny symmetry transformation may change the Lagrangian $L$ by a total time derivative of some function $f$. This is a basic fact used in the proof of Noether's theorem. How can we see the effect of ...
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Instructions for mapping the independent Riemann coefficients to the redundant Riemann coefficients

Introduction: I have been developing a General Relativity utility for working out the stress tensor coefficients for a given metric and all the related Riemannian coefficients which build up to it: ...
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Noether's Theorem. Continuity and Symmetry

Noether's Theorem: whenever there's a continuous symmetry there is a conservation law. Symmetry is when the transformation in coordinate, coordinate velocity and time does not affect the ...
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1answer
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How does the shell theorem play into two objects just outside of a planet's boundaries gravity towards each other?

So the scenario I envision to represent this would be two meteors on opposites sides of a planet heading directly towards the planet. How would the shell theorem play into the two meteors ...
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40 views

How can we prove that correlation function depends only on the spatial difference if Hamiltonian is translationally invariant?

If $H$ is a translationally invariant Hamiltonian, how can I convince myself that the correlation function (on the ground state $\left|G\right\rangle$) $\left\langle G|\psi(x)\psi(x’)|G\right\rangle$ ...
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How does an object's volume affect its gravitational pull?

Two instances. An object is in front of two different planets with the same masses, but two different volumes. How does the gravitational pull vary from each planet? I am thinking with more given ...
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Will I be destroying spherical symmetry if I write the mass of the body as a function of time?

Will I be destroying spherical symmetry if I write the mass of the body as a function of time? If yes, then how can I write a metric for a body with mass as a function of time?
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Non-static spherical symmetry spacetime

The Schwarzschild solution is a static spherically symmetric metric. But I wanted to know that how would the space-time interval look in a Non-Static case. I tried to work it out and got $$ds²= Bdt² -...
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What is the symmetry of a Hamiltonian?

Recently while I was reading a paper on integrability of Rabi model by D Braak. In this paper there is a discussion about the symmetry of a model and that in the case of the Rabi model it is $\mathbb{...
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Exercise about symmetry in the Lagrange equations [closed]

This question was asked during a classical mechanics exam (no solutions were given afterwards). Suppose a free particle in $\mathbb{R}^n$ with the following Lagrangian: $$L = \frac{m}{2}\sum_{i=...
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Mermin Wagner theorem proof, what does the K stand for ?

I've been reading about the Mermin-Wagner theorem recently. I think I understand pretty much every computation need to derive its result from the Bogoliub inequality, but there is one thing I don't ...
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2answers
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What is the equivalent resistance between $A$ and $B$ in the given circuit? [closed]

Hi, I've been doing some current electricity problems by using Kirchhoff's laws. I've tried applying KVL(Kirchhoff Voltage law) to this circuit, but to no avail. There happens to be too many variables ...
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Coordinate Systems vs Reference Frames vs States of Motion [closed]

This is a broad conceptual question. I am really trying to understand symmetry as deeply as possible. Please let that guide your responses. In particular, I'm looking for help finding clarity on the ...
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1answer
67 views

Goldstone theorem in Weinberg vol 2

I was reading the proof of Goldstone's theorem (the operator proof starting on page 170) in Weinberg's book on QFT (Volume II) and got confused. I am able to follow each line of the proof, but as a ...
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2answers
82 views

Isometry group on a coset manifold

In ''Einstein Gravity in a Nutshell'' Zee says ''On a coset manifold $G/H$, the isometry group is evidently just $G$'' when discussing the relation between the Killing vector fields and Lie ...
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1answer
56 views

Computing a matrix element with the Wigner-Eckart-theorem

I learned about the Wigner-Eckart theorem and want to apply it to the following matrix element \begin{equation} \langle j \, m | r_kr_l | j' \, m'\rangle. \end{equation} I know this can be done by ...
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85 views

Generators in Field Theory and Derivatives

Let's consider a representation of the multiplicative group $(0,\infty)$ on Minkowski space $\mathbb{R}^4$ by dilations. \begin{align} \rho:(0,\infty)&\rightarrow\text{GL}(\mathbb{R}^4)&\\ a ...
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2answers
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Commutator generating transformations

Lately I am encountering the commutator of variations of the variables and I'm not quite sure about its physical meaning. Some examples. 1) "The composition of two supersymmetries generates a time ...
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1answer
44 views

Is it possible to construct a quiver diagram for electromagnetism?

I have been trying to learn about quiver diagrams and quiver gauge theory for a summer project. All of the lecture notes/papers on the topic give example diagrams that are mathematically simple but ...
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3answers
113 views

Operators commutation and relation between eigenvalues

If $H$ and $L_i$ are commuting ( $[H, L_i] = 0$ ) could we deduce that the eigenvalues of $H$ depend/ do not depend on $m$ and $\ell$ ( eigenvalue of $L_z, L^2$ )? I don't think so since it does not ...
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Why is the projective symmetry group a group?

I am reading the paper from X. Wen about quantum orders and symmetric spin liquids. It can be found here: https://arxiv.org/abs/cond-mat/0107071 The Hamiltonian he is writing about looks like this: \...
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1answer
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Is there a useful way to visualize the symmetries of the relativistic Riemann curvature tensor?

I find it useful to see diagrams such as trees, colored 2D and 3D arrays, etc., which illustrate how terms combine in composite expressions. For example, the following is my visualization of the ...
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1answer
48 views

Where do I go from here to show that linear momentum is conserved under all instances of translation symmetry?

I've worked through a simple derivation of symmetries implying conservation laws from an invariant Lagrangian. Namely a quantity $Q$ is conserved in the equation below, where $i$ is a degree of ...
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Time reversal in electromagnetism

In classical electrodynamics, we know that under time reversal the electric and magnetic potentials should transform as $$\phi'(x,t)=\phi(x,-t) \qquad A'(x,t)=-A(x,-t) $$ Now, using $(+,-,-,-)$ ...
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1answer
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Problem using Noether's theorem in time-dependent lagrangian

I have some problems calculating the conserved quantity for a lagrangian of the form $$ L = \frac{1}{2}m\dot{q}^2 - f(t) a q, $$ because I found the general problem too abstract, I tried at first ...
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Why do we care only about canonical transformations?

In Hamiltonian mechanics we search change of coordinates that leaves the Hamilton equation invariant: these are the canonical transformations. My question is: why we want to leave the equations ...
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81 views

Universal symmetry preserving generators

Given initial state $|\psi\rangle_i$, we can use unitary operations to evolve this state to any final state $|\psi_f\rangle = U_N\ldots U_2U_1|\psi\rangle_i$. With restriction $U_k = e^{-i\theta_k s_k^...
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1answer
51 views

Can we abstractly deduce the $L^2$ is conserved assuming only rotational symmetry of Hamiltonian?

Here $L^2$ is defined as $$ L^2=L_x^2+L_y^2+L_z^2 $$ representing the observable of the magnitude of the angular momentum. There are a lot of proofs showing the $z$-projection of the angular ...
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1answer
56 views

Why are infinitesimal shifts sufficient to prove that a symmetry holds

Why are infinitesimal shifts in the Lagrangian sufficient to prove that a symmetry holds? Couldn't a lot of things happen at higher orders? Especially when I am introducing an infinitesimal shift of a ...
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How to justify studies on fractal cosmology?

What are the arguments (theoretical and experimental) to support or to justify a fractal distribution of matter on all scales in cosmology? I see only one justification: On some small scales, matter ...
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1answer
114 views

Why is $(\vec \sigma \cdot \vec B)\psi$ in Schrodinger-Pauli equation rotationally invariant?

In the Schrodinger-Pauli equation: $$ i\partial _{t} \psi = \left[(\frac{1}{2m}(i\vec \nabla - e \vec A)^{2} - e A_{0}) 1_{2\times2} + \mu_{B} \vec B \cdot \vec \sigma\right]\psi $$ Why is $(\vec \...
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3answers
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Does Noether's theorem apply to constrained system?

The Lagrangian of a constrained system will be $$L-\lambda_1f_1-\lambda_2f_2-...\lambda_kf_k.$$ If a transformation will not affect the constrained Lagrangian, the there is some corresponding ...
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Commutator of $\hat {L}_x$ and $\hat{V}(\hat{r})$ [duplicate]

Consider the angular momentum operator $\hat{L_x}=\hat y\hat{p}_z-\hat{z}\hat{p}_y$ and the potential operator $\hat{V}$ where the potential $\hat{V}=\hat{V}(\hat{r})$ is spherically symmetric. It ...
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Is the shell theory, at least in concept, applicable to a ring world?

The Shell Theory tells us that inside a homogeneous sphere there is no gravity. It seems to me that if you cut off the top and bottom of the sphere and leave a ring, equal in width from the equator ...
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Clarifying doubt related to gravitation inside a shell

I proved that gravitational field due to a ring would be $-GMz\over\sqrt{z^3+R^3}$ for any particle lying on the axis perpendicular to its plane and passing through centre. My teacher told me ...
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1answer
79 views

Is this a “good enough” statement of Wigner's theorem from Quantum Mechanics?

I posted this on math StackExchange and got no replies, so I'm trying my luck here! I'm a fourth year physics and math student who is writing up a report on some quantum mechanical symmetries and ...
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3answers
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Is there a parameter which describes the degree of isotropy/anisotropy of a single source?

Our task is to analyse how isotropic a random collection of vectors is. All of them start at the origin and have the same length. Is there a parameter which describes the isotropy for this case? How ...
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Proving the first Bianchi identity only from the other three Riemann curvature tensor identities [closed]

Given that $R_{abcd}=-R_{bacd}$, $R_{abcd}=-R_{abdc}$ and $R_{abcd}=R_{cdab}$ can I prove that $R_{abcd}+R_{acdb}+R_{adbc}=0$ without using the definition of the Riemann curvature tensor? Are the ...
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1answer
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Achiral system with Dzyaloshinskii-Moriya interaction?

From my tentative understanding, Dzyaloshinskii-Moriya (DM) interaction determines a certain chirality by its special mixed product form while its existence only requires the breaking of inversion ...
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1answer
46 views

$U(1)_V$ invariance

I'm working with an interaction Lagrangian of the form: $${\cal L}_{int} = \bar{\psi}\Theta\chi \tag1$$ Where $\Theta$ contains other operators, coupling constants, etc. I'm trying to unveil if ...
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33 views

How to determine symmetry of the system from the term symbol?

I'm studying term symbols. I can derive them mechanically from the electron configuration using the complete table of microstates. Let's consider a typical example - an atomic carbon with the ...
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1answer
69 views

Why aren't coordinates induced vector fields always Killing fields?

We have that $$ L_K g_{\mu\nu}=\nabla_\mu K_\nu + \nabla_\nu K_\mu$$ A vector field $K$ is a Killing field if $ L_K g_{\mu\nu}=0$, but consider the coordinate induced vector field $\partial_\alpha$, ...
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Why are we only interested in unitary/anti-unitary transformations of the underlying Hilbert space when considering symmetries in quantum mechanics?

Background to question: We briefly looked at 'symmetries' in my quantum mechanics course. I was dissatisfied with the fact that we only considered unitary (touched on antiunitary) operators when ...
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1answer
59 views

Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?

In the book of Classical Mechanics by Goldstein, at page 88, it is given that However, the orbit might not be bounded, so there might not be two turning point; just one. In such a case, how can we ...
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1answer
94 views

Symmetry factor in $\phi^4$ theory

I'm having trouble while trying to understand what the symmetry factor of a Feynman diagram really is. From books I get that it is a geometrical factor that you get by the number of ways in which you ...
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Show the conformal transformation of the components of the Schouten tensor at the Spatial Infinity in an asymptotically flat spacetime

In Ashtekar & Hansen, the authors discussed a unified treatment of null and spatial infinity in general relativity. In Section 5.D., they derived the relation (20). I failed to reproduce it. Let ...
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2answers
111 views

Counterexample to spherical symmetry definition in general relativity

In practical terms we say a spacetime is spherically symmetric in GR when we have coordinates in which the spacetime metric takes the form: $$ds^2 = -f(r,t)dt^2 +g(r,t)dr^2+h(r,t)d\Omega^2 \tag{*}$$ ...
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1answer
88 views

Lagrangian of free particle - classical case

I have a question, more related to a mathematical aspect of physics, which seems I am not understanding very well. So, by applying Galilean transformation between two reference frames, which move at ...