# Tagged Questions

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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### Historical vs modern presentation of special relativity

I have noticed that historical or brief introductions of special relativity will discuss it in terms of inertial frames and postulates: Principle of Relativity - (from Einstein's 1905 paper) "the ...
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### Is it possible to define a symmetry group for the Einstein metric?

I was just wondering if there exists a group of transformations that act on the metric such that the EFE are invariant. At first I thought it would be the group of 2nd roots of unity. That is, the set ...
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### Why does the preservation of transition probabilities imply the preservation of all quantum probabilities?

I have a question about symmetries in quantum mechanics. Let $H$ be a Hilbert space, and $\mathbb{P}H$ the corresponding projective Hilbert (ray) space. In quantum mechanics, a symmetry is usually ...
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### Constructing Killing tensors from Killing vectors

Background: After reading about Carter constant and symmetries in GR, I became interested in Killing tensors. I tried reading this paper by Alan Barnes, Brian Edgar and Raffaele Rani, discussing ...
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### Gravitational force and potential in infite slab

Let's say that we have an infinite slab of height $2h$ and mass density $\rho$. Let's define $x,y$ as the axis parallel to the slab and $z$ as the perpendicular one, with $z=0$ at the middle of the ...
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### Killing Vectors in Schwarzschild Metric

Given the Schwarzschild metric with $(-,+,+,+)$ signature, $$\text ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2+r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$ the lack of ...
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### Transformations of states in quantum mechanics

In Classical Mechanics we usually describe the possible configurations of a system by points on a smooth manifold $M$ which is the configuration manifold of the system. In that case, when we talk ...
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### Examples of non-linear field symmetries?

Consider a Lagrangian theory of fields $\phi^a(x)$. Sometime such a theory posseses a symmetry (let's talk about internal symmetries for simplicity), which means that the Lagrangian is invariant under ...
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### Maintaining symmetry? [closed]

Minkowski metric is found to be $$ds^2=-dt^2+dr^2+r^2d\Omega^2$$ where $d\Omega^2$ is the metric on a unit two-sphere. Why should we keep track of the $d\Omega^2$ so that spherical symmetry holds ...
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### How to find symmetry transformations?

For a given Lagrangian $${\cal L} = - \frac{1}{4} F_{\mu \nu} F^{\mu\nu} + |D_{\mu} \phi|^2 -V (\phi)$$ with $\phi = \frac{1}{\sqrt{2}} (\phi^1 + i \phi^2)$, there are the infinitesimal local ...
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### Advanced Quantum Mechanics (Galilean transformations)

I have been reading quantum mechanics textbook by Ballentine, and in the third chapter, he says that the eigenvalues of the transformed operator, A', must remain same as those of A. I am confused ...
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### Isotropic of Inertial frame?

My understanding of isotropic is the a particular physics law remain same no matter at what direction I look at it? Now suppose in case of inertial frame, we know that its is homogeneous and ...
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### Symmetry of retarded R-current correlator in $\mathcal{N}=4$ Super Yang-Mills

The retarded correlator of the R-current $J_\mu$ of $\mathcal{N}=4$ Super Yang-Mills theory is $$C_{\mu\nu}(x-y)=-i\theta(x^0-y^0)\langle[J_\mu(x),J_\nu(y)]\rangle.$$ In this paper in eq. (2.4), I ...