# 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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### 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 ...