# 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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### Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
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### Kitaev chaing, time reversel symmetry, particle hole symmetry

I was wondering if the Kitaev chain has time reversal symmetry. I think it probably doesn't because by staking Kitaev chains it is possible to create a so called Chern insulator with propagating ...
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### Conservation Laws and Symmetry

The toughest of topics in physics, like Quantum Mechanics, Relativity, String theory, can be explained in layman words and many have done so. Though there is no substitute to the understanding a ...
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### Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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### Inversion symmetry points of graphene

I have question about graphene. When you have the graphene lattice two types of atoms can be distinguished, let's call them type A and B.You can draw a unit cell that has the shape of a ...
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### Using symmetry to determine a hydrogen electron's decay route from $|300\rangle$ to $|100\rangle$

Lets say we have an electron in state $|nlm\rangle = |300\rangle$ of the hydrogen atom. By selection rules, we know that it can only decay to ground state in 3 ways, namely through the $|21m\rangle$ ...
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### What are the assumptions behind the Lagrangian derivation of energy?

What are the assumptions behind the Lagrangian derivation of energy? I understand that we're searching for a function $L$ that describes a set of physics so that solving the energy minimization ...
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### Crossing Symmetry in Bhabha scattering and Moller scattering

Given the amplitude for a particular process, it may be possible to obtain the amplitude for another similar process by a so called crossing symmetry. I know there is a $s \leftrightarrow u$ crossing ...
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### Lorentz invariance & Noether theorem of classical ED

I want to check invariance of the action under Lorentz boosts for classical electrodynamics. The action is $$S = \int \mbox{d}^4x F_{\alpha \beta} F^{\alpha \beta}$$ I assumed that the fields ...
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### Symmetrical rising of dust [closed]

What is the most symmetrical way in which a cloud of dust, say from a carpet or any other dusty object can rise? Does it maybe rise on the shape of a funnel? A mushroom cloud perhaps? The shape of ...
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### Electric field on the surface of a charged sphere

We know that the electric field for a point charge is $$E = \frac{KQ}{R^2}.$$ If $R$, i.e. distance from the electric field producer to the point where we want to find the electric field becomes ...
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### Effect symmetry on points in momentum space

I have to study some material for a condensed matter physics course and cam across a passage that I don't understand. "In momentum space time reversal symmetry and particle hole symmetry only have ...
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### effect of inversion symmetry on the bandstructure

I have a very general question, but I hope that someone can answer it. Can someone describe what the effect of inversion symmetry is on the bandstructure. (Or is there not a general effect?). ...
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### What does it mean for a topological phase to be “symmetry protected”?

I have seen some very nice and enlightening awnsers to questions related to topological order and insulators, such as here, or here. However, I'm still puzzled by the concept of "symmetry protection" ...
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### What is gate symmetry?

I just read this interesting interview with Frank Wilczek and he talks a couple of times about gate symmetry, without ever defining the term. This isn't a term I've come across, and google throws up ...
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### Symmetries in physics (specifically condensed matter physics)

Symmetries play a big role in physics. Some symmetries are translation symmetry, rotation symmetry, time translation symmetry, timereversal symmetry etc. It seems that in condensed matter physics ...
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### Intuition for S-duality

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
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### What is the definition of particle-hole symmetry in condensed matter physics?

People often talk about particle-hole symmetry in solid state physics. What are the exact definition and physics picture of particle-hole symmetry? How to define the density of particles and holes?
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### Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
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### Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?

For if I started by trying to make the Hamiltonian Lorentz invariant, I would have failed. Indeed, the Hamiltonian is part of a covariant tensor. But how do I know that the Lagrangian is not a part of ...
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### Global Anomaly and Ward Identity

This question is a continuation of the answer posted for this question about anomalies. What happens to the Ward identity corresponding to a global symmetry if that symmetry is anomalous? I mean, is ...
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### How does the surface of a material always break inversion symmetry?

I am trying to visualize this for an HCP structure. Take the profile view as such: just working in 2d. So my understanding is if we can take a point (x,y) -> (-x,-y) and get the same crystal than ...
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### What is physically irreducible representation?

When I use bilbao crystallographic server recently, I noticed a notation called physically irreducible representation. Paper says it is a direct sum of two complex conjugate representations (if ...
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### Water dipole by symmetry argument [closed]

I'm a mathematician and I'm studying Group and Representation theory and I came across with an interesting exercise involving physics, although I don't know physics, since I'm a mathematician, I found ...
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### Why does exchanging coordinates produce a phase of $\pm 1$ in an identical particle wavefunction?

Consider a system of two identical particles described by a wavefunction $\psi(x_1, x_2)$. There are two kinds of exchange operators one can define: Let $P$ be physical exchange. This operator swaps ...
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### Metallic and Semiconducting Nanotubes, symmetry discussion

I'm interested in band gaps of Single-walled Carbon Nanotubes (SWNTs). I know that there are three kinds of SWNTs: Zigzag : $(n,0)$ Armchair : $(n,n)$ Chiral : $(n,m)$ Electical properties of ...
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### Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?)

I'm convinced I'm missing something so obvious but here goes Typically, one can define something like a "general" expansion of an order parameter, ${\boldsymbol \Gamma}$, up to 6th order as follows ...
When defining a central force, some sources, like Wikipedia, say that the magnitude of the force only depends on the distance $r$: In classical mechanics, a central force on an object is a force ...