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.
3,097
questions
0
votes
1
answer
100
views
How to correctly use Gauss Law? Why is it used the way it is? [closed]
Gauss Law
$$\oint \vec E . d \vec A = \frac{Q_{enclosed}}{\epsilon _○}$$ From this question, Gauss Law is more fundamental than Coulomb's Law. This seems counter intuitive to me when it comes to ...
- 105
2
votes
0
answers
31
views
Why $|H_1(\Sigma,\mathbb{Z}_N)|$ can be interpreted as an 1+1d $\mathbb{Z}_2$ gauge theory?
I am reading the article https://arxiv.org/abs/2204.02407, and I am struggling with the definition of a condensation defect, which is given by
\begin{align}
S(\Sigma)=\frac{1}{\sqrt{|H_1(\Sigma,\...
- 371
0
votes
0
answers
21
views
A question about space inversion symmetry of parity in a rotated disk
In a rotated disk (say, Faraday disk), is the space inversion symmetry of parity still preserved?
1
vote
0
answers
85
views
Construction of an $N$ electron orbital and spin state
Consider a system of $N$ electrons. Their Hilbert space is the antisymmetric subspace of $\mathcal H = \mathcal H_e^{\otimes N}$, where $\mathcal H_e \cong L^2(\mathbb R^3)\otimes \mathbb C^2$ is the ...
- 321
-2
votes
0
answers
50
views
Symmetric and Antisymmetric states for 3 Quarks
I think we suppose to have 27 states if we are talking about three quarks.
can anyone explain to me how to identify the symmetric states and antisymmetric ones ?
or even a keyword in which I use it to ...
0
votes
0
answers
20
views
Electron momentum in a one-dimensional lattice and conservation issue
A one-dimensional lattice is a periodic array of atoms or ions where any two adjacent ions are separated by a fixed distance, the lattice spacing $a$. The Hamiltonian of an electron moving in this ...
- 11.1k
0
votes
0
answers
53
views
Why can't we gauge the Lorentz group? (Or can we?)
One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
- 557
2
votes
1
answer
67
views
Symmetry Factor and Wicks Theorem
I have a problem with a particular kind of exercise. The question is:
Consider $\phi^4$-theory with $\mathcal{L}_\text{int}=-\frac{\lambda}{4!}\phi^4$. Give the symmetry factors of the diagram and ...
- 23
0
votes
1
answer
54
views
Can you prove the possibility to rewrite any lorentz invariant equation as the component of a 4-tensor?
When studying special relativity, there is usually a point where 4-tensors get introduced. Since all of physics equations are supposed to be lorentz-invariant, it is assumed that these equations are ...
- 51
0
votes
1
answer
66
views
All Michelson-Morley experiments have only been done in non-inertial conditions. Does special relativity apply or not?
As far as I know not a single Michelson-Morley experiment has been done in non-inertial conditions. Shouldn't it be general relativity that applies to Michelson-Morley experiments done so far?
- 31
0
votes
1
answer
59
views
Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so which one is right? [closed]
Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so can the electric potential depends also on the direction?
- 629
-2
votes
0
answers
68
views
What does it mean that the standard model Lagrangian obeys a symmetry?
It is said that the standard model has a SU(3) $\times$ SU(2) $\times$ U(1) symmetry. Sometimes I see that the precise symmetry is slightly different. Which one is the precise one?
And in what sense ...
- 1,423
0
votes
1
answer
43
views
For what reasons of symmetry does the magnetic field inside an infinite solenoid not have an azimuthal component?
When deriving the magnetic field inside of an infinitely long solenoid carrying a stationary current, it's useful to take into consideration the symmetries of the problem, in order to understand which ...
- 183
0
votes
0
answers
17
views
How check the c4v symmetry in a hamiltonian?without using geometry
In the 2D square ssh model, how to check that the Hamiltonian does not change under c4v symmetry. Based on the square geometry of this model, it is possible to realize the existence of c4v symmetry, ...
- 1
0
votes
0
answers
52
views
Algebra equation for rank-3 tensor
Suppose I work in $4$ dimensions. I have an algebraic equation in the following form, which contains a rank-3 tensor $X ^{\alpha \lambda \mu }$
\begin{equation}
X ^{\alpha \lambda \mu }\eta ^{\beta \...
- 1
0
votes
0
answers
57
views
Why is it not Pin(1,3) or Pin(3,1) in condensed matter physics?
In electron systems (or condensed matter physics), it is well known that $T^2=-1$ and $M^2=-1$, where $T$ and $M$ are time reversal and reflection along some axis. But in general, the symmetry of ...
- 41
3
votes
2
answers
98
views
Static spacetime and metric invariance
I'm studying General Relativity using Ray D'Inverno's book "Introducing Einstein's relativity". I don't understand what the author writes in paragraph 14.3 ("Static solutions") ...
- 65
0
votes
1
answer
62
views
Isotropy of space doubts
From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we ...
0
votes
3
answers
138
views
Doubts about isotrophy and homogeneity of space
From the following answer, we note that space is isotropic if everything (force, amount of things, separation by distance, e.t.c) is the same in every direction. To call a space isotropic, it shouldn'...
7
votes
1
answer
1k
views
Equation in Noether's paper
When I was reading the paper by Emmy Noether about the famous Noether Theorem, there is an equation I don't know its meaning and why it holds on page 5.
$$\phi\frac{\partial^{\sigma} p(x)}{\partial x^{...
- 159
1
vote
1
answer
70
views
Homogeneity of space doubts [duplicate]
This question might have been asked so many times, but here we go again. I'm wondering what homogeneity of space means. All the descriptions say:
there's no special point in space, every point looks ...
0
votes
1
answer
53
views
Why must Hamiltonian of a system be invariant under every operation of the relevant point group?
It is always claimed in any group theory books: "Hamiltonian of a system must be invariant under every operation of the relevant point group" or $RHR^{-1}=H$.
Suppose I have a Hamiltonian of ...
- 81
0
votes
0
answers
21
views
Lattice symmetry operations in strongly spin-orbit coupled systems
I think this is a FAQ when we are studying the rotation operations of lattice spin systems, but I can't find much references.
Background
Considering a Hamiltonian defined on a triangular lattice:
\...
4
votes
1
answer
91
views
Please help me to understand calculation of the symmetry factor of Feynman diagrams (Lancaster & Blundell's Quantum field theory)
I am reading the Lancaster & Blundell's Quantum field theory for the gifted amateur, p.183, Example 19.5 (Example of symmetry factors of several Feynman diagrams) and stuck at understanding ...
- 285
1
vote
2
answers
81
views
Are all actions time reparameterization invariant?
Let's concentrate on point particle mechanics on a one dimensional manifold for simplicity. The action is $$S [q,\dot{q}]=\int dt L(q,\dot{q},t).$$ Time reparameterization would involve $t \to t'=f(t)$...
- 81
2
votes
1
answer
29
views
Change of action after a transformation with space-time dependent parameters
I've been following David Tong's lecture on introduction to quantum field theory. In his lecture notes page number 19 (and his video class on Youtube), he talks about global transformation that ...
4
votes
1
answer
748
views
Do Killing vectors form a Lie-algebra?
In Arnold's book on "Mathematical Methods of Classical Mechanics" it is said that vector fields on manifolds form a Lie-algebra (see chapter 8 on sympletic geometry/manifolds). I consider ...
- 8,628
3
votes
0
answers
50
views
Resources and Problems on Generalized Symmetries
There has been some recent buzz around generalized/higher form/categorical(?) symmetries in the physics community. I understand Seiberg's papers are a popular resource, and I am aware of McGreevy's ...
1
vote
1
answer
64
views
$p$-state Potts Model and symmetry [closed]
Consider a lattice spin system where the spin variable is the $i$th site
can have $p$ values, 0, 1, . . . , p − 1, and the nearest-neighbor Hamiltonian describes the system
This is called a $p$-state ...
0
votes
0
answers
66
views
Do we know a reason for why exactly $\rm U(1)$, $\rm SU(2)$ and $\rm SU(3)$? [duplicate]
I always found it a curiousity that in the symmetry groups of the known fundamental forces we find the nice arithmetic progression $1,2,3$: first there is $\DeclareMathOperator{\U}{U}\...
- 514
2
votes
1
answer
65
views
Some doubts about action symmetry
We know that Symmetry of the Lagrangian ($\delta L = 0$) always yields some conservation law.
Now, if $\delta L \neq 0$, that doesn't mean we won't have conservation law, because if we can show action ...
- 495
0
votes
0
answers
47
views
Symmetry of the non-degenerate ground state
From Quantum field theory and condenced matter by Shankar, pp67, he mentioned that
In normal
problems, the symmetric state, or more generally the state with eigenvalue unity for the
symmetry ...
- 9
6
votes
1
answer
123
views
Symmetry group of a two-dimensional isotropic harmonic oscillator
The Lagrangian and the Hamiltonian of a two-dimensional isotropic oscillator (with $m=\omega=1$) are
$$L=\frac{1}{2}(v^2_1+v_2^2-q_1^2-q_2^2)\tag{1}$$ and $$H=\frac{1}{2}(p^2_1+p_2^2+q_1^2+q_2^2),\tag{...
- 11.1k
5
votes
2
answers
105
views
What is the gravity in the center of Earth?
Let's suppose the earth is perfect sphere and let's ignore its rotation and movement.
What would happen if i would be in the center of the earth? Would the gravity be zero in any direction so i wouldn'...
- 159
2
votes
2
answers
95
views
Orthochronous condition - Lorentz transformations
I'm trying to learn by myself some special relativity. By reading online I've come across the fact that Lorentz transformations are rotations on a 4D spacetime with a Minkowski metric. A rotation $\...
- 520
7
votes
4
answers
289
views
Justification of form $L(v^2)$ of Lagrangian for a free particle in Landau-Lifshitz vol 1
See the screenshot below for Landau's argument on the form of a free particle lagrangian.
My question is regarding whether the Lagrangian $L$ of a free particle must only be dependent on $v^2$. In my ...
- 191
4
votes
3
answers
164
views
Why the free Lagrangian does not dependent on the velocity vector direction, only its speed?
For freely moving particle, It's said $L$ can't depend on the velocity vector, but only its magnitude.
Question: I'm looking for the contra-argument. Let's say $L$ depends on velocity vector. Then, ...
- 495
1
vote
1
answer
104
views
Confusion on proofing Noether's theorem in field theory
I've been following along Gleb Arutyunov and Henk Stoof's Classical Field Theory lecture notes. It basically want to proof the Noether's theorem in field theory by considering an infinitesimal ...
2
votes
1
answer
47
views
Relation between the $U(1)$ symmetry and the excitation number operator in quantum optics
Firstly, we consider the Hamiltonian of Jaynes-Cummings model, i.e.,
$$H=\omega_c a^\dagger a + \omega_e\sigma^\dagger \sigma + g(a^\dagger \sigma+\sigma^\dagger a).$$
Obviously, it satisfies the $U(1)...
- 23
1
vote
0
answers
46
views
Global form of flavour symmetry groups in gauge theories
How do we work out the global nature of a flavour symmetry group? To be concrete, consider the simplest example of QED, preferably in D dimensions, with $N$ flavours of fermions with Lagrangian
$$\...
- 51
11
votes
2
answers
4k
views
I don’t understand Noether’s theorem… there is nothing to prove?
I don’t understand Noether’s theorem… there is nothing to prove?
If I understand Noether’s theorem correctly it says: if there is coordinate where the Lagrangian is invariant, then the conjugate ...
- 1,855
0
votes
0
answers
53
views
Does the translation rule of wavefunctions remain valid regardless of whether space is homogeneous or not?
When we actively translate a system, we assume that its wave function also suffers a rigid translation without changing its shape. From which we get the standard result, relating the translated ...
- 11.1k
3
votes
0
answers
54
views
How to understand non-invertible symmetries from stacking TQFTs?
I'm reading section 3.3.3 of https://arxiv.org/abs/2305.18296. The idea is to stack a 1d TQFT with G symmetry on a quantum field theory T with symmetry G, then gauge the diagonal G symmetry, the 1d ...
- 81
0
votes
1
answer
38
views
Space Symmetry and Conservation of Linear Momentum
I am trying to understand Noether's Theorem which links Space Symmetry and Conservation of Linear Momentum from an intuitive perspective.
Let's say we have car rolling down a frictionless surface ...
- 253
0
votes
0
answers
28
views
Total spin for the ground state of the Kitaev honeycomb model is 0?
We consider the Kitaev honeycomb model:
\begin{align}
H=\sum_{\langle ij\rangle_{\mu}}J_{\mu}S^{\mu}_iS^{\mu}_j.
\end{align}
If $J \equiv J_x=J_y=J_z$, the Hamiltonian can be written in
\begin{align}
...
1
vote
0
answers
38
views
How can you immediately check if a lagrangian contains a cyclic coordinate, regardless of coordinate system choice? [duplicate]
If we look at a simple cannonsball that gets shot out we quickly see the cyclic coordinate in the Lagrangian:
$$L=\frac{1}{2}m{\dot{x}}^2+\frac{1}{2}m{\dot{y}}^2-mgy$$
Since the coordinate $x$ isn't ...
- 1,855
0
votes
1
answer
57
views
Antisymmetrization of the electronic wave function
I'm studying systems of many electrons (for Theoretical Quantum Chemistry) from Landau, Quantum Mechanics (non-relativistic theory), chapters 61, 62, and 63.
I wanted to ask for good references to ...
15
votes
5
answers
2k
views
Why does time-translational symmetry imply that energy (and not something else) is conserved?
I'm trying to understand Noether's theorem from an intuitive perspective. I know that time-translational symmetry implies the conservation of energy. Is it possible to convince oneself that time-...
- 253
1
vote
1
answer
33
views
Is there a shape associated to point charge? [duplicate]
This is puzzling to me because I have learnt that a charged sphere has the same electric field and electric potential at a point beyond its surface. So does it mean that a point charge is also ...
1
vote
0
answers
31
views
If isospin is only approximately conserved by strong interaction, why do we never see isospin violation?
Due to the mass difference between the $u$-quark and the $d$-quark, SU(2) isospin symmetry is only an approximate symmetry (even in a universe devoid of weak and EM interactions). This suggests to me ...
- 11.1k