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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what kind of system respects $SU(N)$ symmetry?

I read this post, Is the symmetry group of two spin 1/2 particles $SU(2) \times SU(2)$ or $SU(4)$? If the picked answer is correct, can I believe that an $N$-degenerate system respects $SU(N)$ ...
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36 views

Energy conservation in space but not in scale? [on hold]

Quite a few previous question of mine have been tumbling around the fact that energy is conserved locally and not globally. Due to various provided answers I have been struggling with a peculiar ...
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77 views

Solving the Schrodinger equation with appropriate symmetry

In the paper Markov Fields by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger ...
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27 views

What is the symmetry associated with electric charge conservation [duplicate]

Is there a kind of symmetry that yields the conservation of charges? and if so , how it works for both type of charges? Electrical Charges
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1answer
25 views

Is the singlet state $\eta '$ stable under the strong nuclear force?

According to group theory, the $SU(3)$ flavor symmetry for two quarks decomposes into an octet and a singlet. Is the prediction of this decomposition that the particles in the octet can only transform ...
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30 views

Symmetry argument about degeneracy of graphene energy band at Dirac point

This question is very related to the thread here. In the answer given by @BebopButUnsteady , the statement is that as long as the inversion and time-reversal symmetry are respected, the Dirac points ...
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1answer
53 views

Internal and spacetime symmetries?

I am trying to understand Wiki's explanation about correlation. Part of this article talks about internal and spacetime symteries: If the probability distribution has any target space symmetries, ...
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240 views

Why is the Symmetry Group for the Electroweak force SU(2)xU(1) and not U(2)

Let me first say that I'm a layman who's trying to understand group theory and gauge theory, so excuse me if my question doesn't make sense. Before symmetry breaking, the Electroweak force has 4 ...
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56 views

What transformation is the metric of general relativity invariant under?

My limited understanding of metrics comes from Cartan. From there, I understand that a metric is something invariant under certain transformations, e.g. Lorentz in special relativity. But with the ...
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2answers
44 views

Is it possible that Cauchy stress be asymmetric?

According to conservation of linear momentum and angular momentum, one can derive that Cauchy stress tensor is symmetric and hence has only 6 independent components. Is it possible that, when breaking ...
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74 views

How symmetry is related to the degeneracy?

I have several questions about symmetry in quantum mechanics. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a ...
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1answer
120 views

Symmetries in physics

Can you explain me some of the mathematical details of such concept as symmetries? In physics, we have some manifold, and fields are functions on this manifold. On the one hand, we have symmetries of ...
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50 views

Alternative symmetries for the Maxwell Lagrangian?

I'm wondering about how to show that $A_a\rightarrow A_a+\alpha\partial_0A_a$, with $\alpha$ infinitesimal, is an infinitesimal symmetry of $\mathcal L=-\frac14F_{ab}F^{ab}$. \begin{equation} ...
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76 views

Symmetry and Degeneracy of Free Particles

Consider the hamiltonian $H=\frac{p_x^2}{2m}$ in 1-D. It is invariant under $p_x \rightarrow -p_x$. Again, this hamiltonian also has translational symmetry. Which one of these two is responsible for ...
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121 views

Galilean, SE(3), Poincare groups - Central Extension

After having learnt that the Galilean (with its central extension) with an unitary operator $$ U = \sum_{i=1}^3\Big(\delta\theta_iL_i + \delta x_iP_i + \delta\lambda_iG_i +dtH\Big) + ...
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2answers
88 views

Argument for symmetry of potential

Consider the following electrostatic charge configuration of a spherically symmetric, perfect conductor with total charge $Q = 2q$, where $q > 0$. A point charge $q$ is placed at the position ...
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1answer
138 views

Lie group of Schrodinger Wave equation

In Ballentine's book on quantum mechanics (in 3rd chapter), he introduces the symmetry transformation of Galilean group associated with Schrodinger equation. Now the Galilean group as such has 10 ...
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24 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
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3answers
618 views

Why am I wrong about how to view gauge theory?

Edit: I know there have been some similar questions but I don't think any had quite articulated my particular confusion. If gauge symmetries are really just redundancies in our description accounting ...
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55 views

Reissner-Nordström Black Holes

The Reissner-Nordström black holes are described by the metric, \begin{align} ds^2 = -\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2 + \frac{1}{1-\frac{2M}{r}+\frac{Q^2}{r^2}}+r^2d\Omega^2 ...
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1answer
173 views

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
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0answers
87 views

Parity violating Dirac particle

We normally write down the Dirac Lagrangian as \begin{equation} {\cal L} _D = \bar{\psi} ( i \partial _\mu \gamma ^\mu - m ) \psi \end{equation} but are the Lagrangian's, \begin{equation} ...
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2answers
110 views

Tadpole symmetry factor

Can someone help me with symmetry factor of one-loop tadpole diagram (one loop correction to one point Green function in phi-3 theory)?
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2answers
153 views

If nature exhibits symmetry, why don't up and down quarks have equal magnitude of electric charge?

I always hear people saying symmetry is beautiful, nature is symmetric intrinsically, physics and math show the inherent symmetry in nature et cetera, et cetera. Today I learned that half of the ...
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138 views

Why do we assume local conformal transformations are symmetries in 2D CFT

The global conformal group in 2D is $SL(2,\mathbb{C})$. It consists of the fractional linear transforms that map the Riemann sphere into itself bijectively and is finite dimensional. However, when ...
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1answer
78 views

What's a good book for an advanced undergraduate/early graduate student to learn about symmetry, conservation and Noether's theorems?

What's a good book (or other resource) for an advanced undergraduate/early graduate student to learn about symmetry, conservation laws and Noether's theorems? Neuenschwander's book has a scary review ...
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360 views

How are symmetries precisely defined?

How are symmetries precisely defined? In basic physics courses it is usual to see arguments on symmetry to derive some equations. This, however, is done in a kind of sloppy way: "we are calculating ...
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50 views

Complex scalar fields conserved charges

I'm currently studying field theory and I'm having some trouble with conserved charge given in field components. If we have a complex scalar action of a field $\phi=(\phi_1,\phi_2)^T$ that is ...
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1answer
90 views

Does a Super Noether Theorem exist?

I am wondering if an extension of Noether theorem to supergroups exists. In particular the analogy with the usual case should be that supersymmmetries are in 1 to 1 correspondence to certain ...
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94 views

Maxwell equations and symmetry

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry? I believe the homogeneous Maxwell equations obey parity and time ...
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42 views

Lepton number conservation and global phase transformation

Why the lepton number conservation is connected with the invariance of the lagrangian under global phase (U(1)) transformation of the wave function? How to distinguish global gauge phase and global ...
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2answers
188 views

Must every isometry have an associated Killing vector?

I understand that the flows of Killing vector fields are isometries, and that one-parameter groups of isometries have an associated Killing vector which generates them, but are your Killing vectors ...
2
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1answer
89 views

Noether Charge For Scalar Fields Under Lorentz Transformations

The conserved charge associated with the Lorentz transfomation of a scalar field is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ is ...
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1answer
40 views

Implementing a transformation as $UaU$ and not $UaU^{-1}$?

I know one associates to each symmetry transformation a unitary/antiunitary operater...etc. But equation 3.123 in Peskin and Schroeder (PS) says that parity is implemented as $(\mathbf{p}$ is the ...
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235 views

Symmetries of the Standard Model: exact, anomalous, spontaneously broken

There are a number of possible symmetries in fundamental physics, such as: Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and ...
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2answers
98 views

Changing vector basis in AdS_3

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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1answer
63 views

Quantum explanation of Newton's Third Law of Motion

Newton's law states that for every action there is equal and opposite reaction. This law explains how rockets fly in space and accounts for the the majority of the lift action generated by a ...
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1answer
81 views

Does action really have to be Lorentz-invariant in SR?

From Landau & Lifshitz The Classical Theory Of Fields it is said: To determine the action integral for a free material particle (a particle not under the influence of any external force), we ...
3
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3answers
81 views

Rotational invariance and operator-squares

My mind is drawing a blank right now. In systems with spin and orbital angular momentum, I know that rotational invariance implies that $[H, \mathbf{J}]=0$ where $\mathbf J=\mathbf L+\mathbf S$. But ...
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3answers
152 views

Defining left and right independent of a human body?

Is it possible to define right and left independent of the asymmetric human body? I am unable to think of such a definition without circular reasoning. Example: If you are facing east, your left ...
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1answer
64 views

Symmetry of Minkowksi Metric -> Conserved Current?

My understanding of the Minkowski Metric is that we have the freedom to choose whether to place the negative sign on the time-component or on the spatial-components. That is, either basis should ...
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3answers
284 views

Difference between $SU(2)$ and $SU(2)$ gauge transformations?

I hear this jargon all the time, so what is the difference? (Of course this is nothing special to $SU(2)$, but rather I just took it as an example)
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Does the projected spin state of the $d+id$ mean-field Hamiltonian on a triangular lattice has time-reversal(TR) symmetry?

Consider the following $d+id$ mean-field Hamiltonian for a spin-1/2 model on a triangular lattice $$H=\sum_{<ij>}(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$$, with $\chi_{ij}=\begin{pmatrix} 0 & ...
2
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1answer
147 views

Is Lagrangian a scalar?

I may be wrong: Lagrangian are scalars. They are NOT invariant under coordinate transformations. The simplest example is when you have a gravitational potential ($V=mgz$) and you translate $z$ by $a$ ...
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1answer
107 views

Symmetry, Transformations and non-linear transformations

I am a physics student. My mathematical background is quite weak. I just want to know the similarities (if there are any) or differences between coordinate transformation of two kinds : Rotation of ...
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1answer
116 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
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0answers
30 views

Axis of reflection in a mirror [duplicate]

When I look at my reflection in a planar mirror, the image I see is reflected about a vertical axis. Why is it this axis and not the horizontal axis?
5
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1answer
95 views

Are conformal, Killing and homothetic vector fields the same in pseudo-riemannian manifolds?

I work in the Lorentzian manifolds, more generally in pseudo Riemannian manifolds and applications to general relativity. I know the definitions of conformal, Killing and homothetic vector fields in ...
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57 views

Symmetry of wave pulse

How can one decide whether a wave pulse is symmetrical by looking at its equation? $$y(x,t)=\frac{0.8}{[4x+5t]^2} $$ represents a moving pulse will it be symmetric?
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1answer
81 views

What if the kinetic energy of a particle was some other function $f(v)$?

This is a "what if this was how the universe worked" kind of question. I don't know if those belong in Physics StackExchange, and I apologize if they don't. Suppose we have two reference frames ...