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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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2answers
211 views

What is a local operator in quantum mechanics?

In quantum mechanics, what exactly is meant by "local" operator? What about a "global" or a "non-local" operator? Are these the same? Can you also also help me understand what exactly is a local ...
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1answer
80 views

Symmetries of Wigner $3j$-symbols by exchange

I know that Wigner $3j$-symbols have certain symmetry factors arising by exchange of two columns within one symbol. But what happens if you have two 3j symbols and do an exchange like this: $ \left(\...
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1answer
59 views

Why is $L_z$ operator more important the $L_x$ or $L_y$ operators?

When we talk about orbital angular momentum, we always use L_z but never talk about L_x or L-y. Why is that?
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35 views

Symmetry relation of Wigner-Eckart

I saw a symmetry relation following from the the Wigner-Eckart Theorem looking like this $$(\xi j|| T_L || \xi'j') = (-1)^{j-j'} (\xi' j'|| T_L || \xi j)^*$$ I know that it must come somehow under ...
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37 views

Why are Goldstone bosons associated to translation symmetry breaking corresponding to the coordinates transverse to the D-brane?

In some lecture notes, in the presence of a Dp-brane, translational symmetry is broken in the direction transverse to the brane. However, they identify the coordinates, $$\Phi^a,\quad a=p+1,\cdots,D-1$...
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175 views

$SU(2)$ symmetry of $\mathcal{L}=\partial_{\mu}\Phi^{\dagger}\partial^{\mu}\Phi - \Phi^{\dagger}M\Phi$

I'm considering a Lagrangian of two complex scalar field: $$\mathcal{L}=\partial_{\mu}\phi_1^{*}\partial^{\mu}\phi_1-m_1^2\phi_1^{*}\phi_1+\partial_{\mu}\phi_2^{*}\partial^{\mu}\phi_2-m_2^2\phi_2^{*}\...
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1answer
88 views

Parametrizing $SU(2)$ with Hermitian matrices

There is something that is not clear to me Here is what I know: Pauli matrices are $\sigma_1 = \begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$, $\sigma_2 = \begin{pmatrix}0 & -i \\ i & 0\...
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Difference continous - discrete symmetry

I am trying to understand the difference between the two types of symmetries.Wiki Wikipedia says that Translation in time : $t \rightarrow t + a$ is a $\textbf{continuous}$ symmetry, for any real $...
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62 views

Custodial Symmetry in SM Higgs

this excercise is about the custodial $SU(2)_R$ symmetry in the SM Higgs Mechanism. Step by step I have to develop the theory. I get the generel idea of the global custodial symmetry and why we need ...
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13 views

How to know the symmetries of a coupling in the Hamiltonian

Suppose you have an interaction term in your hamiltonian that looks like \begin{equation} H=\sum_{ijkl}U_{ijkl}c^\dagger_ic^\dagger_jc_kc_l \end{equation} where $U$ is the coupling and $c$, $c^\...
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1answer
25 views

Mcintyre Quantum Mechanics - Angular Momentum Conservation

I have two questions regarding this topic. 1. I captured the part of the section I'm referring to. If I didn't my question would probably not make sense. My first question is to the second to last ...
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43 views

Masslessness of Goldstone Bosons

I have a question about the origin of the massless nature of Goldstone bosons. This is what I understood: we know thanks to Goldstone's theorem that from the breaking of continuous symmetries emerge ...
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65 views

Legendre transformation and correspondance between Noether charges and quasi-symmetries

I have been trying to understand the Legendre transformation (in mechanics, in the hyperregular case: when the Legendre transformation is one-to-one) and the correspondence between symmetry $\to$ ...
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2answers
194 views

Even and odd solutions to time independent Schrodinger equation on symmetric potential

I have to solve the following problem: Consider the potential well: $$ V(x)=-V_0, \hspace{10px} |x|<a/2 $$ and $0$ everywhere else. $a$ is also a positive constant and so is $V_0$. Find the ...
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2answers
76 views

Why expression of energy occurs in triplet?

I have basically two questions in mind,which are Why expression of energy occurs in triplet? Why the expressions are somewhat symmetrical? Coming to elaborated form of 1st part, we have $$U=\frac{...
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51 views

Adding a total derivative to the Lagrangian does not preserve $\int\mathrm{d}^3\mathbf{x}~ T^{00}$

In problem 3.3 of Schwartz's QFT, the first two questions ask us to prove that if we add a total derivative to the Lagrangian: $$ \mathcal{L}\mapsto\mathcal{L}+\partial_\mu X^\mu\tag{1} $$ then $$ \...
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1answer
117 views

Misconceptions in spontaneous symmetry breaking

Spontaneous symmetry breaking occurs when we have a potential like a mexican hat as shown in figure (right) and is unbroken for the potential shape as shown in left figure. Under the Symmetry ...
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19 views

What is meant by cubic symmetry with regard to thin films growth?

I am reading a paper on epitaxial thin film growth of an alloy and it mentions that for one conditions the films grow with a cubic symmetry and for another they have an in-plane anisotropy. I would ...
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27 views

Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics

Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
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1answer
70 views

Are there other theories (apart from string theory) that combined with inflation, would produce universes with different laws?

In chaotic inflation, space would stop expanding in some points, creating hubble volumes that could experience different spontaneous symmetry breaking, which would result in different properties, such ...
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2answers
83 views

Inertial frames as in Landau & Lifshhitz mechanics 1st chapter

If we see inertial frames from a basic point of view (precisely more basic axiom from which I can at least derive the law of free body as in landau mechanics first chapter) that inertial frames are ...
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1answer
98 views

Why is baryon number conservation an accidental symmetry

I have to write a report surrounding the subject of baryogenesis and I wanted to start this report off with explaining how the first Sakharov condition: Baryon number violation is possible within the ...
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95 views

Feynman's proof for Newton's shell theorem [closed]

I have two questions concerning this proof: Firstly, what is the difference between the increments ds and dx? Are they not just the same thickness of the strip? Secondly, why can the integral ...
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39 views

What is the relationship between the Cosmological Constant and the Cosmological Principle?

I believe I've misunderstood a relationship between the cosmological constant and the cosmological principle having read: Einstein introduces his cosmological constant which attributes, in the ...
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56 views

Shift symmetric scalar field

Suppose I study a quantum field theory in which among other fields a shift symmetric scalar field appear: $$\phi\rightarrow\phi+c$$ with $c$ a real constant. Can this always be interpreted as a Nambu-...
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25 views

Atoms & Time Reversal

I've recently started learning Nuclear and Particle Physics, and had a question regarding time reversal. Apparently particles that can be described with a Hamiltonian which is invariant under time, ...
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1answer
42 views

How to construct invariant forms under the effect of an arbitrary group?

First I would like to mention that I do not know that should I post this question here or in the math community, but since my background is in physics and this kind of question is usually asked by ...
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1answer
30 views

Transformation of position operator

Consider a dilation of space $x\mapsto ax$ for some non-vanishing number $a$. Let $Q$ be the position operator defined by $(Q\psi)(x)=x\psi(x)$ on function $\psi$ of space. Suppose $\psi$ transforms ...
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1answer
86 views

Non-Hermitian Hamiltonian for electron conductance in electric field?

Electron conductance in a solid state is usually driven by electric field - making some direction of jumps more likely. It makes (e.g. Hubbard's) Hamiltonian no longer self-adjoint, how to simulate ...
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1answer
45 views

How to obtain the Noether charge for two interacting fields. Correct mode expansion for field operators

If I have two interacting fields $$ \mathcal{L} = \frac{1}{2}(\partial_\mu \phi_1)^2 - \frac{1}{2}m^2\phi_2^2 + \frac{1}{2}(\partial_\mu \phi_2)^2 - \frac{1}{2}m^2\phi_2^2 - g^2(\phi_1^2 + \phi_2^2)^...
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1answer
79 views

Invariance of Liouville action under rescaling

I was studying the Liouville action $$S=\frac{1}{8\pi} \int d^2 x\ \left[ \partial_\mu \phi \partial^\mu \phi + e^{\beta\phi} \right] \tag{1}$$ under the following general form of transformation: $$...
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27 views

What happens to the (Wilsonian) effective action if a symmetry is spontaneously broken?

A spontaneously broken symmetry is a symmetry of the action which does not manifest itself in physical states. Since the action is still invariant under this symmetry, can we say the same about the ...
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1answer
58 views

Conservation of a topological current

I am trying to prove the conservation of a topological current, as you can see in the picture. I show that the two of the three terms vanish. However, the last one doesn't. Any suggestions/hints?
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153 views

Why can't Gauss surface be a cube?

For calculating field outside a charged plane conductor, a gaussian surface of Cylinder is considered. I have been said that we consider cylinder because the circle in its upper end is in equal ...
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1answer
521 views

What is $U(1)$ symmetry?

I saw there are three intrinsic symmetries in physics,U(1),SU(2) and SU(3).What's the U(1) symmetry talking about?I would appreciate it if you can give me some explaination.
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54 views

Energy-momentum tensor of the electromagnetic field

I have to derive the electromagnetic energy-momentum tensor from Noether's theorem and translation invariance. Due to translation invariance and gauge transformation: $$\delta A_\mu= a^\nu F_{\mu\nu}$$...
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0answers
21 views

Normal mode decomposition of a triangular hexagonal lattice

I was trying to understand and redo the methods used in a previous question: Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice ...
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4answers
145 views

Understanding intuition behind time translation in classical mechanics

In V.Arnold book "Mathematical Methods of Classical Mechanics" he says that invariance with respect to the time for isolated systems means that "the laws of nature remain constant", i.e., if $\phi(t)$ ...
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1answer
138 views

Is universe symmetric about a point?

We have a good amount of discussion and theories on the formation of universe. I want to ask is universe symmetric about a point? I think that the answer should depend upon the uniformity of ...
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1answer
108 views

How to define time in a time-dependent solution?

If a spacetime has no timelike killing vector, how can we define "time" in such spacetime, in order to calculate the time evolution behaivor of some quantities in it?
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87 views

If the gauge symmetry is not broken by spontaneous symmetry breaking, what symmetry is broken?

In this post, the answer by buzhidao showed that the $U(1)$ gauge symmetry is not broken by spontanous symmetry broken and Higgs mechanism. What role does "spontaneously symmetry breaking" ...
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101 views

Why symmetry leads to stability?

In the whole course of physics I observed a very common thing present around us which is symmetry. Symmetry leads to stability everywhere. For example:-Pauli's Exclusion principle tends to make the ...
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1answer
80 views

Invariance of Maxwell action

I have to show that the Maxwell action $$S=-\frac{1}{4}\int d^4x F^{\mu\nu}F_{\mu\nu}\,$$ is invariant under translation: $\delta_aA_\mu=a^\nu \partial_\nu A^\mu$ with $a^\mu$ as arbitrary and ...
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1answer
36 views

Equality between derivatives of the metric

In one of my lecture, it is said: Let us use the freedom of the choice of parametrization to demand that the variation of $\lambda$ after a small displacement along the curve is proportional to the ...
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3answers
543 views

Why symmetry transformations have to commute with Hamiltonian?

Let us consider a unitary or antiunitary operator $\hat{U}$, that associates with each quantum state $| \psi \rangle$ another state $\hat{U} | \psi \rangle$. I have read that to $\hat{U}$ be a ...
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1answer
60 views

No hair theorem and Killing tensors

I have 2 questions regarding Killing Tensors : A practical question is how to guess whether a spacetime has Killing tensors or not. We can guess some simple Killing vectors by looking at the ...
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1answer
64 views

Killing tensor and Conserved quantities

The definition of the killing tensor is written above, as taken from Wikipedia. My question here is two-fold: Can all Killing tensors be build from the Killing vectors of that spacetime? Do Killing ...
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4answers
253 views

Confusion in Proof of Noether's theorem

This question is related to this Noether's theorem under arbitrary coordinate transformation and this Transformation of $d^4x$ under translation disregarded? To proof Noether's theorem every ...
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2answers
106 views

Noether's theorem under arbitrary coordinate transformation

Noether's theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. Suppose our action is of the form $S = \int d^4x\, \mathcal{L}(\...
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0answers
48 views

Lagrangian density invariace under $\phi_{a} \rightarrow \phi_{a} + \theta\epsilon_{abc}n_{b}\phi_{c} $

PROBLEM Verify that the Lagrangian density $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi_{a}\partial^{\mu}\phi_{a}-\frac{1}{2}m^2\phi_{a}\phi_{a}$$ for a triplet of real fields $\phi_{a} (a = 1, 2, 3)$ ...