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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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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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Why expression of energy occurs in triplet?

I have basically two questions in mind,which are 1) Why expression of energy occurs in triplet? 2)Why the expressions are somewhat symmetrical? Coming to elaborated form of 1st part, We have, U=1/...
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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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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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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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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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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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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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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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Feynman's proof for Newton's shell theorem

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 $\phi_{a} (a = 1, 2, 3)$ ...
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Why does nature favour the Laplacian?

The three-dimensional Laplacian can be defined as $$\nabla^2=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}.$$ Expressed in spherical coordinates, it ...
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Gravitational field at point just outside the sphere using integration

consider a point P at a distance k*R from a hollow sphere The Gravitational field at point P can obtained by the summation of gravitational fields due to small rings which make up the ring. the ...
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Galilei group and Constrained QM

Let's assume spin-0 for simplicity. So far as I understand the issue, the Galilei simmetries constraints the possible hamiltonians of a quantum systems so that the only possible interactions of a ...
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Using Isospin symmetry to find the decay width of an interaction

Say we have two decays $\Delta^+\rightarrow \pi^+n$, and $\Delta^+\rightarrow \pi^0p$. I want to show, using isospin symmetry that the probabilities for these decays is in the ratio $\tfrac{Γ(\Delta^+\...
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How to map the symmetry property of the lattice unit cell to the symmetry properties of eigen modes

For example, in $\mathbf{r}$ space, a honeycomb lattice (like graphene) has C6v symmetry about the center of the unit cell. The ground state (singlet) eigen mode has C6v symmetry and the 1st order ...
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Combinatorics geometric series two-point function

In this answer Proof of geometric series two-point function it is said: Now what about the coefficients in front of each Feynman diagram? Due to the combinatorics/factorization involved it ...
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1answer
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Proof of Noether's theorem: How to deal with transformations in time?

I was following the proof of Noether's theorem in Lemos - Analytical Mechanics, page 73. He considers a full infinitesimal transformation: $$t'=t+\epsilon X(q(t),t),$$ $$q'(t')=q(t)+\epsilon\Psi(q(t),...
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Feynman diagram combinator and multiplier value

Dear experts, I try to learn by self feynman diagram from examples of x^3 and x^4 for first and second order consolidated from different reading material. For x^3, combinator values of 3 * 3 for n=1 ...
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Energy momentum tensor of EM field written in symmetric form

I'm reading A. Zee's book, Einstein Gravity in a Nutshell. In problem 7 of chapter IV.2, it is said that the energy momentum tensor of the electromagnetic field \begin{align} T^{\mu\nu}=\eta_{\lambda\...
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Is polarization matrix always diagonalizable?

In chapter 31 of Feynman lectures Vol 2, he covers polarization , polarization tensor and its diagonalisation, he proves that for a crystal, the tensor matrix is symmetric hermitian and hence ...
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Symmetry transformations that are self-inverse and global symmetries of the Hamiltonian

I have the simplified Ising model. The Hamiltonian is given by $$ \mathcal{H} = -\mathrm{J}\sum_{<ij,i' j'>} \sigma_{ij} \sigma_{i'j'}. $$ Where the sum over $<ij,i'j'>$ means just the ...
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Riemann tensor Contracted with full antisymmetric tensor

I'm not able to show that $\epsilon^{abcd} R_{bcae} = 0$ Note: Properly, I have to show that $\epsilon^{Iabc} R_{abIL} = 0$, where $I,L$ are tetrad index and $a,b,c$ are spacetime index, but it ...
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Three spin states of a spin-1 particle

For a spin-1 particle at rest, it has three spin states(+1, -1, 0, along the z axis). If we rotate the z axis to -z direction, the spin +1 state will become the spin -1 state. Can we transfer the spin ...