# 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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### Noether's Theorem: Lie algebra, Lie groups

I've had a brief look through similar threads on this topic to see if my question has already been answered, but I didn't find quite what I was looking for, perhaps it is because I'm finding it hard ...
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### Noether currents in QFT

I am trying to organize my knowledge of Noether's theorem in QFT. There are several questions I would like to have an answer to. In classical field theory, Noether's theorem states that for each ...
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From Becker, Becker and Schwarz String Theory and M-Theory: For the infinitesimal conformal transformation $$\tag{3.25}\delta z=\varepsilon(z)\quad\text{and}\quad \delta\bar ... 0answers 114 views ### How can gauge invariance be unphysical? Gauge symmetry is said to be "unphysical" because the transformations - unlike changes of reference frame - do not correspond to real physical operations. But the consequences of gauge symmetries are ... 1answer 46 views ### Silicon: conduction band minima Why do the energetic minima of the silicon conduction band lie not in a high-symmetry point like a X-point, but somewhere in \Delta-direction between points \Gamma and X? What is the physical ... 1answer 102 views ### Schrodinger equation, commutative operators, and Symmetry When solving Schrodinger's equation in 3D with a spherical laplacian you reach a point at which you introduce a separation constant and can see that the same eigenvalue satisfies the radial and ... 3answers 160 views ### Ideal, isotropic fluid and stress tensor An ideal fluid is the one which cannot support any shearing stress. It also doesn't have viscosity. My question is what does it mean by a fluid to be isotropic? Is an ideal fluid necessarily isotropic ... 3answers 262 views ### How to understand this symmetry in the wavefunctions of a diatomic molecule? In Wikipedia (and elsewhere), a particular symmetry of the quantum system of a diatomic molecule is mentioned: symmetry under reflection along a plane containing the internuclear axis. The ... 0answers 123 views ### What is the symmetry group of this Hamiltonian? Consider a Hamiltonian$$\hat H=-\partial_x^2-\partial_y^2+(x-y)Q,$$where x,y\in[0,a] (homogeneous Dirichlet boundary conditions assumed), and Q is some real parameter. When Q=0, the ... 1answer 76 views ### Relation between gauge symmetry and mass difference Usually (like in Georgi's Lie Algebra book) people argue the reason why Gellmann SU(3) flavor symmetry (u,d,s) can't extend to SU(4) (u,d,c,s) or higher flavour symmetry is the their mass ... 0answers 60 views ### What is the difference between the groups PSU(N) and SU(N)? [closed] What is the difference between the groups PSU(N) and SU(N)? For example how is PSU(2,2|4) different than SU(2,2|4)? 7answers 479 views ### What does the statement “the laws of physics are invariant” mean? In the first paragraph of Wikipedia's article on special relativity, it states one of the assumptions of special relativity is the laws of physics are invariant (i.e., identical) in all inertial ... 0answers 94 views ### Does point group symmetry also act within “spin space” for a lattice spin system? As an example, let's consider a quantum spin system on a 2D square lattice. The lattice point group symmetries include C_4 rotation, parities, etc.... And let's take C_2 symmetry (2-fold rotation) ... 3answers 102 views ### SO(3), SU(2) and symmetries in quantum mechanics [duplicate] A rotation in the vector space \mathbb{R}^3 is represented by the known 3x3-matrices. But at this point I'm really confused how to get from there to Quantum Mechanics. The group of ... 1answer 80 views ### Why does Weyl invariance imply a traceless energy-momentum tensor? I've begun to self-study String Theory from Polchinski and Becker, Becker and Schwarz. I don't see why the fact that the Polyakov action is invariant under Weyl transformations is related to the ... 2answers 209 views ### Changing vector basis in AdS_3 I have AdS{}_3 given as a surface embedded in a 4 dimensional pseudo-Riemannian space$$x^2+y^2-u^2-y^2=-l^2$$With metric:$$ds^2=dx^2+dy^2-du^2-dv^2$$I have Killing vectors of that space ... 2answers 192 views ### What are spin and valley symmetries in graphene? I have been assigned a presentation on a part of a paper (http://arxiv.org/abs/1303.6942). My task is to present on the spin and valley symmetries in graphene, and relate it back to the paper above. ... 2answers 97 views ### Definition of Duality (opposed to Symmetry) I'm learning basic string theory right now and we came across T-duality which was presented as a symmetry of the formula for the mass of a string in the context of compactification. There was a remark ... 0answers 32 views ### Can any global symmetry be promoted to the local symmetry? [duplicate] Can any global symmetry be promoted to the local symmetry? Does there exist counterexample? 1answer 222 views ### What exactly do we mean by symmetry in physics? I'm referring here to invariance of the Lagrangian under Lorentz transformations. There are two possibilities: Physics does not depend on the way we describe it (passive symmetry). We can choose ... 2answers 136 views ### Global symmetry and particle multiplets In chapter 20, of Peskin and Schroeder's quantum field theory book, they start with a comment that a global symmetry that is manifest lead to particle multiplets with restricted interactions. Can ... 2answers 218 views ### Is there a mathematical reason for the Lagrangian to be Lorentz invariant? The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant. The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if ... 2answers 116 views ### How can I prove that \langle\Omega\vert \phi(x) \vert\Omega\rangle \langle\Omega\vert\phi(y)\vert\Omega\rangle=0 for a scalar field? From Peskin-Schroeder, p.212: The term$$ \langle \Omega | \phi(x) | \Omega \rangle \langle \Omega |\phi(y) | \Omega \rangle$$is usually zero by symmetry; for higher-spin fields, it is zero ... 1answer 252 views ### Does time invariance conclude conservation of energy? [closed] I find it hard to understand that time-translation invariance necessarily implies conservation of energy. As I understand it, Noether's theorem says that there is an energy conservation because the ... 2answers 1k views ### Symmetrizing the Canonical Energy-Momentum Tensor The Canonical energy momentum tensor is given by$$T_{\mu\nu} = \frac{\partial {\cal L}}{\partial (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$A priori, there is no reason to ... 1answer 48 views ### What conserved quantities does a one-dimensional non-symmetric lattice have? When I asked what leads to degeneracy of eigenstates of free particle, the answer was parity. But it appears that even if we consider a lattice with non-symmetric cell, so the potential looks as shown ... 1answer 218 views ### Why does renormalization need an unbroken symmetry? Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ... 1answer 92 views ### How to diagonalise the Lagrangian mass term with SU(4) symmetry and self-dual tensors I should write the mass term of the Lagrangian with global SO(4) symmetry in tensor representation with anti-symmetric tensors and then diagonalise this term with defining a new set of tensors ... 0answers 60 views ### Weaker Formulations of Bulk-boundary Correspondence for Interacting Systems From this post, it seems that bulk-boundary correspondence does not hold in general for interacting systems. What is meant by bulk-boundary correspondence there appears to be the existence of robust ... 1answer 36 views ### Finding a basis for minimal representation of a wavefunction (extracting symmetries) I asked something like this on Math StackExchange, but now that I think about it, this probably belongs better over here. I want to find all linear operators (non necessarily hermitian) \{\hat{A}\} ... 3answers 165 views ### Do algorithms have an intrinsic time direction? This article says There is no intrinsic time direction in Newton's mechanics nor in the differential equations of the new physics. My question is, do other types of mathematics, say a cellular ... 1answer 228 views ### Why do we need spontaneous symmetry breaking in Lagrangian formalism? I have always struggled with the concept of spontaneous symmetry breaking. It seems to me that many others don't find it very intuitive as well, but that could be just me having difficulties with the ... 1answer 172 views ### Why are large scale structures isotropic in the Ising model? I have at least a qualitative understanding of why the critical state of the Ising model is scale invariant, by arguments to do with renormalisation, which I understand only very roughly. However, in ... 1answer 361 views ### Solving Special Function Equations Using Lie Symmetries The lie group + representation theory approach to special functions & how they solve the ode's arising in physics is absolutely amazing. I've given an example of it's power below on Bessel's ... 0answers 15 views ### Explain materials with 4 fold symmetry having same reflectance when shone with LCP and RCP This is my first post here. I am currently reading "Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation" by Do-Hoon Kwon, Pingjuan L. Werner, and ... 1answer 80 views ### Question about global internal SO(n) symmetry I have the following Lagrangian (density) for bosons$$L = \partial_{\mu} \phi^i \partial^{\mu}\phi^i+ m^2\phi^i \phi^i$$and I am trying to understand why this Lagrangian is invariant under ... 1answer 84 views ### Is the weak interaction Lagrangian invariant under parity transformations? The weak interaction term in the Lagrangian reads$$ \bar \Psi \gamma_\mu P_L \Psi W^\mu. $$Under parity transformations, because of \Psi \rightarrow \gamma_0 \Psi and \gamma_5 \rightarrow ... 0answers 132 views ### Why is electric charge the conserved quantity corresponding to global U(1) symmetry? [duplicate] An example of a symmetry transformation for certain Lagrangians (notably the canonical complex scalar field Lagrangian) is multiplication of the fields by a complex phase. When we multiply the fields ... 0answers 79 views ### Solve symmetric circuits by a glance [closed] How to know with just a cursory glance that the Voltage needed is zero ? i think there must be a way to know it , by symmetry or something 1answer 317 views ### What happens in the twin paradox if the ship doesn't return? What happens if the twin in the spaceship doesn't return? Would he still be younger than his other twin? Is the symmetry broken simply by accelerating out of earth? If it is still symmetrical when ... 1answer 96 views ### Origin of momentum. Noether's theorem My professor talked about Noether's theorem and how translation is the origin of momentum conservation. But why is it not velocity that is conserved but mass times velocity. And on the same note why ... 3answers 1k views ### A question on the existence of Dirac points in graphene? As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2\times2 Hermitian matrix H(k_x,k_y) has two degenerate points K ... 0answers 306 views ### How to count and 'see' the symmetry factor of Feynman diagrams? Could somebody explain how one can derive the symmetry factor both by counting possible contractions and by looking at the symmetry of a diagram. Consider for example this diagram in \phi^4-theory ... 0answers 99 views ### Is global gauge symmetry really a symmetry and local conserved current in gauge theories? One way to define a gauge theory is that whenever the Lagrangian is invariant under some local transformations, we say these local transformations are local gauge transformations and the theory is a ... 0answers 59 views ### Symmetry Group of system to a given Hamiltonian I want to determine the symmetry group of the following system: I consider a charged particle in a spherically symmetric potential V and a homogeneous electric field of magnitude E in ... 1answer 180 views ### Explanation for the minus sign in \Omega_3 in the Kappa symmetry of the Green - Schwarz formalism for F1 strings Just so that there can be more higher - level physics questions here, let me post this question + answer. Also because I'm a bit sad that there are almost no questions on the Green-Schwarz ... 1answer 2k views ### Physical significance of Killing vector field along geodesic Let us denote by X^i=(1,\vec 0) the Killing vector field and by u^i(s) a tangent vector field of a geodesic, where s is some affine parameter. What physical significance do the scalar quantity ... 0answers 53 views ### Finding conserved quantities from Hamiltonian when Symmetry is not evident [closed] A particle is moving in 3D space, under a potential$$V = -\frac{\alpha}{r}-\frac{\vec{r} \cdot \vec{\mu}}{r^3 }  where $\vec{\mu}$ is some constant vector. I need to show there are three ...
I have been calculating the classical action of the harmonic oscillator, the problem I have is that I am only able to solve it if I set the integration limits of the action integral to be $t=T$ and ...
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 ...