# 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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### Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
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### Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field ...
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### 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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### Is the converse of Noether's first theorem true: Every conservation law has a symmetry?

Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is the converse true: Any conservation law of a physical ...
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### When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?

My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an equation,...
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### Are black holes perfect spheroids?

What I know about black holes (correct me if I'm wrong) is that they are the most compact objects in the universe that have been discovered. Due to all that gravity, wouldn't black holes be a perfect ...
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### Can Noether's theorem be understood intuitively?

Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. ...
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### Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
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### What is the usefulness of the Wigner-Eckart theorem?

I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's Modern Quantum Mechanics. I was wondering if someone could tell me why ...
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### Why are Killing fields relevant in physics?

I'm taking a course on General Relativity and the notes that I'm following define a Killing vector field $X$ as those verifying: $$\mathcal{L}_Xg~=~ 0.$$ They seem to be very important in physics ...
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### When can a global symmetry be gauged?

Take a classical field theory described by a local Lagrangian depending on a set of fields and their derivatives. Suppose that the action possesses some global symmetry. What conditions have to be ...
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### Elegant approaches to quantum field theory

I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles. I was wondering if anyone familiar with the book ...
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There seem to be two different things one must consider when representing a symmetry group in quantum mechanics: The universal cover: For instance, when representing the rotation group $\mathrm{SO}(... 1answer 214 views ### Any use for$F_4$in hep-th? In high energy physics, the use of the classical Lie groups are common place, and in the Grand Unification the use of$E_{6,7,8}$is also common place. In string theory$G_2$is sometimes utilized, ... 4answers 5k views ### Why are snowflakes symmetrical? The title says it all. Why are snowflakes symmetrical in shape and not a mush of ice? Is it a property of water freezing or what? Does anyone care to explain it to me? I'm intrigued by this and ... 1answer 1k views ### Why does charge conservation due to gauge symmetry only hold on-shell? While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ... 1answer 670 views ### Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ... 1answer 2k views ### What is the difference between scale invariance and self-similarity? I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same ... 1answer 1k views ### Gauge redundancies and global symmetries [closed] It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ... 2answers 188 views ### Can symmetry generators be used for quantization? Take the Poincaré group for example. The conservation of rest-mass$m_0$is generated by the invariance with respect to$p^2 = -\partial_\mu\partial^\mu$. Now if one simply claims The state where ... 2answers 843 views ### What is precisely a Yangian symmetry? The terms Yangian and Yangian symmetry appear in a list of physical problems (spin chains, Hubbard model, ABJM theory,$\mathcal{N}= 4$super Yang-Mills in$d=4$,$\mathcal{N}= 8$SUGRA in$d=4$), ... 1answer 367 views ### Quantum symmetries that are not classical symmetries An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing ... 4answers 852 views ### What sort of experiment would directly test time reversal invariance? I guess the title says it all: how could/would you experimentally test whether our universe is truly time reversal invariant, without relying on the CPT theorem? What experiments have been proposed to ... 3answers 2k views ### What is the symmetry which is responsible for preservation/conservation of electrical charges? Another Noether's theorem question, this time about electrical charge. According to Noether's theorem, all conservation laws originate from invariance of a system to shifts in a certain space. For ... 1answer 677 views ### Spontaneous breaking of Lorentz invariance in gauge theories I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ... 2answers 1k views ### Is this Landau's other critical phenomena mistake? There was an old argument by Landau that while the liquid gas transition can have a critical point, the solid-liquid transition cannot. This argument says that the solid breaks translational symmetry, ... 2answers 498 views ### Coulomb gauge fixing and “normalizability” The Setup Let Greek indices be summed over$0,1,\dots, d$and Latin indices over$1,2,\dots, d$. Consider a vector potential$A_\mu$on$\mathbb R^{d,1}$defined to gauge transform as $$A_\mu\to ... 4answers 3k views ### QM and Renormalization (layman) I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ... 5answers 3k views ### Noether charge of local symmetries If our Lagrangian is invariant under a local symmetry, then, by simply restricting our local symmetry to the case in which the transformation is constant over space-time, we obtain a global symmetry, ... 3answers 2k views ### Why is the Symmetry Group for the Electroweak force SU(2) \times U(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 ... 3answers 10k views ### Definite Parity of Solutions to a Schrödinger Equation with even Potential? I am reading up on the Schrödinger equation and I quote: Because the potential is symmetric under x\to-x, we expect that there will be solutions of definite parity. Could someone kindly ... 5answers 734 views ### Why can a solution show optical rotation? Why can a solution show optical rotation? A solution, as a liquid, is rotationally isotropic, right? So, even if the molecules are chiral, because of the random orientation of the molecules, shouldn't ... 2answers 1k views ### Conformal Compactification of spacetime I have been reading Penrose's paper titled "Relativistic Symmetry Groups" where the concept of conformal compactification of a space-time is discussed. My other references have been this and this. In ... 1answer 439 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 ... 2answers 2k 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} $$A priori, there is no reason to ... 2answers 1k views ### What is the role of the vacuum expectation value in symmetry breaking and the generation of mass? Consider a theory of one complex scalar field with the following Lagrangian.$$ \mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2. $$The ... 6answers 3k views ### What is the symmetry which is responsible for conservation of mass? According to Noether's theorem, all conservation laws originate from invariance of a system to shifts in a certain space. For example conservation of energy stems from invariance to time translation. ... 3answers 1k views ### What does “the {\bf N} of a group” mean? In the context of group theory (in my case, applications to physics), I frequently come across the phrase "the {\bf N} of a group", for example "a {\bf 24} of \mathrm{SU}(5)" or "the {\bf 1} ... 1answer 1k views ### Do an action and its Euler-Lagrange equations have the same symmetries? Assume a certain action S with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations. Can ... 3answers 593 views ### How are symmetries precisely defined? How are symmetries precisely defined? In basic physics courses it is usual to see arguments on symmetry to derive some equations. This, however, is done in a kind of sloppy way: "we are calculating ... 3answers 3k views ### Galilean invariance of Lagrangian for non-relativistic free point particle? In QFT, the Lagrangian density is explicitly constructed to be Lorentz-invariant from the beginning. However the Lagrangian$$L = \frac{1}{2} mv^2$$for a non-relativistic free point particle is ... 1answer 211 views ### Highest symmetric non-maximally symmetric spacetime What is the highest number of symmetries (Killing vectors) that a (4-dimensional) spacetime can have without being maximally symmetric? From what I can see, it seems to be 7 (which includes the ... 3answers 1k 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 ... 4answers 4k views ### Symmetry in resistor circuits Given 6 points that are connected with each other with a resistor of resistance$R$, find the resistance between any two points. (Answer:$R/3$) (All the conducting wires have the same ... 2answers 2k views ### What does “soft” in “soft symmetry breaking” mean? For example it is stated that if supersymmetry breaking is soft then stability of gauge hierarchy can be still maintained. 4answers 731 views ### What is meant by the phrase “the mass is protected by a symmetry”? In a particle physics context I've heard this phrase used. I guess it means that the mass of a particle is less than you'd naively expect from$E=mc^2$after computing the momentum uncertainty ... 4answers 2k views ### If all conserved quantities of a system are known, can they be explained by symmetries? If a system has$N$degrees of freedom (DOF) and therefore$N$independent1 conserved quantities integrals of motion, can continuous symmetries with a total of$N$parameters be found that deliver ... 1answer 213 views ### Are possible gauge fields in a Lagrangian theory always determined by the structure of the charged degrees of freedom? An elementary example to explain what I mean. Consider introducing a classical point particle with a Lagrangian$L(\mathbf{q} ,\dot{\mathbf{q}}, t)$. The most general gauge transformation is$L \...
It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...