The symmetry tag has no wiki summary.
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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 a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
21
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4answers
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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 ...
19
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1answer
67 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, ...
17
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5answers
811 views
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 ...
16
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2answers
88 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 ...
16
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1answer
211 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 ...
15
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4answers
359 views
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 ...
15
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4answers
493 views
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 ...
14
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2answers
827 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, ...
14
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3answers
795 views
Why does dilation invariance often imply proper conformal invariance?
Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also ...
13
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6answers
2k views
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. ...
13
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1answer
600 views
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 point-views:
Anomalies are due to the fact that quantum field ...
13
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1answer
214 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 ...
12
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4answers
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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 ...
11
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6answers
1k 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.
...
11
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1answer
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Schrödinger Equation
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 explain ...
11
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1answer
66 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 ...
11
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4answers
941 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 ...
11
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1answer
433 views
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 ...
10
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4answers
727 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 ...
10
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1answer
237 views
Time reversal symmetry and T^2 = -1
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
9
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1answer
64 views
Global symmetry in string theory
It is often stated that in quantum gravity only charges coupled to gauge fields can be conserved. This is because of the no hair theorem. If a charge is coupled to a gauge field then when it falls ...
9
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2answers
275 views
When “unphysical” solutions are not actually unphysical
When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity:
...
9
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2answers
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The Ozma Problem
The "Ozma problem" was coined by Martin Gardner in his book "The Ambidextrous Universe", based on Project Ozma. Gardner claims that the problem of explaining the humans left-right convention would ...
8
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1answer
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Spontaneous Time Reversal Symmetry Breaking?
It is known that you can break P spontaneously--- look at any chiral molecule for an example. Spontaneous T breaking is harder for me to visualize. Is there a well known condensed matter system which ...
8
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3answers
843 views
What is the symmetry which is responsible for preservation 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 ...
8
votes
2answers
882 views
Poincare group vs Galilean group
One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
8
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2answers
76 views
More general invariance of the action functional
I will formulate my question in the classical case, where things are simplest.
Usually when one discusses a continuous symmetry of a theory, one means a one-parameter group of diffeomorphisms of the ...
8
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3answers
196 views
Symmetries of a Free Massless Scalar in Two Dimensions
On p. 49 of Polchinski's book, he says: "Incidentally, the free massless scalar in two dimensions has a remarkably large amount of symmetry -- much more than we will have occasion to mention."
Does ...
8
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1answer
251 views
Why does a transformation to a rotating reference frame NOT break temporal scale invariance?
Naively, I thought that transforming a scale invariant equation (such as the Navier-Stokes equations for example) to a rotating reference frame (for example the rotating earth) would break the ...
8
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1answer
122 views
Why do we classify states under covering groups instead of the group itself?
Why do we always classify states under covering group representations instead of the group itself? For example see the following picture I lifted from 'Symmetry in physics' by Gross
So in the first ...
7
votes
2answers
179 views
Particles mass determined by SO(D-2) vs SO(D-1)
I've recently come across this statement that massless particles arise from $SO(D-2)$ symetry and massive particles from $SO(D-1)$.
I would have guessed that it would be the exact opposite way, but ...
7
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3answers
405 views
Noether theorem with semigroup of symmetry instead of group
Suppose You have semigroup instead of typical group construction in Noether theorem. Is this interesting? In fact there is no time-reversal symmetry in the nature, right? At least not in the same ...
7
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1answer
306 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 ...
7
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2answers
93 views
Group of symmetries of Lagrange's equations
Consider the following statements, for a classical system whose configuration space has dimension $d$:
Lagrange equations admit a smaller group of "symmetries" (coordinate change under which ...
7
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2answers
322 views
Groups acting on physics - a clarification on electrons and spin
My first question is fairly basic, but I would like to clarify my understanding. The second question is to turn this into something worth answering.
Consider a relativistic electron, described by a ...
7
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3answers
89 views
Rotationally invariant body and principal axis
Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$).
Is it true that in this case the ...
7
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1answer
75 views
Representation on Hilbert space of the product of two symmetry transformations
We know by Wigner's theorem that the representation of a symmetry transformation on the Hilbert space is either unitary and linear, or anti-unitary and anti-linear.
Let $T$ and $S$ be two symmetry ...
7
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2answers
187 views
How to model a symmetry using Lie Groups?
I have been reading lately about Lie groups, and although all books keep listing the groups, and talk about Lie algebras and all that, one thing I still don't know how is it made, and I guess it's the ...
7
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2answers
274 views
Conjugate Variables, Noether's Theorem and QM
What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
7
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1answer
255 views
Relativistic center of mass
Recently I realized the concept of center of mass makes sense in special relativity. Maybe it's explained in the textbooks, but I missed it. However, there's a puzzle regarding the zero mass case
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6
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3answers
130 views
From Manifold to Manifold?
Tensor equations are supposed to stay invariant in form wrt coordinate transformations where the metric is preserved. It is important to take note of the fact that invariance in form of the tensor ...
6
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5answers
262 views
Form of the Classical EM Lagrangian
So I know that for an electromagnetic field in a vacuum the Lagrangian is $\mathcal L=-\frac 1 4 F^{\mu\nu} F_{\mu\nu}$, the standard model tells me this. What I want to know is if there is an ...
6
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3answers
261 views
Is hydrogen the same everywhere?
Silly thought. Feel free to shoot it down
Does a hydrogen atom undergo any kind of change subject to it's environment?
If one were to study a hydrogen atom on the surface of Mercury, another above ...
6
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3answers
383 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 ...
6
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1answer
77 views
Precise statement of Mermin–Wagner theorem
Roughly speaking, Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions ...
6
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1answer
105 views
Request for Reference: BRST formalism/transformations
Could anyone please suggest a very basic paper/reference/literature on BRST symmetry/formalism that requires rudimentary knowledge of Dirac's method for dealing with constrained systems and generation ...
6
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1answer
128 views
Are group representations possible when the solution space is not a vector space?
As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
6
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4answers
297 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 ...
6
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2answers
376 views
Why are conformal transformations so prevalent in physics?
What is it about conformal transformations that make them so widely applicable in physics?
These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
