Symmetries play a big role in modern physics and have been a source of powerful tools and techniques for understanding theories and their dynamics. 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 forms a group, and the name of this group is used as the name of the symmetry of the object.
Questions tagged [symmetry]
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What conservation law corresponds to Lorentz boosts?
Noether's Theorem is used to relate the invariance of the action under certain continuous transformations to conserved currents. A common example is that translations in spacetime correspond to the conservation of four-momentum.
In the case of…
Warrick
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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 similar statement for discrete symmetries?
Tobias Kienzler
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Why exactly do sometimes universal covers, and sometimes central extensions feature in the application of a symmetry group to quantum physics?
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 $\mathrm{SO}(3)$, it turns out that one must allow also…
ACuriousMind
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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 does not have such a nice form. But I could define…
Sam Jaques
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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 theories (and maybe quantum mechanical theories…
Diego Mazón
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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 system has a differentiable symmetry of its action?
Larry Harson
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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, but that's about it.
Similarly, I can follow…
BMS
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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. However I don't know of any, do you?
*Independence of…
Gerard
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What's the interpretation of Feynman's picture proof of Noether's Theorem?
On pp 103 - 105 of The Character of Physical Law, Feynman draws this diagram to demonstrate that invariance under spatial translation leads to conservation of momentum:
To paraphrase Feynman's argument (if I understand it correctly), a particle's…
Mark Eichenlaub
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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 Lorentz invariance proper),
conformal invariance (i.e.,…
Gro-Tsen
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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, and hence a corresponding Noether…
Jonathan Gleason
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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 it happen that the equations of motion derived by…
Dilaton
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What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?
In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneous symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of local gauge symmetry, some people says that we can…
an offer can't refuse
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Do all Noether theorems have a common mathematical structure?
I know that there are Noether theorems in classical mechanics, electrodynamics, quantum mechanics and even quantum field theory and since this are theories with different underlying formalisms, if was wondering it is possible to find a repeating…
Filippo
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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 it is useful and perhaps just help me understand…
Cogitator
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