Symmetry Definition and 907 Threads

I've bumped into a few interesting papers talking about time-reversal symmetry in QM (eg: https://arxiv.org/abs/1507.07745) but I can't seem to wrap my head around the concept. 1) What does it mean for one to say that standard QM isn't time-reversal symmetric? Does this have to do with the...

Does quantum mechanics follow causality, phase transition, critical point, symmetry, asymmetry, order, disorder, continuation, discontinuation, limitation, without limitation, convergence, divergence, similarity, hierarchical structure, singularity, plurality?

Can an electron in a spherically symmetrical potential energy function have non-zero spin angular momentum?

I suppose that the principle of conservation of angular momentum holds also for a cloud of particles weekly interacting at low pressure, density and temperature. And it should be still applicable when the particles or the atoms would start condensing and forming fusion products or simply solid...

Hi, Let be a scalar field φ that permeates all space. The quantum of the field has a mass m. The field is at the minimum of its potential. When this minimum is for φ≠0 (a broken symmetry), the quantum may be observed by exciting the field, as with the Higgs boson. But if the symmetry is not...

I am currently studying this paper on quantum synchronization. The first page gives an introduction to synchronization and the basic setup of the ensembles in the cavity. My query is on the second page where the following statements are made. Can anyone see why the implication is that all...

hi, I'm currently taking a classical field theory class (electromagnetism in the language of tensors and actions and etc) and we have just encountered the gauge symmetry, that is for the 4 vector potential we can add a gradient of some smooth function and get the same physics (if we take Aμ →...

By the Wigner theorem, symmetries transformations are implemented by operators ##\hat{U}## that are unitary or antiunitary. This is what is written in most books. But I have read somewhere that, to ##\hat{U}## represent a symmetrie, it's necessary that ##\hat{U}^{\dagger} \hat{H} \hat{U} =...

I used a matrix to calculate the Fourier transform of a lorentzian and it did generate a decaying exponential but that was followed by the mirror image of the exponential going up. I am referring to the real part of the exponential. If I use an fft instead I also see this. Shouldn't the...

Suppose we are in communication with aliens who live in a different universe. I know, that's impossible, communication requires the exchange of mass or energy, which implies that we live in the same universe. But suppose it is true. I am wondering, can we and the aliens, via this communication...

Homework Statement ABC is an isosceles triangle such that AB = AC A has coordinates (4, 37) B and C lie on the line with equation 3y = 2x + 12 Find an equation of the line of symmetry of triangle ABC. Give your answer in the form px + qy = r where p, q and r are integers. Show clear...

Symmetry transformations are changes in our point of view that preserve the possible outcomes of experiment: $$\Psi \rightarrow U(\Lambda) \Psi$$ In the Heisenberg picture, observables in a fixed reference frame evolve according to: $$P(t) = U^\dagger (t)PU(t)$$ while in the Schrodinger...

How certain can we be that the four fundamental forces as identified in modern cosmology, owe their existence to broken symmetry?

Homework Statement Homework EquationsThe Attempt at a Solution I need help in solving second part of this question. I put ## e^{i \alpha }\psi ## instead of ##\psi ## and got to see that the integrand doesn't change which means the given transformation is a symmetry of the given action. But...

I am wondering if it existes some discret version of the Noether symmetry for potential with discrete symmetry (like $C_n$ ). The purpose is to describe the possible evolution of the phase space over the time without having to solve equations numerically (since even if the potential may have...

Derivation of the Onsager symmetry in many textbooks and papers is as follows: First, assume that the correlation function of two state variables,##a_i## and ##a_j## satifsies for sufficiently small time interval ##t## that $$\langle a_i(t) a_j(0) \rangle = \langle a_i(-t) a_j(0) \rangle =...

In a problem in Landau’s mechanics (end of section 9) he asks for the quantity conserved in the field of “an infinite homogenous cylindrical helix.” The solution is that the Lagrangian is unchanged by a rotation of dΦ together with a translation of hdφ/(2π) (about and along the symmetry axis)...

Wald and Zoupas discussed the general definition of ``conserved quantities" in a diffeomorphism invariant theory in this work. In Section IV, they gave one expression (33) in the linked article. I cannot really understand the logic of this expression. Would you please help me with this?

One of the interesting new ideas in BSM model building began with this paper: https://arxiv.org/abs/1706.08749 Are neutrino masses modular forms? Ferruccio Feruglio A modular form is a kind of two-dimensional analogue of the periodic trigonometric functions. Just as trigonometric functions can...

I am exploring the behaviors of complex integers (Gaussian and Eisenstein integers). My understanding is that when a complex integer z with norm >1 is multiplied by itself repeatedly, it creates a series of perfect powers. For instance, the Gaussian integer 1+i generates the series 2i, -2+2i...

I read in various sources (such as page 8 of these notes) that the dielectric permittivity tensor of a lossless medium is always symmetric. I am wondering how this can be the case, when: Phase accumulation in the medium could in theory depend on direction Coordinate system may be rotated to...

This is not a technical question. I'd like to have a more conceptual discussion about what - if anything - gauge invariance tells us about reality. If we could, please try to keep the discussion at the level of undergrad or beginning grad. To focus my questions and keep things elementary, I'd...

https://phys.org/news/2018-11-infinite-dimensional-symmetry-possibility-physicsand-particles.html quote: In a recent paper in Physical Review Letters, Prof. Krzysztof Meissner from the Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, and Prof. Hermann Nicolai from the...

How do we know that the stress tensor must be symmetric in the Navier-Stokes equation? Here are some papers that discuss this issue beyond the usual derivations: Behavior of a Vorticity Influenced Asymmetric Stress Tensor In Fluid Flow http://www.dtic.mil/dtic/tr/fulltext/u2/a181244.pdf...

How is symmetry used to solve electrical circuits? I have seen several problems in books in which currents in two resistors are said to be equal due to 'symmetry'. That is a concept that I fail to understand and thus cannot apply. In class, we were shown a few circuit diagrams which were...

Hello people, I have been thinking about a concept that I was taught whilst learning GR, If I understand correctly it is that Lorentz symmetry becomes local when we consider GR. This makes sense to me as then the metric is generally speaking not Minkowski, only for a...

In the recent thread about the gravitational field of an infinite flat wall PeterDonis posted (indirectly) a link to a mathpages analysis of the scenario. That page (http://www.mathpages.com/home/kmath530/kmath530.htm) produces an ansatz for the metric as follows (I had to re-type the LaTeX -...

Hello I was reading some article on angular momentum. And at some point, the author started talking about the symmetric objects and axis of symmetry. Now I am wondering if the author means the geometrical symmetry or the symmetry in physics. For an example, if we take a uniform rod of length...

One could argue that this question should be posted on the maths forum, but I see it so frequently in physics that I find it more productive to ask it here. In a symmetry group, do we have freedom of choice of how the group is going to act in the coordinates? Or is the way the group act on the...

It is said that Newton's laws of motion or laws of Quantum Mechanics posses time reversal symmetry but the second law of Thermodynamics does not. What I understand by the first part of the sentence is the following. The dynamical state of a system changes with the increase of time. The state at...

It is known that Maxwell equations have the time reversal symmetry. I.e. by changing t by -t, J by -J (which can be understood as the charges going in the opposite direction when time is reversed, which makes sense), E to E and B to -B, the equations are still satisfied. However, it is also...

I have a cylinder with radius r and height h and a uniform charge density. Now I am supposed to calculate the E field inside the cylinder. If the cylinder was infinitely long the symmetry would dictate that the field can only point radially outward, so gausses law would give me a field of zero...

How could electrically charged particles be massless before the symmetry breaking? Wouldn't the energy stored in the electric field contribute to particles mass?

What would the world look like if there was no translational symmetry? How would certain laws be different and what wouldn't change?

Is symmetry a general aspect of physical nature?

Spontaneous symmetry breakingI’m not sure if I understand spontaneous symmetry breaking.In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider...

I am exploring Gaussian integers in terms of roots, powers, primes, and composites. I understand that multiplying two integers with norm 5 result in an integer with norm 25. I get the impression that there are twelve unique integers with norm 25, and they come in two flavors: (1) Four of them...

Homework Statement Hi everyone! Just wondering if there's a way to prove the symmetry property of the Riemann curvature tensor $$ R_{abcd} = R_{cdab}$$ without using the anti-symmetry property $$ R_{abcd} = -R_{bacd} = -R_{abdc} $$? I'm only able to prove it with the anti-symmetry property and...

I'm trying to better understand how people refer to symmetry in Physics and Differential Geometry. In "Exterior Differential Systems and Euler Lagrange Partial Differential Equations," by Bryant, Griffiths and Grossman, it seems a vector field is a symmetry of a Lagrangian if the Lie derivative...

1-As you know classical electrodynamics has conformal symmetry. But does this symmetry survive renormalization? if not, can anyone give an explanation on why? 2-What is the situation with QCD? Does it have conformal symmetry at a classical level? If yes, does it survive renormalization? Thanks

Hi, Just curious. One of the requirements for a data set to be normally-distributed is that of symmetry. Question: Is there or could one define a statistic to this effect, meaning to determine the level of symmetry on the data set and use that to determine at certain confidence level if the...

I'm curious to know what Lorentz symmetry is, and how it works. The wiki description is a bit too difficult for me to understand. And how does it differ from a computer's cubic symmetry? I understand that in cubic symmetry, the laws of physics or physical things look different depending on what...

Hello! The time reversal operator, ##\hat{\Theta}## transforms a Bloch state as follows: ##\hat{\Theta} \psi_{nk}=\psi^*_{nk}##. How does one proceed to prove the condition that ##\psi_{nk}## and ##\psi^*_{nk}## must satisfy in order for our system to be time reversal invariant? Thanks in advance!

Homework Statement Homework EquationsThe Attempt at a Solution I am trying to solve this question by symmetry .If I draw a line perpendicular to the line joining AB then points C and D are symmetric . Now I am unsure how to proceed further .

Why is it that bosons (particles having symmetric wave functions) have integral spins and fermions (particles having antisymmetric wave functions) have half integral spins? A lot of books state this without specifying the reason. I was wondering if this is a theoretical deduction. Or is it an...

Hello everyone :) Not too long ago, I was thinking about planetary motion around a sun, both with circular orbits and elliptic orbits. However, when thinking a little longer about these two cases in a broader sense, I spotted a big difference which I found quite odd (assume purely classical...

Hi, The article below states that they made a material that blocks the motion of molecules in only one way but passing the other way is possible. See the article. https://physicsworld.com/a/blocking-the-symmetry-of-motion/ This seems to me in contrast with the second law. You can for example...

Hello Can somebody explain for me what is the meaning of inversion symmetry in solids? and why does it breaks at the surface? and also why this inversion symmetry breaking leads to SOC(spin orbit coupling)? If somebody also know a document that explain this in full details(from A to Z) please...

Our standard model breaks the Higgs Su(2) electroweak symmetry via the Higgs mechanism. In official beyond the standard models. May I know the different lists of models where the Higgs field can be part of larger symmetry group like SU(10) and different ways to break it?