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.

learn more… | top users | synonyms

3
votes
1answer
50 views

Generators of a certain symmetry in Quantum Mechanics

In Classical Mechanics to describe symmetries like translations and rotations we use diffeomorphisms on the configuration manifold. In Quantum Mechanics we use unitary operators in state space. We ...
0
votes
1answer
42 views

Properties of a body with spherical symmetry

I'm studing Gauss law for gravitational field flux for a mass that has spherical symmetry. Maybe it is an obvious question but what are exactly the propreties of a spherical simmetric body? A ...
0
votes
0answers
32 views

Transformation applied to system without symmetry

Imagine we have a central potential which gives us the Hamiltonian of the form: $$\hat H=-\frac{\hbar^2}{2m} \nabla^2 +V(r)$$ In general this is not symmetric under translation. But let us say that I ...
3
votes
1answer
47 views

Symmetry responsible for equality of masses of particles

During my studies of basic particle physics the following question came up. What symmetry is responsible for equality of masses of particles and their antiparticles? In particular, is this symmetry ...
1
vote
0answers
47 views

Example of a symmetry and the group with which it is modelled? [duplicate]

Could you please provide a specific example of a symmetry and the group with which it is modelled? I am beginner to study symmetry in physics, please answer with just an example. This question is ...
0
votes
0answers
19 views

Fermion Trucation

I recently posted about truncating fermions in supergravity Lagrangians and got a good answer about how this gives a vev to the bosonic content and therefore freezes it to a stationary point of the ...
4
votes
4answers
298 views

Noether's theorem for space translational symmetry

Imagine a ramp potential of the form $U(x) = a*x + b$ in 1D space. This corresponds to a constant force field over $x$. If I do a classical mechanics experiment with a particle, the particle behaves ...
0
votes
1answer
40 views

scalar potential and vector potential behave symmetry properties

How the scaler potential Q(x,t) and vector potential A(x,t) behave under parity and time-reversal transformations.
3
votes
0answers
72 views

What is physically irreducible representation?

When I use bilbao crystallographic server recently, I noticed a notation called physically irreducible representation. Paper says it is a direct sum of two complex conjugate representations (if $\...
1
vote
0answers
24 views

Water dipole by symmetry argument [closed]

I'm a mathematician and I'm studying Group and Representation theory and I came across with an interesting exercise involving physics, although I don't know physics, since I'm a mathematician, I found ...
6
votes
1answer
46 views

Why does exchanging coordinates produce a phase of $\pm 1$ in an identical particle wavefunction?

Consider a system of two identical particles described by a wavefunction $\psi(x_1, x_2)$. There are two kinds of exchange operators one can define: Physical exchange $P$, i.e. swap the positions of ...
15
votes
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 ...
4
votes
0answers
89 views

Completely positive maps and symmetric states

Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on $\mathrm{...
4
votes
2answers
43 views

Does a central force have to be independent of angle?

When defining a central force, some sources, like Wikipedia, say that the magnitude of the force only depends on the distance $r$: In classical mechanics, a central force on an object is a force ...
0
votes
0answers
14 views

Isolated system and mutual interaction potential

We know that the total linear momentum of a closed (isolated) system is conserved due to homogeneity of space (Landau and Liftshitz, page 15, Mechanics). Hence for an isolated system of two bodies ...
1
vote
2answers
165 views

Symmetry and degeneracy in quantum mechanics

If an operator commutes with the Hamiltonian of a problem, does it always must admit degeneracy? For example, parity operator commutes with the Hamiltonian in case of a free particle and we have two ...
1
vote
0answers
71 views

Why are symmetrical structures highly stable? [closed]

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
4
votes
1answer
42 views

Symmetry Arguments: Flow Through Cylinder

Why can for symmetry reasons a steady, viscous, incompressible flow, obaying the N.S equation: $$\rho(v \nabla)v = -\nabla p + \eta \Delta v $$ That flows through a cylindrical(very long) pipe not ...
2
votes
0answers
29 views

$SU(2)$ symmetry and conservation law in condensed matter systems [closed]

My question has a few parts, I know from Noether that if there is a symmetry in a Hamiltonian, there is a conservation law. What would be the conservation law associated with $SU(2)$ symmetry? $...
7
votes
1answer
154 views

Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?)

I'm convinced I'm missing something so obvious but here goes Typically, one can define something like a "general" expansion of an order parameter, ${\boldsymbol \Gamma}$, up to 6th order as follows $...
1
vote
1answer
44 views

Is it necessary to prove the existence of an operator representing symmetry on Hilbert space?

Is there any need to prove the existence of an operator $U$ which represents the action of symmetry transformation on rays in Hilbert space? Or is it enough just to prove that it is unitary and linear ...
0
votes
1answer
89 views

Deeper principles in classical mechanics

While teaching introductory physics, my professor explained that the conservation of linear momentum, conservation of energy and conservation of angular momentum are based on deeper principles in ...
0
votes
1answer
53 views

Coleman Mandula theorem and translations

I don't know what Coleman Mandula theorem is, however if I were forced to say something about it, I will say it is a statement that suggests that internal and spatial symmetries have no unique ...
6
votes
1answer
151 views

Derivations of Newton's laws?

I feel convinced that the mathematics behind newtons laws can be derived from Noether's symmetry theorems. The fact that displacement s can be described by a cartesian coordinate system with a ...
0
votes
0answers
27 views

Understanding what a tranformation on a Ray and Hilbert space

I've been referring to Chapter 2 of Introduction to Quantum Field Theory by Weinberg where he talks about symmetries and how they go about. Now, there are two points that he mentions. A ray, which by ...
2
votes
0answers
76 views

Part of a Wigner theorem [closed]

I was trying to understand why there should exist operator in Hilbert space to correspond to any symmetry transformation and found about Wigner's theorem. In it, I can see that any transformed vector ...
0
votes
1answer
39 views

Existence of representation of symmetry transformation

There is a simple fact that we can change our point of view and that physical laws should remain the same, id est, outcomes of our experiments should be the same no matter from which frame of ...
4
votes
2answers
159 views

Does the conservation of the Wronskian follow from Noether's principle?

Noether's principle is the paradigm that symmetries of Hamiltonian and Lagrangian systems correspond to conservation laws of various kinds. Consider a one-dimensional harmonic oscillator $$\tag{*} \...
1
vote
0answers
43 views

Symmetries of a Lagrangian density

Given some Lagrangian density as this how in general can one finds it's symmetries that give conserved currents? For example in this case U(1) is ok, but are there others? Do you know some book ...
0
votes
3answers
99 views

Thinking about the properties of 'nothing' [closed]

If a certain identifiable part of space that has no type of measurable energy fields manifesting 'in it' for a given duration ; is such a totally empty space the same as 'nothing'? Anything with any ...
2
votes
2answers
31 views

Bloch Functions as an implication of the Crystallographic Restriction Theorem?

I'm studying Bloch Functions and it seems to me safe to assume that they are the most general Eigenfunction of a Hamiltionian with the crystal periodicity. Now the only considerations made in deriving ...
0
votes
1answer
50 views

How exactly do we know how should transformations of vectors of Hilbert space look like?

There are transformations on physical states which induce unitary transformations of vectors in Hilbert space that correspond to these physical states. We demand that operators in Hilbert space be ...
2
votes
0answers
67 views

Representation of Lorentz Tranformation on Fields and Wigners theorem

I've been reading about symmetries and I haven't been able piece this information together. I've the Lorentz transformation $$x^\mu \mapsto x^{\rho} = \Lambda_\nu^\mu x^\nu$$ First off, arn't we ...
3
votes
1answer
73 views

Does Birkhoff's theorem hold inside the event horizon?

Can Birkhoff's theorem be used to say that the blackhole exterior and interior sections of Kruskal-Szekeres's solution (or coordinate transformations of it like Gullstrand–Painlevé coordinates, etc.) ...
1
vote
1answer
104 views

Is the cosmological time grosso modo isochrone?

Is the cosmological time grosso modo isochrone? by analogy with space isotropy. Or else do we have possibly great differences by analogy with great voids in the space. We know that it's not strictly ...
1
vote
0answers
52 views

What is conformal symmetry physically?

I'm reading a paper by t'Hooft http://arxiv.org/abs/1410.6675. There is an argument in the paper that I could not understand: "Now that system, described by Maxwell’s equations, does have conformal ...
4
votes
0answers
52 views

Identifying Lorentz Covariant Equations

Statement: $\phi , A^{\mu}, T^{\mu \nu}$ are a Lorentz scalar, vector, and tensor. Which of the following equations are Lorentz covariant. a. $\phi = A_{0}$ b. $\phi = A^{\mu}A_{\mu}$ c. $\phi = ...
1
vote
0answers
18 views

Chiral tunneling in Weyl Equation

I am trying to understand perfect tunneling of particles obeying Weyl equation through a potential barrier at normal incidence. I know that this has something to do with chirality, but I am not ...
0
votes
1answer
33 views

Relation between homotopy theory and symmetry transformation of the Lagrangian

What is the relation between the symmetry transformations of the Lagrangian and homotopy theory? If yes, how? Not sure if this is a math or physics questions. References would be very helpful.
0
votes
1answer
36 views

Implication of rotational symmetry on scattering matrix/ scattering cross-section [closed]

How does the rotational invariance helps simplifying Non-relativistic quantum scattering problems? Is there any any additional information that can be extracted about the scattering amplitude? It ...
0
votes
0answers
40 views

Free Complex scalar field and conservation principle

In a free complex scalar field, the difference between the number of Particles and antiparticles is conserved. This constarint can be satisfied with a simultaneous creation of equal number of ...
0
votes
0answers
21 views

Symmetry and present value problems

Suppose we don't know any physical law of nature and we're studying, a system. Let's say a uniformly spherically charged distribution. Now this distribution has the property, that if you rotate this ...
2
votes
0answers
25 views

Symmetry arguments and plane sheet of charge [duplicate]

The electric field due to a infinite plane sheet of charge is given by $\sigma/\epsilon_o$. Now could we have deduced by symmetry that the electric field's magnitude won't depend on distance?
0
votes
1answer
101 views

Galilean relativity in QM

Intro I've been trying to show that the generator of boosts can be written in operator form as can be seen here, as: $$ B = \sum_i m_i x_i(t) - t \sum_i p_i $$ As a reminder the transformation ...
1
vote
0answers
72 views

Why do three-scalar correlation functions vanish by parity?

We have the following Lagrangian: $$ \mathcal L = \frac12 (\partial_\mu \phi)^2 - \frac12 m^2 \psi^2 + \bar\psi(\mathrm i \gamma^\mu \partial_\mu -M) \psi - \mathrm i g \bar\psi \gamma^5 \psi \phi \,. ...
0
votes
1answer
46 views

What is a Schrödinger background or a Schrödinger symmetry?

In some string theory paper, they mention "Schrödinger background" and "Schrödinger symmetry", which I never heard before. What does that mean?
0
votes
0answers
26 views

How can intuitively guess what conserved quantities has the system that I am studying?

I'm taking a course in Classical Electrodynamics and in one problem my teacher introduced us to a triplet of fields ($\phi^a$) invariant under internal rotations, i.e. transformations like: $$\phi'^...
2
votes
1answer
85 views

Symmetry and Group theory book

I would like to start learning about symmetries in physics and how they affect physical quantities. As far as I know, the mathematical language that describes symmetries is the Group Theory. So, I ...
2
votes
0answers
31 views

What is the global Virasoro symmetry generators in BTZ spacetime?

This is the case of AdS3, how about BTZ? The picture is from arxiv:1506.01353.
0
votes
1answer
88 views

Why are Brillouin zones for graphene and monolayers of transition metal dichalcogenides the same?

The geometrical model of graphene is the flat honeycomb lattice, so the Brillouin zone is also flat honeycomb lattice. However, monolayer of transition metal dichalcogenides is not flat as it consists ...