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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How to prove by symmetry that tension in a section of rapidly rotating wheel act tangentially?

Suppose a thin uniform wheel of radius $r$ is rotating rapidly about its axis; its spokes have almost negligible strength. According to the book, the centripetal force is provided by the tension ...
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3answers
193 views

What is the exact meaning of homogeneity in cosmology?

I understand that, in general, homogeneity is the physical attribute of being uniform in composition (" of the same form at every point"), but I'm slightly confused when it is used in cosmology as ...
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1answer
100 views

Does Conformal Invariance of the Polyakov Action in Conformal Gauge imply Conformal Invariance of the Pre-gauge-fixed Polyakov Action?

In bosonic string theory the Polyakov action can be put in into conformal gauge. It is then possible to show that the resulting gauge fixed action is conformally invariant. Actually it's shown that ...
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Killing vectors of AdS space with the metric given in Poincaré coordinate [closed]

I am trying to solve this problem: Find the Killing vector correspond to the symmetry of the scale invariant for the AdS(n+1) $$ (t,{\bf x}) \rightarrow (at, a{\bf x}) $$ when the metric of the AdS ...
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1answer
34 views

Particle hole symmetry of single site?

Let's consider I have a system with equal number of spin up and spin down particles Now I consider a single site of system,I have a state $c_{i\uparrow} ^{\dagger}\mid 0\rangle$ under particle hole ...
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86 views

What does Lee Smolin mean when he says that the most fundamental theory can have no symmetries?

Quote: There are some lazy ideas about unification that reflect uncritical thinking, such as the idea that the more fundamental a phenomena [sic] is the more symmetry it must have. When you think ...
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1answer
71 views

Symmetry of Bloch Hamiltonian

If a crystal system preserve a symmetry C, why its Bloch Hamiltonian satisfy $H(C\vec k)=CH(\vec k)C^{-1} $
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1answer
38 views

$B$ field around an infinite wire symmetry argument

Consider the infinity current carrying wire wire drawn below along with the three possible components of the magnetic field at a point a distance $r$ from the centre. I know how to use symmetry to ...
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34 views

Symmetry arguments for valley physics in graphene with broken inversion

I am trying to understand this paper: http://link.aps.org/doi/10.1103/PhysRevLett.99.236809 (Here is an arXiv version: http://arxiv.org/abs/0709.1274) In the introduction, they mention certain ...
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3answers
58 views

Principle of Sufficient Reason on light travelling in straight line

I was reading a book Laws and Symmetry by Bas C. Van Fraassen I found that there is an argument for arguing that light travel in straight line: Leibniz's reconstruction of these arguments goes ...
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24 views

Non-abelian current transformation

This is my firs post ever here and I just registered on this site but I want to say that this site has helped me a lot and you guys are great! On to the question: I have the equation of motion that ...
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1answer
73 views

General construction of equations of motion for free particles

I've got a question regarding the different Symmetrie-Lie-Groups of Newtonian Mechanics and special realtivity. Is there a canonical way to obtain the equations of motion for a free particle only by ...
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20 views

How can we determine the Hypercharges in a GUT like SO(10)?

I understand how the assignment works for a symmetry breaking like $$SO(10) \rightarrow SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_X$$ The Hypercharge can then easily computed by $$ ...
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1answer
27 views

Is the Singlet state for Helium with 2 electrons symmetric rather than anti-symmetric as is meant to be for fermions?

I'm looking at two-electron Helium atoms where one electron is in the ground state (due to if it were in other states, it's de-excitation would simply lead to the ionization of the electron). The ...
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1answer
27 views

Why performing axial symmetry, results in the same masses for pion and sigma mesons?

Under axial transformations, $\sigma$ and $\pi$ are rotated into each other: $\vec{\pi} \rightarrow \vec{\pi}+ \vec{\theta} \sigma $, $\sigma \rightarrow \sigma+ \vec{\theta}.\vec{\pi} $. In ...
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1answer
50 views

Why should Ward identities only be used with the effective action (as opposed to the generating functional for connected diagrams)?

My question is about the derivation of Ward identities. I will sketch it here in the case of an O(N) symmetric model and point out what it bothering me when I am done. I am being very sloppy with the ...
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2answers
60 views

Why do the $u$ and $d$ quark not have an associated quantum number?

All the other quarks ($c$,$s$,$b$ and $t$) have quantum numbers of charmness, strangeness, bottomness and topness that are conserved in strong interactions. This allows, among other things, flavour ...
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1answer
49 views

Local translations in curved spacetime

A global Poincare transformation on a scalar field induces $$\delta(a, \lambda)\phi(x) = [a^{\mu}+\lambda^{\mu\nu}x_{\nu}]\partial_{\mu}\phi(x). \tag{11.46}$$ In curved spacetime we replace $a^{\mu} ...
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2answers
93 views

Why is $p_\phi$ conserved in a Schwarzschild orbit?

This arises from the question What is the relationship between $a$ and $m$, which I'm afraid I answered just by looking it up in Schutz's book. However Schutz (as he frequently does) glosses over ...
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427 views

Why aren't orbitals symmetric?

In an hydrogen-like atoms the orbitals are solutions to the Schrodinger equation suitable for the problem. They describe the regions where an electron can be found. So, why don't they have spherical ...
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2answers
61 views

Scalar and vector defined by transformation properties

In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix ...
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32 views

Name for the transformation into an accelerated frame?

A transformation into a frame that looks at an experiment from a rotated perspective is called a rotation. A transformation into a frame that moves with a different constant velocity is called a ...
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0answers
55 views

Why is the electric field inside a solenoid tangential?

I have been looking at some derivations for the electric field inside a solenoid. I know how to find it, but I don't get the symmetry argument used. This is often of the form: Since if we choose ...
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0answers
64 views

Antimatter universe and Noether's theorem

I am studying Feynman's "symmetry in physical laws", where he talks about conservation laws for corresponding symmetries. (I know this is Noether's theorem, I am studying this from David Tong's ...
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42 views

Landau theory of phase transation

In his article http://www.ujp.bitp.kiev.ua/files/journals/53/si/53SI08p.pdf, Landau defines probability distribution $\rho$ which is related to symmetry of crystal. If crystal has certain symmetry ...
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142 views

Spontaneous Symmetry Breaking - struggling with physics based understanding?

Although I am a mathematician by nature, I'm writing an essay in my third year of my undergraduate on Spontaneous Symmetry Breaking in Physics, and as such I've become a little confused by how the ...
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1answer
46 views

Parity transformation is proper orthochronous?

In 3+1 dimensional spacetime the parity transformation is $$P^\mu_{\;\,\nu}=\begin{pmatrix}+1&&&\\&-1&&\\&&-1&\\&&&-1\end{pmatrix}.$$ This is ...
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1answer
35 views

Parameterization of an arbitrary element of $U(2)_L \times U(2)_R$ (Chiral symmetry with two quarks)

When you write down the Lagrangian for two quarks : \begin{equation} \mathcal{L}_\text{QCD}^0 = -\frac{1}{4} G_{\mu\nu}^a G^{a\mu\nu}+ \bar\Psi i \gamma^\mu D_\mu \Psi \end{equation} you find an ...
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1answer
73 views

How do states in Hilbert Space act like irreducible representations?

I am reading Georgi's book on group theory and I came across this sentence..." Hilbert space of any parity invariant system can be decomposed into states that behave like irreducible representations". ...
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1answer
37 views

Is there a sensible fully-discretized Hamilton's principle?

In computational physics it is common to formulate Hamilton's principle in a semi-discrete way, where space is continuous but time is discrete: in other words the Lagrangian $$L(q, \dot q, t): ...
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1answer
93 views

Symmetry argument for a toroid?

When using Ampere's law for a toroid (in the toroid and around a circular path) please can someone explain the symmetry argument (or an alternative argument) which allows us to assume the field is ...
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33 views

Any importance of $i$ before the time reversal operator for spin-1/2 system?

I've read about that: For systems with spin 1/2, time-reversal symmetry has the operator $\mathcal{T}=i\sigma_y K$. I wonder if the imaginary unit $i$ has any importance. Without $i$, ...
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48 views

Does invariance under infinite small transformation imply invariance to the finite one?

Let's say that I have finite chiral transform and I would like to show invariance of Dirac's Lagrangian when $m=0$ under it. The chiral transform is defined as: $$\psi(x) \rightarrow \psi'(x) =e^{i ...
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78 views

Intuition for S-duality

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
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1answer
86 views

Why is a hexagon such a stable shape for materials?

A hexagonal lattice is famously the shape of graphene, the source of the 2010 Nobel prize. The shape also shows up in beehives and in the basalt columns of Giant's Causeway in County Antrim. ...
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36 views

How to define conserved charges in Euclidean field theory?

In a field theory with signature (1,d), conserved charges are obtained by integrating the time component of a conserved current over a spatial region. What are the corresponding equations and ...
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1answer
38 views

Conserved current in a complex relativistic scalar field

For my field theory class I have the following Lagrangian density $$\mathscr{L}=\frac{1}{2}\eta^{\mu\nu}\partial_\mu\phi^*\partial_\nu\phi-\frac{1}{2}m^2\phi^*\phi$$ Where $\eta^{\mu\nu}$ is the ...
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1answer
39 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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46 views

Laplace's demon and spontaneous symmetry breaking

One interpretation of Quantum mechanics is the hidden variable theory. This suggests that if we were to have a complete knowledge of the system at one time then the future states of the system are ...
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841 views

Can conservation of momentum be violated?

The law of the conservation of momentum has been established for hundred of years. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. ...
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1answer
62 views

Given potentials, how does one find conserved quantities using Noether's theorem?

I've been asked to find the conserved quantities of the following 3D potentials: $U(\vec{r}) = U(x^2)$, $U(\vec{r}) = U(x^2 + y^2)$ and $U(\vec{r}) = U(x^2 + y^2 + z^2)$. For the first one, ...
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31 views

Does the similarity of gamma matrices correspond to a conserved quantity?

Gamma matrices have a similarity property, $\gamma^\mu\to S\gamma^\mu S^{-1}$ is a good transformation. Does this transformation correspond to a symmetry of the QED Lagrangian?
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normal degeneracy and the “span” of an irreducible representation

In Tinkham's "Group Theory and Quantum Mechanics", Tinkham defines normal degeneracy so that the span of the action of the Hamiltonian's symmetry group on any energy eigenstate yields all possible ...
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1answer
60 views

Why Levi-Civita term signal the breaking of parity and time reversal?

For example, referring to Zee's QFT book, in Chern-Simons matter theory, after writing a term $$\gamma {\varepsilon ^{\mu \nu \lambda }}{a_\mu }{\partial _\nu}{a_\lambda }$$ he said The ...
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1answer
74 views

Does an on-shell symmetry necessarily change the Lagrangian by a total derivative?

This is a follow-up question to: Does a symmetry necessarily leave the action invariant? Qmechanic writes here: Here the word off-shell means that the Lagrangian eqs. of motion are not assumed to ...
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Why does it take a projectile as long to get to its apex as it does to hit the ground?

I was once asked the following question by a student I was tutoring; and I was stumped by it: When one throws a stone why does it take the same amount of time for a stone to rise to its peak and then ...
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108 views

Does a symmetry necessarily leave the action invariant?

A symmetry maps a configuration with stationary action to another configuration with stationary action. However, does it necessarily preserve the value of the action exactly? It seems that it should ...
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How to show OPE coefficients are symmetric in three indices ?

May it is very trivial, but I am stuck here, given (I have suppressed the conjugate coordinates) $$ \phi_i(x) \phi_j(y) \sim \sum_{k} c_{ijk} (x-y)^{h_k - h_i - h_j} \phi_k(y) $$ $$ \langle ...
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122 views

Derivation of Rashba spin-orbit coupling in tight-binding model

Rashba spin-orbit coupling Hamiltonian in free space can be written as: $H_{\text{so}}=\int d^3r \Psi^{\dagger}(\mathbf{r}) \gamma (p_{x}\sigma _{y}-p_{y}\sigma _{x})\Psi(\mathbf{r})$. I expand ...
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1answer
46 views

Infinitesimal transformations and Poisson brackets [duplicate]

I want to understand how bracket operations in general are related to symmetry and infinitesimal transformations (in hindsight of quantumfieldtheory), so I calculated an example with a particle that ...