Symmetries Definition and 173 Threads

Hi. First let me recall that there are two equivalent classical bosonic string actions, the Nambu-Goto action S_\mathrm{NG} = - T \iint \mathrm d\sigma \, \mathrm d\tau \sqrt{ (\dot X X')^2 - \dot X^2 {X'}^2} and the Polyakov action S_\mathrm{Pol} = - \frac{T}{2} \iint \mathrm d\sigma...

How many symmetries (and what symmetries) and how many elements do the transformation groups of the equilateral triangle and the icosahedron have? thanks

hello all gauge symmetries are redundencies of the description of a situation. Therefore they are not real symmetries. So in what sense does it mean to spontaneously break a gauge symmetry? ian

Hi... A group G is proken to a subgroup H. Let t_{\alpha} the generator of G and t_i the generator of H. The t_i form a subalgebra. Take the x_a to be the other indipendent generator of G. Why any finite element of G may be expressed in the form g=exp[i\xi_ax_a]exp[i\theta_i t_i] even if...

Hello everybody! I have a general question concerning DEs :0 Can one use the symmetry of the equation to somehow get the solution faster? What does such symmetry tell us? e.g.: \dot x=y \dot y=x is the symmetrical system to the second order DE \ddot x-x=0 Now we can easily see the...

"A manifold (with a metric tensor) is said to be spherically symmetric iff the Lie algebra of its Killing vector fields has a sub-algebra that is the Lie algebra of SO(3)." Why? The statement is paraphrased from texts such as Schutz or D'Inverno, where it is always expressed like a definition...

If we consider nonrelativistic QM, we will find Galilean group under the hood. Thanks to this, group theory enables us to find equations of motion directly from the symmetry principles. For example, if we take only geometric symmetries, we will get that the state space is broken into irreducible...

http://img180.imageshack.us/img180/9589/simplell9.jpg Is 1. c) as simple as i think it is? I have gone through my notes and can't find anything to do with it, the module for it is Numbers, symmetries and groups, any ideas or do i simple just wack in 13/7 on my calculator and write down...

This question comes from reading Schwarz' string theory book, which is why I put it in this section. But it seems like a general QFT question, so maybe this isn't the right forum for it. Starting with the sigma model action, reparametrization and Weyl invariance allow us to "gauge fix" the...

I know that if a particle is in a spherically symetric potential its angular momentum will be conserved, but what about if somehow we manage to produce say an elliptically symmetric potential? Will the particle then have a momentum along the curve of the ellipse conserved? Thanks

As I'm interested in the simplifications of property tensors due to crystal symmetry, I have been trying to find the symmetries of silicon (i.e. the diamond structure). As silicon belongs to the m3m point group I would e.g. expect to find a mirror plane perpendicular to the [100], [010] and...

Hi, I want to take this course next term. One reason is because I think it will help me with mechanics, classical and quantum, which are taken next year at advanced level. The problem is I'm taking calc2 atm, and its a listed prereq for this group course. I got all the other prereq's...

So i began reading up on some group theory and I came across an interesting question, what is the order of the group of symmetries on of a n-sided regular polygon? with a square it's 8, triangle it's 4. I feel like I'm missing something with the pentagon because I'm only finding these: the 5...

Hello. As some of you know I'm a chemistry student, but I plan to take some math for the hell of it next summer. I've come across a course called "Groups and Symmetries" and intend to take it, mainly because it is one of the few upper maths avaialbe in the summer. I've never heard of this...

Does motion break existing symmetries? Observations suggest that the observable universe is spatially flat and, on the largest “cosmic”scale, highly symmetric. On this scale it is modeled as always isotropic and homogeneous. In this situation Birkhoff’s theorem tells us that “exterior” matter...

I recently noticed there's something that escaped me in Lagrangian mechanics. I recently browsed though the first volume of Landau and L., where it is explained that two systems have identical dynamics if their lagrangians differ only by a total differential to time of a function (because the...

Does the single-handedness of DNA and RNA indicate that life originated few times, if more than once? What might the sameness between early sequences (in bacteria, say) indicate in this regard?

" Classical and nonclassical symmetries for Helmholtz Equation " solitions help. Thank you.

new preprint http://arxiv.org/abs/hep-th/0511086 Calabi-Yau Manifolds and the Standard Model John C. Baez 4 pages "For any subgroup G of O(n), define a "G-manifold" to be an n-dimensional Riemannian manifold whose holonomy group is contained in G. Then a G-manifold where G is the Standard Model...

I have a matrix A which satisfies: A_ij(+B) = A_ji (-B) (the matrix is a 4x4 matrix) EDIT: i also know that each row and line summes to 1. i want to prove that the inverse matrix of A sattisfies the same symmetry property. (But, with no success) Do you have an idea how to do that...

Assign specific lepton generation numbers and distincguish between antineutrinos and neutrinos for the following reactions. Make appropriate fixes to show that you know about all the conservation laws not just lepton number conservation \mu -> e^{-}\nu \nu \nu n -> e^{-}p \tau^{-} ->...

How do i show that a group of symmetries of a regular quindecagon has order |G| = 30 ? And how do i describe the elements of G and classify them by their order? Thanks

I'm searching informations about the Gauge simmetries and their application in physics; where can i search in internet and where on books? thanks for answers