Hope I can make my question clearer: Why does the first line of Hadlock's proof begin "By Hilbert's irreducibility theorem..."?
ie Hadlock starts with rationals beta1 etc to make G irreducible and I don't see the connection back down to F.
Can anyone explain the idea behind Hadlock's proof that there is an Sn for every poly of degree n? Theorem 37 page 217
I can follow how to build up G from F using symmetric functions and the primitive element theorem. A lso I get the idea of constructing a poly of deg n! from one of deg n...
Many thanks for all the replies.
Found a really useful web reference that does it for me: http://web.mit.edu/molly/Public/8.06/final.pdf
Thanks again, over and out.
Many thanks for the replies, still don't get it. Suppose we have a family of related particles which share in several properties, then anyone particle can be thought of as a state of a generic particle. Using column vectors of ones and zeros we can describe an interaction between two...
No, it's just that whenever I've seen groups in the past there has been a clear mapping between the objects in question and the group elements and operation. E.g., the vertices of an equilateral triangle and S3.
Can anyone give an answer (or give a web reference) to the following question: How is a group assigned to a particle? I've seen groups assigned to shapes, polynomials, permutations, rotations and transformations. But how is a group assigned to a point particle?
Still not not there, obviously an operator valued field is a mathematical construction, that's the original point. Why are the creation and anhilation operators lodged in a field?
Many thanks for the replies, but I still don't get it. After a collision I know the ouctome of the collision, if I know the outcome of a collision, why do I need a field?
Can anyone tell me why it is necessary to express a field as annhilation and creation operators? I just don't see why we need a field to explain the creation of particles in relativity, after all two colliding particles with enough energy produce some more.
Can anyone help me with this simple question based on Feynman's Vol 3? Suppose I have a sequence of filters designed to show the suprising result that extra filters allow previously blocked photons, polarised light, spin one and spin one half particles etc. to get through. Then matrix...
Many thanks for the replies. The quantisation of EM fields is still a puzzle to me. Speaking strategically, I get the idea of using a Hamiltonian in a wider variety of non-mechanical situations, but I still can't see what the goal is is. For example, there is no doubt even at the beginning of...
Particle energy and momentum are obtained from the wave function as eigenfunctions of the spatial and time derivative operators.
Is this true of ElectroMagnetic fields? In other words are E and B eigenfunctions of a differenial operator? I can see that E and B could be interpreted as a...
1. Feynman says all of electromagnetism follows from Maxwell equations.
2. Somebody (Pointing to a Feynman diagram of a photon/electron reaction) said all of electromagnetism is in that one diagram. So, can anyone help me with these two questions: how does point 1 come from point 2. And, how...
Pete, Many thanks for your reply. Your rendition is about a million times clearer than the book's. Among the points you made two points in particular made it all fit together for me: the symmetry between the rod and world line, and the reversal of the direction of the relative motion. Neither...