Talk:Invariance mechanics

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Invariants from actions Should there be more about how to find the invariants of a particular theory from the action of that theory. For example in chromodynamics one can use 4-point invariants from the term AAAA? Qloop 10:06, 5 April 2007 (UTC)


Four-point interaction The four-point scalar interaction from φ4 theory is given by:

\int {e^{i((x-w).q+(y-w).r+(z-w).s)} \over q^2 r^2 s^2 (q+r+s)^2 } dq^4 dr^4 ds^4 = f( |x-w|,|x-y|,|x-z|,|y-w|,|y-z|,|w-y| )

but I can't find what the function f is in terms of the 6 invariants of the 4-point complete graph. I think it can be written as an infinite sum in which the powers of each term sum to -4. This would be interesting to put in since it has similarities with the 4-point amplitude from string theory. Maybe this should be put in the scalar field theory article.

86.148.25.43 18:37, 7 April 2007 (UTC)

Can you tell me more about how the constraints polynomials might have the monster group symmetry? Qloop 18:41, 7 April 2007 (UTC)

A complete graph with n vertices has n(n-1)/2 lines, so assume that there are two invariants per line. The Standard model particles, all leptons, quarks and bosons, including all spinors and vector polarisations has about 300(?) degrees of freedom. So a constraint polynomial for this would have about 2*300^2 =180000 variables. The monster group actions in lowest dimension 196884. Hence, perhaps, the polynomial representing the constraints on the invariants of nature has the symmetries of the monster group. It is also interesting to look at it the other way around and to start with a symmetry group and to see if one can construct laws of physics from it. These calculations are pretty rough but we should get an answer in the next few years. Remember that the monster group has also been linked to a type of string theory in 26 dimensions, so it should not be surprising that it crops up again. Drschawrz 21:52, 7 April 2007 (UTC)