## The Master Formula for the U-Matrix Finally Found?

**Authors:** Matti Pitkänen

In zero energy ontology U-matrix replaces S-matrix as the fundamental object characterizing
the predictions of the theory. U-matrix is defined between zero energy states and its orthogonal
rows define what I call M-matrices, which are analogous to thermal S-matrices of thermal QFTs.
M-matrix defines the time-like entanglement coefficients between positive and negative energy
parts of the zero energy state. M-matrices identifiable as hermitian square roots of density
matrices. In this article it is shown that M-matrices form in a natural manner a generalization
of Kac-Moody type algebra acting as symmetries of M-matrices and U-matrix and that the space of
zero energy states has therefore Lie algebra structure so that quantum states act as their own
symmetries. The generators of this algebra are multilocal with respect to partonic 2-surfaces
just as Yangian algebras are multilocal with respect to points of Minkowski space and therefore
define generalization of the Yangian algebra appearing in the Grassmannian twistor approach to
N=4 SUSY.

**Comments:** 11 Pages.

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### Submission history

[v1] 1 Nov 2011

[v2] 2012-01-30 09:31:36

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