Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-11-05
J.Phys.A41:194002,2008
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, with minor improvements as to appear in J. Phys. A
Scientific paper
10.1088/1751-8113/41/19/194002
The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite dimensional Lie algebra: a central extension of sp(infty,R) corresponding to the field R of reals, of u(infty,infty) associated to the field C of complex numbers, and of so*(4 infty) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N), and U(N,H)=Sp(2N), respectively.
Bakalov Bojko
Nikolov Nikolay M.
Rehren Karl-Henning
Todorov Ivan
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