Non-commutative Field Theory on S^4

Details Non-commutative Field Theory on S^4 Non-commutative Field Theory on S^4

2004-04-13

arxiv.org/abs/hep-th/0404086v2

Prog.Theor.Phys. 112 (2004) 883-894

Physics

High Energy Physics

High Energy Physics - Theory

19 pages; v2 16 pages, changed contents, typos corrected

Scientific paper

10.1143/PTP.112.883

In the previous paper (hep-th/0402010) we proposed a matrix configuration for a non-commutative S^4 (NC4S) and constructed a non-commutative (star) product for field theories on NC4S. In the present paper we will show that any matrix can be expanded in terms of the matrix configuration representing NC4S just like any matrix can be expanded into symmetrized products of the matrix configuration for non-commutative S^2. Then a scalar field theory on NC4S is constructed. Our matrix configuration describes two S^4's joined at the circle and the Matrix theory action contains a projection matrix inside the trace to restrict the space of matrices to that for one S^4.

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