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In the present paper we construct the star products concerning scalar fieldsin the covariant case from a new approach. We construct the star products atthree levels, which are levels of functions on Rd, fields and functionalsrespectively. We emphases that the star product at level of functions isessence and starting point for our setting. Firstly the star product offunctions includes all algebraic and combinatorial information of the starproducts concerning the scalar fields and functionals almost. Secondly, a moreinteresting point is that the star product of functions concerns only finitedimensional issue, which is a Moyal-like star product on Rd generated by abi-vector field with abstract coefficients. Thus the Kontsevich graphs playsome roles naturally. Actually we prove that there is an ono-one correspondencebetween a class of Kontsevich graphs and the Feynman graphs. Additionally theWick theorem, Wick power and the expectation of Wick-monomial are discussed interms of the star product at level of functions. Our construction can beconsidered as the generalisation of the star products in perturbative algebraicquantum fields theory and twist product introduced in [1],[2].

From Kontsevich Graphs to Feynman graphs, a Viewpoint from the Star Products of Scalar Fields