Abstract
The behaviour of products of local fields for lightlike distances is investigated. If a light cone expansion ofA(x)A(y) exists, then already the four point function carries the singularity arising in the expansion for (x−y)2→0. For a special class of field theories, discussed by S. Schlieder and E. Seiler, it is shown that the light cone expansion is possible.
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Notation. the Schwartz space of strongly decreasing testfunctions over ℝn A=scalar field operator, which fulfils the Wightman axioms [we freely writeA(x),x ∈ ℝ4 andA(g),g ∈]. ℋ=Hilbert space. Ω=vacuum state. ℑ ⊂\(\mathfrak{J} \subset \mathfrak{D}\) is the linear hull of the vectors\(\Omega ;A(z_1^1 )\Omega ; \ldots ;A(z_1^n )A(z_2^n ).....A(z_n^n )\Omega ;(z_1^k ,z_j^k - z_{j - 1}^k \in \tau _ + ).\) (With respect to the definition of operators with complex argument cf.[6]!) By δϱ(x 2) (x 2) we denote a sequence of functions which converges to δ(x 2) as ϱ→0.
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Kühn, J., Seiler, E. Light cone expansion and four point function. Commun.Math. Phys. 33, 253–257 (1973). https://doi.org/10.1007/BF01667921
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DOI: https://doi.org/10.1007/BF01667921