Abstract
Let ϕ denote the conformally invariant neutral free scalar field on ℝ×S n. The ‘naive’ lightcone Hamiltonian for a ϕp interaction is given by ∭c∶ϕp⋅, where C denotes a lightcone in ℝ×S n, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n≥3 is odd, p>2, and p(n−1)≡0 mod 4.
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