Quasicanonical quantum field theory

We call a quantum-field-theory model quasicanonical if it is defined by canonical equal-time field commutation relations (e.g., [φ̇(x), φ(0)]δ(x⁰)=-iδ⁴(x)) and local field equations [e.g., □φ(x)=λJ(x)], and is locally invariant to scale transformations [e.g., φ(x)→ρφ(ρ x)]. [These requirements are not consistent if the model is purely canonical, i.e., if J(x) is the simple Wick product:φ³(x):.] Canonical Bjorken scaling is valid in such models provided that the field equations are also locally invariant to R transformations [φ(x)→φ(x)+r] and the physical currents are R-invariant. We discuss here further properties and consequences of these models. (a) We incorporate positivity and R-invariance restrictions on light-cone expansions and deduce the form of the consequent bilocal operators [e.g., ∫daσ(a):φ(ax)φ(0):]. (b) We exhibit a Hamiltonian formulation of the theory, both in the massless and massive cases. (c) We show that the theory is locally conformal- and inversion- [$\phi \left(x\right)\to {\left(x^2\right)}^{-1}\phi (-\frac{x}{x^2})$] invariant. These symmetries are spontaneously broken. (d) We discuss the implications of the model for deep-inelastic electron-positron annihilation. Exact scaling is obtained. (e) We study the possible low-energy consequences of the (spontaneously broken) R symmetry. These include the PCAC (partial conservation of axial-vector current) consistency conditions and the Gell-Mann charge algebra. (f) We consider the arguments for and consequences of a spontaneous breakdown of the dilatation symmetry.