Covariant differential operators and Green's functions

Conformally Covariant Differential Operators: Properties and Applications

We discuss conformally covariant differential operators, which under local rescalings of the metric, δσg μν = 2σg , transform according to δσ∆ = r∆σ+(s−r)σ∆ for some r if ∆ is s th order. It is shown that the flat space restrictions of their associated Green functions have forms which are strongly constrained by flat space conformal invariance. The same applies to the variation of the Green fun...

Conformally Covariant Differential Operators: Symmetric Tensor Fields

We extend previous work on conformally covariant differential operators to consider the case of second order operators acting on symmetric traceless tensor fields. The corresponding flat space Green function is explicitly constructed and shown to be in accord with the requirements of conformal invariance. PACS: 03.70.+k; 11.10.Kk; 11.25.Hf; 11.30.Ly

Gauge-covariant vertex operators

We derive Yang-Mills vertex operators for (super)string theory whose BRST invariance requires only the free gauge-covariant field equation and no gauge condition. Standard conformal field theory methods yield the three-point vertices directly in gauge-invariant form. E-mail address: [email protected] E-mail address: [email protected]

Differential Operators Commuting with Invariant Functions

Interpolation by hypercyclic functions for differential operators

We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed values at the points of the sequence and, simultaneously, having dense orbit in the space of holomorphic functions on Ω . The orbit is taken with respect to any fixed nonscalar differential operator generated by an entire function of subexponential type, thereby ext...