Florin Constantinescu

The integral theorem for supersymmetric invariants

A supersymmetric integral theorem that extends results of Parisi, Sourlas, Efetov, Wegner, and others is rigorously proved. In particular, arbitrary generators are allowed in the integrand (instead of canonical ones) and the invariance condition is very much relaxed. The connection with Cauchy’s integral formula is made transparent. In passing, the unitary Lie supergroup is studied by using elementary methods. Applications in the theory of disordered systems are discussed.

Boundary values of analytic functions

AbstractIt is known that a complex — valued continuous functionS(x) as well as a Schwartz distribution on the real axis can be extended in the complex plane minus the support ofS to an analytic functionŜ(z). In the case of a continuous function the jump ofŜ(z) on the real axis represents exactlyS(x):

Definite and indefinite inner products on superspace (Hilbert-Krein superspace)

\mathop {\lim }\limits_{\varepsilon \to 0 + } [\hat S(x + i\varepsilon ) - \hat S(x - i\varepsilon )] = S(x)

Ultradistributions and quantum fields: Fourier-Laplace transforms and boundary values of analytic functions

. We call regular a pointx on the support ofS such that

The Ising limit of the double‐well model

\mathop {\lim }\limits_{\varepsilon \to 0 + } [\hat S(x + i\varepsilon ) - \hat S(x - i\varepsilon )]

Smeared and Unsmeared Chiral Vertex Operators

exists. Conditions are found for the existence of regular points on the support of a distribution. It is possible to call this limit (if this exists) the valueS(x) of the distributionS in the pointx. Properties of this type occur in the theory of dispersion relations.