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Localization properties of highly singular generalized functions
We study the localization properties of generalized functions defined on a broad class of spaces of entire analytic test functions. This class, which...
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A Note on Superdistributions and Wavefront Set
We present a simple and new method of constructing superdistributions on superspace over a Grassmann-Banach algebra, which close to the de Rham's...
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Microlocal Analysis and Renormalization in Finite Temperature Field Theory
We reassess the problem of renormalization in finite temperature field theory (FTFT). A new point of view elucidates the relation between the...
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Spacetime Causality in the Study of the Hankel Transform
We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a...
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Historical Introduction
At the beginning of the 20th century, Max Planck (1858–1947) and Albert Einstein (1879–1955) completely revolutionized physics. In 1900, Max Planck...
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Hyperfunction Quantum Field Theory: Localized Fields Without Localized Test Functions
This note addresses the problem of localization in quantum field theory; more specifically we contribute to the ongoing discussion about the most...
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Deformation Quantization of Poisson Manifolds
I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of...
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Syzygies and conservation laws
We show how the notion of syzygies of a system of partial differential equations allows to derive some conservation laws, for the case of Maxwell and...
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Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals
We generalize the theory of Lorentz-covariant distributions to broader classes of functionals including ultradistributions, hyperfunctions, and...
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Supersymmetric Positivity and Supersymmetric Hilbert Space
We introduce simple notions of positivity and Hilbert spaces of supersym metric functions naturally suggested by the superspace formulation of...
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The Generalized Representation of Particle Localization in Quantum Mechanics
It has been shown earlier that while strict localization of the free Dirac particle is not describable within the usual mathematical formalism, it is...
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Wick Power Series Converging to Nonlocal Fields
We consider the infinite series in Wick powers of a generalized free field that are convergent under smoothing with analytic test functions and...
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On the quaternionic Weyl algebra
In this paper we introduce the notion of quaternionic Weyl algebra A 1 (ℍ) and we study its main properties. We give some examples of A 1 (ℍ)-modules...
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Quantum Tori, Mirror Symmetry and Deformation Theory
We suggest to compactify the universal covering of the moduli space of complex structures by noncommutative spaces. The latter are described by...
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Singular Systems of Exponential Functions
We attempt to establish a calculus of the Moyal product treating the deformation parameter as a parameter moving in positive reals. We show strange...
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Spectral properties of Wick power series for a free field with an indefinite metric
The properties of infinite series in Wick powers of a free field whose two-point correlation function has singular infrared behavior and does not...
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Test function space for Wick power series
We derive a criterion that is convenient for applications and exactly characterizes the test function space on which the operator realization of a...
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Chiral Charged Fermions, One-Dimensional Quantum Field Theory and Vertex Algebras
We give an explicit L 2 -representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the ‘pure’ case such a...