Generally speaking I may say
that my interests concern Modern Mathematical
Physics. In particular I deal with several
mathematical and physical aspects of Quantum Theories and their
Mathematical Formulation including Algebraic and Axiomatic Theories of Relativistic
Quantized Fields. Here is a list of topics I have treated.
- Mathematical formulation of quantum theories (also real and quaternionic
Hilbert spaces, quanternionic functional analysis, especially spectral
theory) including some experimental application to photonics (violation
of Bell inequality using incoherent and thermal light).
- Axiomatic, algebraic and local aspects of QFT in (generally curved) Lorentzian/Euclidean background;
- geometric formulation of quantum mechanics and its relation with quantum information
- QFT in cosmological models;
- QFT in the presence of conformal invariance (CFT) ;
- I was also concerned with some aspects of Lorentzian noncommutative geometry.
renormalization
procedure (heat-kernel and
zeta spectral function applications in QFT): look at this book I wrote
in collaboration, published by World Scientific. More recently I wrote with I.Khavkine a long review about general aspects of QFT in curved spacetime which appears a chapter of a book.Here is another book by Springer-Verlag about QFT in curved spacetime in collaboration with C.Dappiaggi and N.Pinamonti. Another more recent book I authored still concerning mathematical foundations of Quantum Theories and some general issues like Bell inequality and similar is here. This book reflects my recent lecuires on the subjectin a Master course at the University of Trento. I participate in the international forum LQP Crossroads |
From a mathematical point of
view, this means that I am intersted in several applications of functional
analysis (especially
topics in the theory of operator algebras and C*
algebras), global
analysis (i.e. functional analysis
on Riemannian
and Lorentzian
manifolds, using the intrinsic geometrical
structure), microlocal analysis,
differential
geometry |

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