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 quite incomplete list of some topics I have treated.
- The notion of Localization for relativistic quantum systems where many difficult issues concerning locality and causality pop up.
- 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 CHSH inequality using incoherent and thermal light).
- Quantization Maps (Strict deformation quantization procedures) in the C*-algebraic approach
- Axiomatic, algebraic and local aspects of QFT in (generally curved) Lorentzian/Euclidean background (I participate in the international forum LQP Crossroads);
- 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.
- I might finally mention that I also have participated in some (experimental) projects about quantum technologies and I am also the inventor of a patent on quantum techologies together other colleagues.
functional analysis
on Riemannian
and Lorentzian
manifolds, using the intrinsic geometrical
structure), microlocal analysis,
differential
geometryI authored a book on the mathematical formulation of quantum mechanics (with an introduction to the algebraic formulation of quantum theories) published by Springer-Verlag (see here). In the past, I gave several contributions to the theory of analytical (one-loop) 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 lectures on the subject for a Master course at the University of Trento.Another book, a tutorial on quantum theories from quantim mechanics to QFT, in collaboration with M.Asorey and E.Ercolessi My publication list could help you focus on my research activity. |