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).
- 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 nnother book by Springer-Verlag about QFT in curved spacetime in collaboration with C.Dappiaggi and N.Pinamonti. 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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