Department
of Physics,University
of Genova,
Italy INFN, Sezione di Genova,
Italy
Research group in
Mathematical Methods of
Quantum Mechanics
and
Applied Harmonic Analysis
Research team
Gianni Cassinelli (Professor of Mathematical Methods in Physics, University of Genova)
Ernesto De Vito (Researcher in Probability theory, University of Genoa)
Alessandro Toigo (Researcher in Probability theory, Politecnico di Milano)
Claudio Carmeli (Researcher in Mathematical Physics, University of Genova) [personal webpage]
We collaborate with T.
Ali (University of Montreal), T.
Bracken (University of Queensland, Brisbane, Australia), M.
D'Ariano (Università di Pavia, Italia), P.Lahti
(University of Turku, Finland), T.Heinosaari
(University of Turku, Finland), and V.S.
Varadarajan (UCLA, USA).
The principal fields of interest are
the following ones.
We study the mathematical structure of the symmetries in quantum mechanics using the theory of unitary group representations and differential geometry in infinite dimensional Hilbert spaces.
We deal with the problem of defining generalised Fourier
transfroms and of studying their properties in the context of
harmonic analysis. In particular, we are interested in the
applications to wavelet-Gabor analysis and to quantum
tomography.
Books
G. Cassinelli, E. De Vito, A. Levrero, P. J. Lahti , The Theory of Symmetry Actions in Quantum Mechanics with an application to the Galilei group, Series: Lecture Notes in Physics, Vol. 654 2004, XII, 112 p. [link to Springer online catalogue]
Ph.D. Thesis
A. Toigo, Positive operator measures, generalised imprimitvity theorem and their applications [PDF]
C. Carmeli, Super Lie groups: structure and representations
Laurea Thesis
L. Balduzzi, Rappresentazioni unitarie di super gruppi di Lie [PDF]
F. Zizzi, Tomografia quantistica e la rappresentazione metaplettica [PDF]
Lecture notes
G. Cassinelli, Appunti 2011-2012 [PDF] ,[PDF],[PDF],[PDF],[PDF],[PDF],[PDF],[PDF],[PDF],[PDF],[PDF]
G. Cassinelli, Analisi di Fourier e teoria delle distribuzioni Disponibili su AulaWeb ]
G. Cassinelli, Teoria dei gruppi e sue applicazioni alla fisica [PDF]
G. Cassinelli, Rappresentazioni indotte [PDF]
G. Cassinelli, Lectures on Group Theoretical Quantum Tomography [PDF]
G. Cassinelli, Rappresentazioni unitarie del gruppo di Poincare [PDF]
Recent papers
C. Carmeli, E. De Vito, A. Toigo, V. Umanita', Vector Valued Reproducing Kernel Hilbert Spaces and Universality, Analysis and Applications 8 (2010) no.1, pp 19-61 [PDF]
L. Balduzzi, C.Carmeli, R. Fioresi, The local functor of points of supermanifolds, Expositiones Mathematicae 28 (2010) pp. 201-217 [PDF]
C. Carmeli, T. Heinonen, A. Toigo, Covariant quantum instruments, Journal of Functional Analysis 257 (2009) pp 3353-3374 [PDF]
C. Carmeli, G. Cassinelli, F. Zizzi, Generalized orthogonality relations and SU(1,1)-quantum tomography , Found. of Phys. 39 no. 6 (2009) [PDF]
C. Carmeli, T. Heinossari, J.P. Pellonpaa, Optimal covariant measurements: the case of a compact symmetry group and phase observables, J. Phys. A: Math. Theor. 42 (2009) Issue 14 [PDF]
T. Ali, C. Carmeli, T. Heinosaari, A. Toigo, Commutative POVMs and fuzzy observables, Found. of Phys.39 no 6 (2009) [PDF]
L. Balduzzi, C. Carmeli, R. Fioresi, Quotients in supergeometry, "Symmetry in Mathematics and Physics" Contemporary Mathematics (A.M.S.) vol 490 (2009) [PDF]
L. Balduzzi, C. Carmeli, G. Cassinelli, Super G-spaces, "Symmetry in Mathematics and Physics" Contemporary Mathematics (A.M.S.) vol 490 (2009) [PDF]
C. Carmeli, T. Heinossari, J.P. Pellonpaa, Extremal covariant POVMs: the case of a compact symmetry group, J. Math.Phys. 49 (2008) [PDF]
C. Carmeli, T. Heinonen, A. Toigo, Why unsharp observables?, Int. J. Theor. Phys. 47,1 (2008) [PDF]
C. Carmeli, T. Heinonen, A. Toigo, Intrinsic unsharpness and approximate repeatability of quantum measurements, J. Phys. A: Math. Theor. 40 (2007) 1303-1323 [PDF]
C. Carmeli, E. De Vito, A. Toigo, Vector valued reproducing kernel Hilbert spaces of integrable functions and Mercer theorem, Anal. Appl., Vol. 4, No. 4 (2006) 377-408 [PDF]
C.Carmeli, G.Cassinelli, A. Toigo, Unitary representations of super groups and Mackey theory, Bulg. J. Phys. 33 no.s2 (2006) pp. 269-279, [PDF]
C. Carmeli, G.Cassinelli, A. Toigo, V.S. Varadarajan, Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles , Comm. Math. Phys. 263 (2006) 217-258 [PDF]
C. Carmeli, T. Heinonen, A. Toigo, On the coexistence of position and momentum observables, J.Phys. A: Math. Gen. 38(2005) 5253-5266 [PDF] C. Carmeli, G.Cassinelli, E. De Vito, A. Toigo, B. Vacchini, A complete characterization of phase space measurements, J.Phys. A 37 (2004) 5057-5066 [PDF]
C. Carmeli, T. Heinonen, A. Toigo, Position and momentum observables on R and on R3, J. Math. Phys. 45 (2004) 2526-2539 [TeX-PDF]
G.Cassinelli, E. De Vito, A. Toigo, Positive operator valued measures covariant with respect to an Abelian group, J.Math. Phys. 45 (2004) 418-433 [TeX-PDF]
G.Cassinelli, E. De Vito, A. Toigo, Positive operator valued measures covariant with respect to an irreducible representation, J. Math. Phys. 44 (2003) 4768-4775 [TeX-PDF]
A.J. Bracken., G.Cassinelli, J.G. Wood, Quantum Symmetries and the Weyl-Wigner Product of Group Representations, J. Phys. A,36(2003) 1033-1056 [TeX-PS]
G.Cassinelli, E.De Vito, Square-integrability modulo a subgroup, Trans. A.M.S. 355, (2003) 1443-1465. [TeX-PS]
G.Cassinelli, V.S. Varadarajan, On Accardi's notion of complementary observables, Infinite Dimensional Analysis, Quantum Probability and Related Topics 5, (2002) 1-10. [TeX-PS]
G.Cassinelli, E.De Vito, P.Lahti, J.-P. Pellonpää, Covariant localizations in the torus and the phase observables, J. Math. Phys. 43 (2002) 693-704. [TeX-PS]
G. M. D'Ariano, E. De Vito, L. Maccone, SU(1,1) tomography, Phys. Rev. A 64, (2001) 033805. [PS]
R. Fioresi, A. Levrero, M. A. Lledó, Algebraic and Differential Star Products on Regular Orbits of Compact Lie Groups, Pac. J. Math. (2001). [TeX-PS]
P. Busch, G.Cassinelli, E.De Vito, P.Lahti, A.Levrero, Teleportation and Measurement, Physics Letter A 284 (2001) 141-145. [TeX-PS]
P.Aniello, G.Cassinelli, E.De Vito, A.Levrero, On discrete frames associated with semidirect products, J.Fourier Analys and Appl. 7 (2001) 199-206. [TeX-PS]
G.Cassinelli, G.M. D'Ariano, E.De Vito, A.Levrero, Group theoretical Quantum Tomography, 41 J.Math.Phys (2000) 7940-7951. [TeX-PS]
G.Cassinelli, E.De Vito, P.Lahti, A.Levrero, A theorem of Ludwig revisited, Found.Phys. 30 (2000) 1755-1761 . [TeX-PS]
G.Cassinelli, E.De Vito, P.Lahti, A.Levrero, Phase Space Observables and Isotypic Spaces, J.Math.Phys. 41 (2000) 5883-5896. [TeX-PS]
G.Cassinelli, E.De Vito, A.Levrero, Square-integrable imprimitivity systems, J.Math.Phys 41 (2000) 4833-4859. [TeX-PS]
P.Aniello, G.Cassinelli, E.De Vito, A.Levrero, Frames associetad with imprimitivity systems, J. Math. Phys 40 (1999) 5184-5202. [TeX-PS]
G.Cassinelli, E.De Vito, A.Levrero, Galilei invariant wave equations, Rep.Math.Phys. 43 (1999) 467-498. [TeX-PS]
G.Cassinelli, E.De Vito, P.Lahti, A.Levrero, Symmetry of the Quantum State Space and Group Representations, Rev. Math. Phys 10 (1998) 893-924. [TeX - PS]
P.Aniello, G.Cassinelli, E.De Vito, A.Levrero, Wavelet transforms and discrete frames associated to semidirect products, J. Math. Phys 39 (1998) 3965-3973. [TeX - PS]
P.Aniello, G.Cassinelli, E.De Vito, A.Levrero, Square integrability of induced representations of semidirect products with normal abelian subgroup, Rev. Math. Phys. 10 (1998) 301-313 [TeX - PS]
G.Cassinelli, E.De Vito, P.Lahti, A.Levrero, Symmetry Groups in Quantum Mechanics and the Theorem of Wigner on the Symmetry Transformations, Rev. Math. Phys. 9 (1997) 921-941. [TeX - PS]
G.Cassinelli, E.De Vito, A.Levrero, Integrability of the Quantum Adiabatic Evolution and Geometric Phases, J. Math. Phys. 38,(1997) 6101-6118.[TeX - PS]
G.Cassinelli, E.De Vito, A.Levrero, On the decomposition of a quantum state, J. Math. Analysis and Appl. 210, (1997) 472-483. [TeX - PS]