Published Books

[10] V.Moretti                             Meccanica Analitica Meccanica Classica,Meccanica Lagrangiana, Hamiltoniana, Teoria della Stabilità, Relatività Speciale 2nd revised and enlarged edition (italian) 890 pages Springer  2024 ISBN: 978-3-031-63112-2 [9] V.Moretti                             Analytical Mechanics Classical, Lagrangian and Hamiltonian Mechanics, Stability Theory & Special Relativity 750 pages Springer  2023 ISBN: 978-3-031-27612-5 [8] V.Moretti                             Meccanica Analitica Meccanica Classica,Meccanica Lagrangiana e Hamiltoniana e Teoria della Stabilità (italian) 600 pages Springer  2020 ISBN 978-88-470-3997-1 [7] M.Asorey, E.Ercolessi,  V.Moretti    From Classical Mechanics to Quantum Field Theory. A Tutorial 256 pages  World Scientific Publishing 2020 ISBN 978-981-121-048-8 [6]  V.Moretti Fundamental Mathematical Structures of Quantum Theory Spectral Theory, Foundational Issues, Symmetries, Algebraic Formulation 337 pages Springer  2019 ISBN 978-3-030-18345-5 review of the book by MathSciNet [5]  V.Moretti: Spectral Theory and Quantum Mechanics: Mathematical Structure of Quantum Theories, Symmetries and introduction to the Algebraic Formulation 2nd revised and enlarged edition 950 pages Springer 2018 ISBN 978-3-319-70705-1 review of the book by Zentralblatt MATH ERRATA CORRIGE [4] C.Dappiaggi, V.Moretti, N.Pinamonti: Hadamard States from Light-Like Hypersurfaces 115 pages Springer 2017 ISBN 978-3-319-64343-4 arXiv:1706.09666 [3] V.Moretti: Spectral Theory and Quantum Mechanics: with an introduction to the Algebraic Formulation. 752 pages Springer 2013 ISBN 978-88-470-2834-0 review of the book by MAA Reviews ERRATA CORRIGE [2] V.Moretti: Teoria Spettrale e Meccanica Quantistica. Operatori in Spazi di Hilbert. (Italian) 704 pages Springer 2010 ISBN:978-88-470-1610-1  review of the book by Zentralblatt MATH  [1] A.Bytsenko, G.Cognola,,E.Elizalde, V.MorettiS.Zerbini: Analytic Aspects of Quantum Fields. 350 pages World Scientific Publishing, 2003,  ISBN:981-238-364-6 review of the book by Zentralblatt MATH

In progress

[79] D. Castrigiano, C. De Rosa, V. Moretti: paper about representations of the Causal Logic for massive systems

[78] C.De Rosa and  V.Moretti: Yet another paper about quantum relativistic localization

Submitted

[77] N.Drago, S. Mazzucchi, V.Moretti: Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics and Schroedinger equations  https://arxiv.org/abs/2307.03282

Published or accepted for publication

[76] C.De Rosa, V.Moretti: Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties Lett.Math.Phys. 114: 72 (2024)  DOI: 10.1007/s11005-024-01817-9 https://arxiv.org/abs/2402.13894  60 pages

[75] N. Leone, S. Azzini, S. Mazzucchi,  V.Moretti, M. Sanna, M. Borghi, G. Piccoli, M. Bernard, M. Ghulinyan and L. Pavesi:  Generation of quantum-certified random numbers using on-chip path-entangled single photons from an LED Photonics Research Vol. 11, Issue 9, pp. 1484-1499 (2023). DOI:10.1364/PRJ.488875 https://arxiv.org/abs/2303.15332   15 pages [74] V.Moretti, S. Murro, D.Volpe: Paracausal deformations of Lorentzian metrics and Moller isomorphisms in algebraic quantum field theory,  Selecta Mathematica, New Ser. 29, 56 (2023). DOI:10.1007/s00029-023-00860-z https://arxiv.org/abs/2109.06685  69 pages [73] V.Moretti:  On the Relativistic Spatial Localization for massive real scalar Klein-Gordon quantum particles Lett.Math.Phys. 113, 66 (2023).  DOI:10.1007/s11005-023-01689-5 https://arxiv.org/abs/2304.02133  50 pages [72] V.Moretti S. Murro, D.Volpe: The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators Ann. H. Poincaré 24, 3055–3111 (2023).   DOI: 10.1007/s00023-023-01326-w https://arxiv.org/abs/2210.09278  57 pages [71] S. Mazzucchi,  V.Moretti, I. Remizov, O. Smolyanov: Chernoff approximations for Feller semigroups in Riemannian manifolds, Mathematische Nachrichten 296, 3 (2023) 1244-1284   DOI: 10.1002/mana.202100291 https://arxiv.org/abs/2002.06606    40 pages [70] N. Leone, S. Azzini, S. Mazzucchi,  V.Moretti,  L. Pavesi: Certified quantum random numbers based on single-photon entanglement Phys.Rev.Applied 17, 034011 (2022)  DOI: 10.1103/PhysRevApplied.17.034011 https://arxiv.org/abs/2104.04452  33 pages [69] V.Moretti, C.J.F van de Ven:  The classical limit for Schroedinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as emergent phenomenon Int J. Geom Methods Mod Phys 19, 2250003 (2022)  DOI:10.1142/S0219887822500037 https://arxiv.org/abs/2103.11914     43 pages [68] V.Moretti  On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods Lett.Math.Phys. (2021) 111:130 DOI: 10.1007/s11005-021-01464-4 https://arxiv.org/abs/2107.04903 18 pages [67] S. Mazzucchi, S. Azzini, N. Leone, L. Pavesi, V.Moretti: Entropy certification of a realistic quantum random numbers generator based on single particle entanglement  Phys.Rev.A 104, 022416 (2021) DOI: 10.1103/PhysRevA.104.022416 https://arxiv.org/abs/2104.06092  17 pages [66] S. Pasini, N. Leone, S. Mazzucchi,  V.Moretti,  D. Pastorello,  L. Pavesi: Bell inequality violation by entangled single photon states generated from a laser, a LED or a Halogen lamp  Phys.Rev.A 102, 063708 (2020) DOI:10.1103/PhysRevA.102.063708 https://arxiv.org/abs/2003.09961 32 pages [65]   V.Moretti, C.J.F van de Ven: Bulk-boundary asymptotic equivalence of two strict deformation quantizations Lett.Math.Phys, 110 (2020)  2941-2963  DOI: 10.1007/s11005-020-01333-6 https://arxiv.org/abs/2005.04422  27 pages [64] N.Drago, S. Mazzucchi, V.Moretti: An operational construction of the sum of two non-commuting observables in quantum theory and related constructions Lett.Math.Phys, 110 (2020) 3197–3242 DOI: 10.1007/s11005-020-01332-7 https://arxiv.org/abs/1909.10974  42 pages [63] S. Azzini, S. Mazzucchi, V.Moretti,  D. Pastorello,  L. Pavesi: Single-Particle Entanglement Adv. Quantum Technologies,  Volume3, Issue10, October 2020, 2000014  DOI: 10.1002/qute.202000014 35 pages [62] K. Landsman, V.Moretti, C.J.F. van de Ven:  A Strict Deformation Quantization Map on the state space of M_k(C) and the Classical Limit of the Curie-Weiss model Rev. Math. Phys. Vol. 32 (2020) 2050031  DOI: 10.1142/S0129055X20500312 https://arxiv.org/abs/1909.10947  54 pages [61] N. Drago and V.Moretti: The notion of observable and the moment problem for *-algebras and their GNS representations Lett.Math.Phys, 110(7), (2020), 1711-1758   DOI: 10.1007/s11005-020-01277-x https://arxiv.org/abs/1903.07496 48 pages [60]  V.Moretti  and M. Oppio, Quantum theory in quaternionic Hilbert space: How Poincaré symmetry reduces the theory to the standard complex one Rev. Math. Phys. 31, (2019) 1950013  DOI:10.1142/S0129055X19500132 https://arxiv.org/abs/1709.09246   71 pages [59] I.Khavkine, A.Melati, V.Moretti,  On Wick polynomials of boson fields in locally covariant algebraic QFT Ann. H. Poincaré  26, (2019), 929–1002  DOI:10.1007/s00023-018-0742-y https://arxiv.org/abs/1710.01937   73 pages [58]  V.Moretti  and M. Oppio, The correct formulation of Gleason's theorem in quaternionic  Hilbert spaces Ann. H. Poincaré 19 (2018), 3321-3355 DOI:10.1007/s00023-018-0729-8 https://arxiv.org/abs/1803.06882  37 pages [57] R. Ghiloni,  V.Moretti  and A. Perotti:  Spectral representations of normal operators via Intertwining Quaternionic Projection Valued Measures Rev. Math. Phys. 29  (2017) 1750034 DOI:10.1142/S0129055X17500349 https://arxiv.org/abs/1602.02661  73  pages [56]  V.Moretti  and M. Oppio: Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry Rev. Math. Phys. 29  (2017)  1750021  DOI:10.1142/S0129055X17500210 https://arxiv.org/abs/1611.09029   85  pages [55]  V.Moretti:  Mathematical Foundations of Quantum Mechanics: An Advanced Short Course. Lectures given by the author at the``XXIV International Fall Workshop on Geometry and Physics'' Int. J. Geom. Methods Mod. Phys..13 Issue Supp.1 1630011 (2016) DOI:10.1142/S0219887816300117 https://arxiv.org/abs/1508.06951  103 pages [54] I.Khavkine and V.Moretti: Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT Commun. Math. Phys. 344  (2016), 581-620 34 pages  DOI:10.1007/s00220-016-2618-7 https://arxiv.org/abs/1411.1302  44 pages [53]  V.Moretti and D. Pastorello: Frame functions in finite-dimensional Quantum Mechanics and its Hamiltonian formulation on complex projective spaces Int. J. Geom. Methods Mod. Phys. 13 1650013 (2016) DOI:10.1142/S0219887816500134 https://arxiv.org/abs/1311.1720   30 pages [52] I.Khavkine and V.Moretti: Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction invited contribution (V. Moretti) to Advances in Algebraic Quantum Field Theory by Springer 2015  (Eds R. Brunetti, C. Dappiaggi, K. Fredenhagen, and J.Yngvason)    DOI:10.1007/978-3-319-21353-8_5   59  pages https://arxiv.org/abs/1412.5945 [51] R. Ghiloni, V.Moretti and A. Perotti: Spectral properties of compact normal quaternionic operators, in Hypercomplex Analysis: New perspectives and applications,Trends in Mathematics, Birkhauser, Basel (2014) (Eds S. Bernstein, U. Kaehler, I. Sabadini, F. Sommen), DOI: 10.1007/978-3-319-08771-9 9 11 pages https://arxiv.org/abs/1402.2935 [50] R. Ghiloni,  V.Moretti and A. Perotti:  Slice Functional Calculus in Quaternionic Hilbert Spaces, Proceedings of the 9th ISAAC Congress,  Trends in Mathematics/Research Prospectives (Eds V. Mityushev & M. Ruzhansky) Birkhäuser  (2014), 7 pages [49] G. Collini,  V.Moretti  and N. Pinamonti: Tunnelling black-hole radiation with phi^3 self-interaction: one-loop computation for Rindler Killing horizons Lett. Math. Phys. 104 (2014) 217-232 DOI:10.1007/s11005-013-0663-0 14 pages [48]  V.Moretti and R. Di Criscienzo: How can we determine if a spacetime is flat? Frontiers in Physics 1:12  (2013), DOI:10.3389/fphy.2013.00012 6 pages [47] R. Ghiloni, V.Moretti and A. Perotti: Continuous slice functional calculus in quaternionic Hilbert spaces Rev. Math. Phys. 25, (2013) 1350006, DOI:10.1142/S0129055X13500062 83 pages [46] V.Moretti and D. Pastorello: Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem Ann. H. Poincaré 14 (2013),1435-1443  DOI:10.1007/s00023-012-0220-x  9 pages [45] E. Annigoni and  V.Moretti: Mass operator and dynamical implementation of mass superselection rule Ann. H. Poincaré 14 (2013), 893–924  DOI:10.1007/s00023-012-0197-5  32 pages [44] T.-P. Hack and V.Moretti: On the stress-energy tensor of QFT in curved spacetime - Comparison of different regualrization schemes and symmetry of the Hadamard/Seeley-DeWitt coefficients J. Phys. A: Math.Theor. 45 374019 (2012) 20 pages [43]  V.Moretti,  N. Pinamonti:  State independence for tunneling processes through black hole horizons. Commun. Math. Phys. 309 (2012) 295-311 17 pages [42] C. Dappiaggi,  V.Moretti, and N. Pinamonti: Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime. Adv. Theor. Math. Phys. 15, vol 2, 355-448 (2011) 93 pages [41] V. Moretti:  Local zeta-functions, stress-energy tensor, field fluctuations, and all that, in curved static spacetime, Invited contribution to the volume: Cosmology, Quantum Vacuum, and Zeta Functions, Springer Proc.Phys. 137 (2011) 323-332   9 pages   [40]  V.Moretti and N. Pinamonti: Black Hole Horizons and Thermodynamics: A Quantum Approach. Entropy 12, 1833-1854 (2010), special issue "Entropy in Quantum Gravity". 21 pages [39] R.Brunetti, L. Franceschini, V.Moretti: Topological features of massive bosons on two dimensional Einstein space-time. Ann. H. Poincaré 10, 1027-1073 (2009). DOI  10.1007/s00023-009-0007-x  47  pages                  [38] C.Dappiaggi, V.Moretti, N. Pinamonti:  Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property. J. Math. Phys. 50, 062304  (2009). 39 pages  [37] C.Dappiaggi, V.Moretti, N. Pinamonti: Cosmological horizons and reconstruction of quantum field theories. Commun. Math. Phys. 285, 1129 (2009). 32 pages [36] V.Moretti: Quantum out-states states holographically induced by asymptotic flatness: Invariance under spacetime symmetries, energy positivity and Hadamard property. Commun. Math. Phys. 279, 31  (2008). 44 pages  [35]  V.Moretti: Some recent results in linear scalar quantum field theory in globally hyperbolic asymptotically flat spacetimes, Invited plenary talk given at the XVII SIGRAV Conference, Torino, September 4-7, 2006. Published online by Sigrav (2007). 10 pages (gr-qc/0611125) [34] R. Brunetti and V.Moretti: Quantum Field Theories in Curved Spacetime [topical article], (2007)    Invited (V. Moretti) contribution for Encyclopedia of Mathematical Physics (by Springer). [33]  V.Moretti:  Uniqueness theorems for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence Commun. Math. Phys. 268, 727 (2006). 30 pages [32] C. Dappiaggi,  V.Moretti and N. Pinamonti:   Rigorous Steps towards Holography in Asymptotically Flat Spacetimes Rev. Math. Phys. 18, 349 (2006). 67 pages [31] V.Moretti: Bose-Einstein condensate  and Spontaneous Breaking of  Conformal Symmetry on Killing Horizons II, J. Math. Phys. 47, 032302 (2006). 5 pages [30] V. Moretti: The interplay of polar decomposition theorem and Lorentz group. invited contribution for  Variations on a century of relativity: theory and applications, Lecture notes of  Seminario Interdisciplinare di Matematica,  5, 153, (2006). 18 pages Editor. S. Dragomir [29]  V.Moretti and N. Pinamonti:  Bose-Einstein condensate  and Spontaneous Breaking of  Conformal Symmetry on Killing Horizons J. Math. Phys. 46, 062303 (2005) . 29 pages [28]  V.Moretti and N. Pinamonti:  The interplay of conformal invariance, Quantum Field Theory near the horizon of a 2D black hole and Holography.  invited contribution to the book "Focus in Mathematical Physics Research" 75 pages Nova Science Publishers, Inc. NY, 2004, ISBN:1-59033-923-1 [27]  V.Moretti and N. Pinamonti:  Quantum Virasoro algebra with central charge c=1 on the  horizon of a 2D Rindler spacetime J. Math. Phys. 45, 257  (2004). 28 pages [26]  V.Moretti and N. Pinamonti:  Holography and  SL(2,R) symmetry in 2D Rindler spacetime. J. Math. Phys. 45,  230 (2004).  27 pages [25]  V.Moretti and N. Pinamonti:  QFT holography near the horizon of a black hole. invited contribution for  Quantum Gravity and Cosmology, Special issue of Vestnik of Tomsk State Pedagogical University, 7 (44) 2004)(December). Pages 109-115. 7 pages, ISBN 1609-624X., Editor S.D. Odintsov. [24]  V.Moretti and N. Pinamonti:  Aspects of Hidden and manifest SL(2,R) symmetry in 2D near horizon  black hole background Nucl.Phys.B 647, 131 (2002). 22 pages [23] V.Moretti: Aspects of  noncommutative  Lorentzian  geometry for globally hyperbolic spacetimes Rev. Math. Phys. 15, 1171 (2003). 47 pages [22]  V.Moretti  Comments on the stress-energy tensor operator in curved spacetime. Commun. Math. Phys. 232, 189 (2003). 33 pages [21] E. Elizalde,  V.Moretti , S.Zerbini: On recent strategies proposed for proving the Riemann hypothesis. Int. J. Mod. Phys. A 18, 2189 (2003). 7 pages [20]  V.Moretti :  A review on recent results of the z-function regularization procedure in curved spacetime. Published in Recent developments in General Relativity, Springer-Verlag 2000. Editors: D. Fortunato, M. Francaviglia, A. Masiello, 7 pages [19]  V.Moretti : Proof of the symmetry of the off-diagonal Hadamard/Seeley-deWitt's coefficients in smooth Lorentzian manifolds by a local Wick rotation, Commun. Math. Phys. 212, 165 (2000). 25 pages [18]  V.Moretti :  Proof of the symmetry of the off-diagonal heat-kernel and Hadamard's expansion coefficients in general smoothRiemannian manifolds. Commun. Math. Phys. 208, 283 (1999). 26 pages [17]  V.Moretti :  One-loop stress-tensor renormalization in curved background: the relation between z-function and point-splitting approaches, and an improved point-splitting procedure. J.Math.Phys.40,3843(1999). 33 pages [16]  V.Moretti : Localz-function techniques vs point-splitting procedures: a few rigorous results. Commun. Math. Phys. 201, 327 (1999). 37 pages [15] D. Binosi,  V.Moretti , L. Vanzo, S. Zerbini: Quantum Scalar field on the massless (2+1) dimensional black hole. Phys.Rev. D 59, 104017 (1999). 13 pages [14] D. Iellici and  V.Moretti : z-function regularization and one-loop renormalization of field fluctuations in curved spacetimes. Phys. Lett. B 425, 33 (1998). 8 pages [13] D. Klemm,  V.Moretti , L. Vanzo: Rotating topological black holes. Phys. Rev. D 57, 6127 (1998). 11 pages [12]  V.Moretti :  z-function renormalization of one-loop stress tensors in curved spacetimes: a check on the method in the conical manifold and other cases ( hep-th/9706191 ) Published as a part of Phys. Rev.D 56 7797 (1997). [11]  V.Moretti and D. Iellici : Optical Approach for the thermal Partition Function of Photons Phys. Rev.D 55, 3552 (1997). 11 pages [10]  V.Moretti : Direct  z-function approach and renormalization of one-loop stress tensor in curved spacetimes Phys. Rev.D 56, 7797 (1997). 23 pages [9]  V.Moretti:  Euclidean Thermal Green Functions of Photons in Generalized Euclidean Rindler Spaces for any Feynman-like gauge Int. J. Mod. Phys. A 12, 3787 (1997). 12 pages [8] V.Moretti: Geometric entropy and curvature coupling in conical spaces: z-function approach Class.Quant.Grav. 14 L123 (1997). 5 pages [7]  V.Moretti : Canonical Quantization of Photons in a Rindler Wedge J. Math. Phys. 38, 2922 (1997). 32 pages [6] D. Iellici and  V.Moretti : Kabat's surface terms in the zeta-function approach Published in General Relativity and Gravitational Physics, World Scientific 1996, 5 pages Editors: M. Bassan, V. Ferrari, M. Francaviglia, F. Fucito, I. Modena. [5] D. Iellici and  V.Moretti : Thermal partition function of photons and gravitons in a Rindler wedge Phys.Rev.D 54, 7459 (1996). 5 pages [4] V.Moretti  and S. Steidl : A Bisognano-Wichmann-like Theorem in a certain case of Non Bifurcate Event Horizon related to an Extreme Reisner-Nordstrom Black Hole Class. Quant. Grav. 13, 2121 (1996). 23 pages [3]  V.Moretti : Hessling's Quantum Equivalence Principle and the Temperature of anExtremalReisner-Nordstrom  Black Hole ( gr-qc/9510016 ). Published as a part of Class. Quant. Grav. 13, 985 (1996). [2]  V.Moretti : Wightman Functions' Behaviour on the Horizon of an ExtremalReisner-Nordstrom Black Hole Class. Quant. Grav. 13, 985 (1996). 22 pages [1]  V.Moretti and L.Vanzo : Thermal Wightman Functions and Renormalized Stress Tensors in the Rindler Wedge Phys. Lett.B 375, 54 (1996). 6 pages

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