Abstract
The group of matrices
Funding statement: Fabio Bagarello acknowledges partial support from University of Palermo and from the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM). Yanga Bavuma and Francesco G. Russo thank University of Cape Town for the Emerging Research Programme for the Research Development Grant and National Research Foundation of South Africa for grants with Reference Numbers 150555, 113144, 118517.
Acknowledgements
We thank editor and referee for comments on the original version of the manuscript.
References
[1] G. Alicata, F. Bagarello, F. Gargano and S. Spagnolo, Quantum mechanical settings inspired by RLC circuits, J. Math. Phys. 59 (2018), no. 4, Article ID 042112. 10.1063/1.5026944Suche in Google Scholar
[2] F. Bagarello, Deformed canonical (anti-)commutation relations and non-self-adjoint Hamiltonians, Non-Selfadjoint Operators in Quantum Physics, Wiley, Hoboken (2015), 121–188. 10.1002/9781118855300.ch3Suche in Google Scholar
[3] F. Bagarello, Pseudo-Bosons and Their Coherent States, Math. Phys. Stud., Springer, Cham, 2022. 10.1007/978-3-030-94999-0Suche in Google Scholar
[4] F. Bagarello, Y. Bavuma and F. G. Russo, Topological decompositions of the Pauli group and their influence on dynamical systems, Math. Phys. Anal. Geom. 24 (2021), no. 2, Paper No. 16. 10.1007/s11040-021-09387-1Suche in Google Scholar
[5] F. Bagarello, A. Inoue and C. Trapani, Non-self-adjoint Hamiltonians defined by Riesz bases, J. Math. Phys. 55 (2014), no. 3, Article ID 033501. 10.1063/1.4866779Suche in Google Scholar
[6] F. Bagarello and G. Pantano, Pseudo-fermions in an electronic loss-gain circuit, Int. J. Theor. Phys. 52 (2013), 4507–4518. 10.1007/s10773-013-1769-ySuche in Google Scholar
[7] F. Bagarello and F. G. Russo, A description of pseudo-bosons in terms of nilpotent Lie algebras, J. Geom. Phys. 125 (2018), 1–11. 10.1016/j.geomphys.2017.12.002Suche in Google Scholar
[8] F. Bagarello and F. G. Russo, Realization of Lie algebras of high dimension via pseudo-bosonic operators, J. Lie Theory 30 (2020), no. 4, 925–938. Suche in Google Scholar
[9] Y. Bavuma, A short note on the topological decomposition of the central product of groups, Trans. Comb. 11 (2022), no. 3, 123–129. Suche in Google Scholar
[10] C. M. Bender, Making sense of non-Hermitian Hamiltonians, Rep. Progr. Phys. 70 (2007), no. 6, 947–1018. 10.1088/0034-4885/70/6/R03Suche in Google Scholar
[11] C. M. Bender, PT Symmetry in Quantum and Classical Physics, World Scientific, Hackensack, 2019. 10.1142/q0178Suche in Google Scholar
[12] C. M. Bender, F. Correa and A. Fring, Proceedings for “Pseudo-Hermitian Hamiltonians in Quantum Physics”, J. Phys. 2038 (2021), Article ID 012001. Suche in Google Scholar
[13]
C. M. Bender, M. DeKieviet and S. P. Klevansky,
[14] O. Cherbal, M. Drir, M. Maamache and D. A. Trifonov, Fermionic coherent states for pseudo-Hermitian two-level systems, J. Phys. A 40 (2007), no. 8, 1835–1844. 10.1088/1751-8113/40/8/010Suche in Google Scholar
[15] O. Christensen, An Introduction to Frames and Riesz Bases, Appl. Numer. Harmon. Anal., Birkhäuser, Boston, 2003. 10.1007/978-0-8176-8224-8Suche in Google Scholar
[16] J. Dieudonné, Quasi-Hermitian operators, Proceedings of the International Symposium on Linear Spaces (Jerusalem 1960), Pergamon, Oxford (1961), 115–122. Suche in Google Scholar
[17] F. M. Ellis, U. Günther, T. Kottos, H. Ramezani and J. Schindler, Bypassing the bandwidth theorem with PT symmetry, Phys. Rev. A 85 (2012), Article ID 062122. Suche in Google Scholar
[18] F. M. Ellis, T. Kottos, J. M. Lee, H. Ramezani and J. Schindler, PT-Symmetric Electronics, J. Phys. A 45 (2012), Article ID 444029. 10.1088/1751-8113/45/44/444029Suche in Google Scholar
[19] H. Goldstein, C. Poole and J. Safko, Classical Mechanics, Addison-Wesley, New York, 2000. Suche in Google Scholar
[20] B. C. Hall, Quantum Theory for Mathematicians, Grad. Texts in Math. 267, Springer, New York, 2013. 10.1007/978-1-4614-7116-5Suche in Google Scholar
[21] M. R. Kibler, Variations on a theme of Heisenberg, Pauli and Weyl, J. Phys. A 41 (2008), no. 37, Article ID 375302. 10.1088/1751-8113/41/37/375302Suche in Google Scholar
[22] A. Mostafazadeh, Pseudo-Hermitian representation of quantum mechanics, Int. J. Geom. Methods Mod. Phys. 7 (2010), no. 7, 1191–1306. 10.1142/S0219887810004816Suche in Google Scholar
[23] A. Mostafazadeh, Pseudo -Hermitian quantum mechanics with unbounded metric operators, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 371 (2013), no. 1989, Article ID 20120050. 10.1098/rsta.2012.0050Suche in Google Scholar PubMed
[24] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University, Cambridge, 2004. Suche in Google Scholar
[25] W. Pauli, Zur Quantenmechanik des magnetischen Elektrons, Z. Phys. 43 (1927), 601–623. 10.1007/BF01397326Suche in Google Scholar
[26] D. J. S. Robinson, A Course in the Theory of Groups, Grad. Texts in Math. 80, Springer, New York, 1996. 10.1007/978-1-4419-8594-1Suche in Google Scholar
[27] P. Roman, Advanced Quantum Theory: An Outline of the Fundamental Idea, Addison-Wesley, New York, 1965. Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Open orbits and primitive zero ideals for solvable Lie algebras
- On the Pauli group on 2-qubits in dynamical systems with pseudofermions
- Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
- Perturbation of domain for the linear parabolic equation
- K-theory of flag Bott manifolds
- Some results on Seshadri constants of vector bundles
- Strichartz inequality for orthonormal functions associated with special Hermite operator
- The globally smooth solutions and asymptotic behavior of the nonlinear wave equations in dimension one with multiple speeds
- On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems
- Boundedness of commutators of rough Hardy operators on grand variable Herz spaces
- Beurling densities of regular maximal orthogonal sets of self-similar spectral measure with consecutive digit sets
- An alternative proof of Tataru’s dispersive estimates
- The p-Bohr radius for vector-valued holomorphic and pluriharmonic functions
- Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction
- Decay and Strichartz estimates for Klein–Gordon equation on a cone I: Spinless case
- A class of quaternionic Fourier orthonormal bases
- Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields
- Normalized solutions for scalar field equation involving multiple critical nonlinearities
Artikel in diesem Heft
- Frontmatter
- Open orbits and primitive zero ideals for solvable Lie algebras
- On the Pauli group on 2-qubits in dynamical systems with pseudofermions
- Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
- Perturbation of domain for the linear parabolic equation
- K-theory of flag Bott manifolds
- Some results on Seshadri constants of vector bundles
- Strichartz inequality for orthonormal functions associated with special Hermite operator
- The globally smooth solutions and asymptotic behavior of the nonlinear wave equations in dimension one with multiple speeds
- On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems
- Boundedness of commutators of rough Hardy operators on grand variable Herz spaces
- Beurling densities of regular maximal orthogonal sets of self-similar spectral measure with consecutive digit sets
- An alternative proof of Tataru’s dispersive estimates
- The p-Bohr radius for vector-valued holomorphic and pluriharmonic functions
- Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction
- Decay and Strichartz estimates for Klein–Gordon equation on a cone I: Spinless case
- A class of quaternionic Fourier orthonormal bases
- Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields
- Normalized solutions for scalar field equation involving multiple critical nonlinearities