Fredholm property and essential spectrum of 3-D Dirac operators with regular and singular potentials

References

• Albeverio S, Gesztesy F, Hoegh-Krohn F. Solvable models in quantum mechanics, with an appendix by pavel Exner. 2nd ed., Providence, RI: AMS Chelsea Publishing; 2005.
   Google Scholar
• Albeverio S, Kurasov P. Singular perturbations of differential operators and Schrödinger type operators. Cambridge: Cambridge University Press; 2000.
   Google Scholar
• Brasche JF, Exner N, Arrizabalaga A, et al. Shell interactions for Dirac operators. J Math Pures Appl (9). 2014;102(4):617–639.
   Web of Science ®Google Scholar
• Behrndt J, Exner P, Lotoreichik V. Essential spectrum of Schrödinger operators with δ-interactions on the union of compact Lipschitz surfaces. PAMM Proc Appl Math Mech. 2013;13:523–524.
   Google Scholar
• Behrndt J, Langer M, Lotoreichik V. Schrödinger operators with δ and δ′-potentials supported on surfaces. Ann Henri Poincaré. 2013;14:385–423.
   Web of Science ®Google Scholar
• Behrndt J, Exner P, Lotoreichik V. Schrödinger operators with δ- and δ′- interactions on Lipschitz surfaces and chromatic numbers of associated partitions. Rev Math Phys. 2014;26:1450015. 43 pages.
   Web of Science ®Google Scholar
• Behrndt J, Exner P, Holzmann M, et al. On the spectral properties of Dirac operators with electrostatic δ-shell interactions. J Math Pures Appl. 2018;111:47–78.
   Web of Science ®Google Scholar
• Behrndt J, Exner P, Holzmann M, et al. On Dirac operators in R3 with electrostatic and Lorentz scalar δ-shell interactions. Quantum Stud: Math Found. 2019; Available From: https://doi.org/10.1007/s40509-019-00186-6.
   Google Scholar
• Berezin FA, Faddeev LD. A remark on Schrödinger operators with a singular potentials. Soviet Math Dokl. 1961;137:1011–1014.
   Google Scholar
• Buschmann D. One-dimensional Schrödinger operators with local point interactions. J Reine Angew Math. 1995;467:169–186.
   Web of Science ®Google Scholar
• Rabinovich VS. Schrödinger operators with interactions on unbounded surfaces: math. Meth Appl Sci Math Meth Appl Sci. 2019;42:4981–4998.
   Web of Science ®Google Scholar
• Arrizabalaga N, Mas A, Vega L. Shell interactions for Dirac operators. J Math Pures Appl (9). 2014;102(4):617–639.
   Web of Science ®Google Scholar
• Ourmieres-Bonafos Th, Vega L. A strategy for self-adjointness of Dirac operators: applications to the MIT BAG model and shell interactions. Publ Mat. 2018;62:397–437.
   Web of Science ®Google Scholar
• Moroianu A, Ourmíeres-Bonafos Th, Pankrashkin K. Dirac operators on surfaces large mass limits. J Math Pures Et Appl. 2014;102(4):617–639.
   Google Scholar
• Ourmieros-Bonafos Th., Pizzichlllo F. Dirac operators and shell interactions: a survey. 11 Feb 2019. Preprint arXiv:1902.03901v1 [math-ph].
   Google Scholar
• Rabinovich VS. Pseudodifferential operators on a class of noncompact manifolds. Math USSR-Sb. 1972;18(1):45–59.
   Google Scholar
• Simonenko IB. Operators of convolution type in cones. Math USSR-Sb. 1967;3(2):279–293.
   Google Scholar
• Rabinovich VS, Roch S, Silbermann B. Band-dominated operators with operator-valued coefficients, their Fredholm properties and finite sections. Integr Equ Oper Theory. 2001;40(3):342–381.
   Web of Science ®Google Scholar
• Rabinovich VS, Roch S, Silbermann B. Limit Operators and their Applications in Operator Theory. Birkhäuser Verlag; 2004. (ser. Operator Theory: Advances and Applications; 150).
   Google Scholar
• Rabinovich VS. Essential spectrum of perturbed pseudodifferential operators. applications to the Schrödinger, Klein-Gordon, and Dirac operators. Russ J Math Phys. 2005;12(1):62–80.
   Web of Science ®Google Scholar
• Rabinovich VS. Transmission problems for conical and quasi-conical at infinity domains. Appl Anal. 2015;94(10):2077–2094.
   Web of Science ®Google Scholar
• Agranovich MS. Elliptic boundary problems. in Partial differential equations. Vol. IX, Agranovich MS, Egorov YV, Shubin MA, editors, Berlin, Germany: Springer; 2010.
   Google Scholar
• Lions JL, Magenes E. Non-homogeneous boundary value problems and applications. Berlin, Germany: Springer-Verlag; 1972.
   Google Scholar
• Rabinovich VS. Essential spectrum of Schrödinger operators with δ-interactions on unbounded surfaces. Math Notes. 2017;102(5):698–709.
   Web of Science ®Google Scholar
• Bogolubov NN, Shirkov DV. Quantum fields. Reading, MA: Benjamin/Cummings Publishing Company Inc.; 1982.
   Google Scholar
• Bjorken JD, Drell SD. Relativistic quantum mechanics. New York: McGraw-Hill Book Company; 1964.
   Google Scholar
• Thaller B. The Dirac equation. Berlin, Germany: Springer-Verlag; 1956.
   Google Scholar
• Agranovich MS, Vishik MI. Elliptic problems with a parameter and parabolic problems of general forms. Uspekhi Mat Nauk. 1964;219:63–161. English trans. Russian Math Surveys 1964;19:53–157.
   Google Scholar
• Birman MSh, Solomjak MSh. Spectral theory of selfadjoint operators in Hilbert spaces. Dordrecht: Reidel; 1987.
   Google Scholar