ARAI, Asao
 Research Field
 Analysis
 Position
 Specially Appointed Professor
 Organization
 Department of Mathematics
 Research Interest
 Mathematical Physics, Functional Analysis
 Research Activities

Searches and investigations, from all possible aspects, of mathematical ideas and laws which govern quantum phenomena. Subjects that have been considered in recent years include the following:
Mathematical analysis of quantum systems interacting with quantum fields, mathematical theory of time operator, representation theory of canonical commutation relations, mathematical foundations of quantum electrodynamics, mathematical construction of supersymmetric quantum field theory and a theory of infinitedimensional Dirac operators.
 Papers:
 (1) A. Arai, Spectral analysis of an effective Hamiltonian in nonrelativistic quantum electrodynamics,
Ann. Henri Poincare 12 (2011), 119152.  (2) A. Arai, Heisenberg operators of a Dirac particle interacting with the quantum radiation field, J. Math. Anal. Appl. 382 (2011), 714–730.
 (3) A. Arai, Necessary and sufficient conditions for a Hamiltonian with discrete eigenvalues to have time operators, Lett. Math. Phys. 87 (2009), 67–80.
 Keywords
 canonical commutation relations, Fock space, quantum electrodynamics, quantum field, supersymmetry, time operator