| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
This research deals with the quantum-mechanical propagator, namely, the integral kernel of the Schroedinger unitary group, Green function as well as the heat kernel of the Schroedinger semigroups as its imaginary-time version. In this work, among others, we have considered three different magnetic relativistic Schroedinger semigroups and establish (imaginary-time) path integral representations with the probability measure on the path space connected with the Levy process to clarify their different nature.
Some other topics are also dealt with on influence to resonance of Aharanov-Bohm effect for solenoidal magnetic field quantum mechanical scattering, and on an improved Sobolev inequality for vector-valued functions whose right-hand side has a seminorm involving Dirac operator.
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