| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
(1) We have constructed the Feynman path integral for a relativistic electron in the form of the sum-over-histories, over all paths of one electron in space-time that goes in any direction at any speed, forward and backward in time, especially with a countably infinite number of turns. By this result we have succeeded in introducing a countably infinite number of electrons and positrons at the same time in the theory of the Feynman path integrals as the 2nd quantization of one electron. (2) We have showed that the Feynman path integral defined in (1) is relativistically invariant, i.e. has the property of spinor under the Lorentz transformations. (3) We have showed directly from the Feynman path integral that the probability amplitude for a relativistic electron has the properties of both unitarity and causality. (4) We have constructed mathematically the Feynman path integral for the Schroedinger equations with potentials growing polynomially in the spatial direction.
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