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This book uses a systematic way to investigate the interaction of quantised gravitational and scalar fields, especially in spherically symmetric reduction. Starting from the basic canonical quantisation route, the reduced variables, constraints and their properties are derived and discussed in detail. The relevant knowledge and background are introduced explicitly in order for the ordinary reader to understand easily. It is indicated that the Wheeler-DeWitt Equation which governs quantised gravitational field when coupled with scalar fields can be reduced to a form of Schrodinger Equation which really surprises us. That describes quantised scalar field evolving with respect to a Schwinger-Tomonaga time which increases with the volume of the universe in an inflationary universe if certain conditions are satisfied. This inflationary scenario emerges rather naturally from the Ashtekar-Wheeler-DeWitt Equation. This result gives an evidence to prove the natural connection of quantum and classical regime and allow us to believe it is valid. In conclusion, all of these provide us a belief that we are more closing to triumph of quantisation in gravity.

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Ting-Cheng Yang awards Phi Tau Phi Scholastic Honor Society membership and Presidential Awards from National Cheng Kung University ranked as the first position. Dedicating himself to Cosmology and Gravity is to discover frontier,to deliver lectures to the multitude and to find connection between scientific implication and the humanities.

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