The work presented in this book is relevant to the interaction of quantum fields with the classical background manifested by a strong external field. In other words, the background field is adequately described by a classical theory and does not need to be quantized. A significant simplification comes from considering quantized scalar field interacts only with the gravitational field. The Renormalization using zeta function method is the essential requirement of this study for calculated the expectation values of the energy-momentum tensor, in which the quantum effects in a gravitational...

Many problems in mathematical physics, their solutions are connected with the application of cylindrical and spherical coordinates, solutions called Bessel functions resulted from a differential equation called the Bessel equation. The interesting application is related to a thin homogeneous circular membrane under small free oscillations, when the Bessel function is presented as a solution to describ the gravity by quantum field theory. This book contains simple problems and solutions as an attemp to help to approaching Bessel functions.

Any physical object whose radius becomes less than or equal to the Schwarzschild radius will undergo a gravitational collapse and become a black hole where light cannot escape from the gravitational fields, this one represents a solution of the Einstein equation, introduced by Schwarzschild, it contains two singularities, one describes the center, and the other describes what is called the event horizon, the black hole and its singularities cannot be considered as Einsteinian space-time in the classical sense. Then, a new theory of gravitation combined between General Relativity and Quantum...

Die in diesem Buch vorgestellten Arbeiten beziehen sich auf die Wechselwirkung von Quantenfeldern mit dem klassischen Hintergrund, der durch ein starkes äußeres Feld manifestiert wird. Mit anderen Worten: Das Hintergrundfeld wird durch eine klassische Theorie angemessen beschrieben und muss nicht quantisiert werden. Eine wesentliche Vereinfachung ergibt sich aus der Annahme, dass ein quantisiertes Skalarfeld nur mit dem Gravitationsfeld wechselwirkt. Die Renormierung mit Hilfe der Zeta-Funktions-Methode ist die wesentliche Voraussetzung dieser Studie für die Berechnung der Erwartungswerte...

This book presents the derivation of Dewitt-Wheeler equation in which time-independent equation describes the quantization of the gravitational field in 3-geomtries configuration. This equation may refer as Schrodinger-Einstein equation. This approach of the quantization of the gravity started by Dewitt according to Everett interpretation of quantum mechanics that yields the multiverse idea, and so, the WDW equation introduced a function called lapse function in which each different lapse function according to Dewitt yields a different sequence of 3-geometries that indicates to multiverse. On...