Third quantization and quantum cosmology

This thesis consists of three separate parts. Part one consists of a study of CP violation in the Kaon decay: K → π π γ. To study the short distance contribution to the matrix element the author developed an operator expansion for the effective Hamiltonian. An effective s → dγ vertex arises through operator mixing. He evaluated several two-loop graphs in order to obtain the coefficient of this operator. He studied the long distance contributions to the matrix element and demonstrated that this was the dominant contribution. This explained why the polarization of the emitted photon is primarily of the magnetic type. Part two of his thesis involves the treatment of string theory at finite temperature. He introduced finite temperature into string theory by compactifying time on a twisted torus of radius β = 1/kT, the reciprocal of the temperature. The twisted torus takes into account the different thermal properties of bosons and fermions. He computed the one-loop vacuum amplitude Λ(β) on a twisted torus which is manifestly modular invariant. He found that ell nZ(β) = -βVΛ(β) where Z(β) is the partition function and V the volume of the system. He computed the function σ(E) which counts the number of multi-string states of total energy E by taking the inverse Laplace transform of Z(β). He also studied the effect of finite temperature on the effective potentials which determine a string theory's compactification. The third part of my thesis involved the Wheeler DeWitt equation and a new interpretation of quantum cosmology. He examined a proposal by DeWitt for the normalization of solutions to the Wheeler-DeWitt equation. He avoided negative probability problems with this proposal by reinterpreting the Wheeler-DeWitt wave function as a second quantized field