Theoretical and Phenomenological Aspects of Quantum Field Theory

Edoardo Livolsi

This document provides a technical referee-style analysis of Boundary Liouville Field Theory, focusing on the mathematical conditions required for a quantum field theory with boundaries to be considered functionally complete. Rather than addressing phenomenological results, the review concentrates on structural aspects such as the existence of a generating functional, control of quadratic fluctuations, stability of boundary modes, and infrared–ultraviolet matching. To facilitate a transparent assessment, a model-independent consistency benchmark is included as an appendix. The benchmark formulates minimal functional criteria—variational closure, emergence of operator structure, spectral control, and ultraviolet behavior—that any closed theoretical framework is expected to satisfy. The purpose of this analysis is not to invalidate specific constructions, but to clarify the distinction between formally consistent sets of correlation functions and theories admitting a complete functional and spectral interpretation. The benchmark is intended as a reusable diagnostic tool applicable to a broad class of field-theoretic models with boundaries.

Rudolf Haag

Simon W. Saunders

Angelo Bruno

In this dissertation we discuss several aspects of a two level system (qubit) in the context of quantum mechanics and quantum eld theory. The presence of geometrical phases in the evolution of a qubit state is shown. We study geometric structures, which are correlated to an unitary time evolution and its interesting gauge structure. They can be very useful in quantum computational processes. We illustrate the quantum eld theoretical formulation of boson mixed elds, and oscillation formulas for neutral and charged elds are found. We show that the space for the mixed elds is unitary inequivalent to the state space where the unmixed eld are de ned, and we also derive the structure of the currents and charges for the charged mixed elds. Phenomenological aspects of meson mixing in the presence of the decay are discussed. In particular, we show that the the e ective Hamiltonian is non-Hermitian and non-normal in the Wigner-Weisskopf approximation and we use the biorthonormal basis formalism to diagonalize such an Hamiltonian. Finally, the presence of CP and CPT violations in meson mixing is shown.

V. Tripathi

This chapter provides a microscopic basis to the phenomenological understanding of Landau Fermi liquids. It examines the effect of electron density fluctuations on the Stoner instability, particularly to understand their effect on the mean-field condition for the instability. The temperature dependence coming from the distribution functions in the numerator has a characteristic scale of the order of the Fermi energy. Ward identities provide relations between the self-energy and the vertex functions, thus bridging the phenomenological and microscopic aspects. The microscopic justification of this assumption rests on Ward identities. The ideas of scaling theory, developed in the context of classical critical phenomena, can be generalized to the quantum case. Thus vertex corrections, through their relation to the Ward identity for the self-energy, enable to provide a microscopic justification of one of the key assumptions of Landau Fermi liquid theory.