Title: A study of anomalies using functional integration and perturbative calculations

Abstract: We present two lines of investigation involving anomalies. First, we review mechanisms behind the classical and quantum conservation of symmetries using functional integration. This discussion clarifies conditions for quantum violations, as acknowledged in chiral theories. Then, we elucidate the subject of gauge anomaly cancellation when all fields are quantized. Such an outcome requires gauge invariance of the bosonic measure, so our first object is proving this invariance within Fujikawa's approach. Second, we investigate anomalies in fermionic perturbative amplitudes using Implicit Regularization. The discussion of the single-axial triangle fundaments this analysis, bringing the elements necessary to approach the single-axial box. When organizing their mathematical structure, we highlight the role of traces involving the chiral matrix. Choosing a specific expression for them reflects on the position of symmetry violations, which has implications regarding the linearity of integration. Power counting and tensor structure imply the presence of surface terms related to momenta ambiguities. We present the results without computing these surface terms. In this neutral perspective, we explore possibilities achieved under different prescriptions.