Erice: INTERNATIONAL SCHOOL OF NUCLEAR PHYSICS, 46th COURSE

We explore some regularization prescriptions and how they impact the effective potential and the gap equation. We also explore the role of the integration measure/geometry in momentum space in symmetry breaking. We conclude that every regularization prescription and geometry greatly affect the properties of symmetry breaking/restoration. We also propose a modified representation of proper time, that does not interchange divergences in the effective potential. Finally, with this representation we propose a way to include thermal effects that can be extended to other agents like magnetic field and finite volume.