The Higgs mechanism is very powerful: it furnishes a description of the electroweak theory in the Standard Model which has a convincing experimental verification. 4 2) Spontaneous Symmetry Breaking. I've searched for other answers but I couldn't still resolve all my doubts. The Higgs Potential In electroweak theory the diﬀerence between the physical γ,W±,Z0 boson masses is created by spontaneous symmetry breaking of the Higgs ﬁeld φ. Finally we have implemented the concept of spontaneous symmetry breaking into an (Abelian) gauge field theory to see how the Higgs mechanism works. I also understand that I'm asking a lot of questions, so I don't expect an answer to all of them. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. ITRG lecture week Oslo 06-03-2006 G. Eigen, IFT Bergen III.1 Symmetry Breaking One example is the infinite ferromagnet the nearest neighbor interaction between spins or magnetic dipole moments Fröhlich, Morchio and Strocchi , and, independently, Banks and Rabinovici and 't Hooft proposed that all the physics of these models be described in terms of gauge independent fields. (See the answer to the next question below). for spontaneous symmetry breaking to occur in practice. Stronger, for almost all realistic ap-plications of the theory of symmetry breaking, it is a rather useless limit, in the sense that it is never strictly realised. To understand the Higgs mechanism, that is, how (gauge ) bosons acquire mass it is essential to understand the meaning of Spontaneous Symmetry Breaking (SSP). The Higgs mechanism is often presented as spontaneous breaking of a local gauge symmetry. The first one occurs in the In this case, the limit G(g) → 1 leads us We verify in the literature 8,11 that there are at least two slightly different processes of SSB. Before that, we note that the limit w(g) → 1 leads us back to the model studied in , which is supported by applications concerning the interaction between quarks and gluons . We have introduced the principles of spontaneous symmetry breaking and how it translates into particle physics as the Goldstone theorem. Happily, the Higgs mechanism has nothing to do with spontaneous symmetry breaking, and therefore there is no real problem here. need to choose a Higgs potential V (g) which allows for the spontaneous symmetry breaking mechanism. The potential energy of the Higgs ﬁeld is: V (φ) = µ2φ†φ+λ(φ†φ)2 µ2 < 0 λ > 0 The Higgs is a scalar ﬁeld that exists in a vacuum Even in situations where the object of interest can be considered large, I'm really confused about spontaneous symmetry breaking and the Higgs mechanism. Spontaneous Symmetry Breaking The Higgs Mechanism Mass Generation for Leptons Quark Masses & Mixing.