See also in the math section.
- m(vμ) = m0γ
- Invariant mass:
- Etot = Erel + Epot
- Ekin = Erel − m0c2
- E0 = p0c
- Gravitational field equations:
- Einstein tensor:
- Ricci tensor:
- Riemann tensor:
- Curvature scalar:
For the role of the cosmological constant, see the 5th force.
The invariant Lagrangian of the Standard Model describes massless gauge bosons interacting with massless fermions. In order for mass terms to be generated, one introduces fundamental complex scalar (Higgs) fields φ, which couple gauge-invariantly to the gauge bosons via the covariant derivatives
where and σi / 2,Y / 2 and are the SU(2)L,U(1)Y couplings and group generators and gauge fields, respectively and couple gauge-invariantly to the fermions through the Yukawa coupling of the form
A natural and general way to construct a Higgs Lagrangian compatible with the Standard Model is to require gauge invariance and renormalizability:
where is the scalar potential.
The spontaneous symmetry breaking is driven by the 'mass' term mH. Technically, symmetry breaking is induced by a negative value: mH = :iμH and μH > 0.
The vacuum expectation value is
The mass terms for the fermions and bosons originate from .
So the Higgs mechanism refers to the spontaneous breaking of local (gauge) symmetries by the vacuum.
For a further analysis, go here.