1. The Universe was created out of interacting quantum fields producing forces (Bosons) from integer spin interactions and matter (Fermions) from half-integer spin.
Lagrangian Field Theory formulates the relativistic quantum mechanical theory of interactions. It has dependent variables replaced by values of a field at a point in space-time s (x,y,z,t). The equations of motion are obtained by the Action Principle using S as Action.
The Euler-Lagrange Equation minimizes S and produces the model's equation of motion:
Starting with 1863 Maxwell’s Equations
The L for Classical Electrodynamics:
Next, consider the Lagrangian density function for a massless field:
Adding mass creates the scalar (spin = 0):
Introducing a source term produces J(x)
The EOM for Spin = 0 (Higgs) Klein Gordon Eq.:
The solutions to the Klein Gordon Equation are simple plane waves subject to relativistic constraint:
f(x) = e-+i(p.x-Et)
The EOM for Spin = 1/2 (Fermion) Dirac Eq.:
The EOM for Spin = 1 (Boson) Proca Eq.:
3. Quantum Electrodynamic U(1):
Tomonaga, Schwinger, Feynman) is a precise description of electromagnetic interactions.
A loop in a Feynman diagram indicts a divergence (infinite integral) that must be renormalized for calculations.
A photon is a spin 1 massless Boson interference packet in the electromagnetic field that has no rest mass, but has quanta E = hv and always travels at speed c.
An electron is a spin 1/2 Fermion interference packet in the electromagnetic field that has a rest mass.
A quark is a spin 1/2 Fermion interference packet that interacts with electromagnetic, weak, and strong fields and has a rest mass.
The Quantum Electrodynamics (QED) Lagrangian:
Salam and Weinberg developed a gauge theory requiring three gauge bosons (W+-,Z). The Quantum ElectroWeak (QEW) Lagranian:
5. Quantum Chromodynamics SU(3):
Han, Nambu, Greenburg described the strong force mediated by gauge bosons, called gluons, carrying a unique kind of charge called color. The Quantum Chromodynamics (QCD) Lagrangian:
6. The Standard Model SU(3) x SU(2) x U(1):
The Standard Model (SM) Lagrangian:
The first line represents the kinetic energy carried by W, Z, photon, and gluons. The second line is the interaction terms. The third line contains mass and the fourth line the left right parity interaction.
 Cox, B. and Forshaw, J., Why does E=mc2, Da Capo Press, Cambridge, MA 2009.
 Lancaster, T., and Blundell, S. j., Quantum Field Theory, Oxford, UK, 2014.
 Robinson, M., Symmetry and the Standard Model, Springer, London, 2011.