1. The Universe was created out of interacting quantum fields of harmonic oscillating excitation with particle-like eigenfunctions.
A field is represented at some space-time point by an amplitude (scalar, vector, complex number, spinor, or tensor) that oscillates in space-time to produce wave-like excitation.
Quantum field theory explains why electrons are identical because each electron is an excitation of the electron quantum field with identical properties using Fermi-Dirac statistics.
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 f (x,y,z,t). The equations of motion are obtained by the Action Principle where S is Action. Energy is conserved if the Lagrangian doesn’t change with time.
The Euler-Lagrange Equation produces the model's equation of motion:
2. The Lagrangian density function, L
f(x) = e-+i(p.x-Et)
Introducing a source term produces J(x)
Tomonaga, Schwinger, Feynman) is a precise description of electromagnetic interactions.
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:
The current structure of elementary particle physics is called the Standard Model. The Standard Model (SM) Lagrangian:
 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.