This video provides a very basic introduction to the idea that a particle is an excitation of a relativistic quantum field. The video begins by looking at Hooke's Law and the mathematics of simple harmonic motion, before moving on to explore the mathematics of waves and a possible modification of the wave equation.
The quantum harmonic oscillator is discussed, as well as zero point energy. The basic definition of scalar and vector fields are discussed, along with the concept of a relativistic field. Finally, by combining the ideas of quantum mechanics with the concept of a relativistic field, it is shown that a particle is the smallest possible vibration of a quantum field.
This presentation is inspired by the following sources of information:
Quantum Field Theory in a Nutshell - Anthony Zee
Of Particular Significance (Blog) - Matt Strassler
Quantum Field Theory - Mark Srednicki
Quantum Field Theory for the gifted Amateur - Stephen Blundell and Tom Lancaster
The Feynman Lectures - Richard Feynman