Introduction to QFT

Quantum Field Theory (QFT) is the fundamental framework used in physics to describe particles and their interactions. Instead of treating particles as primary objects, QFT considers fields as the fundamental entities. The fundamental quantities are fields, and particles are excitations.

Definition in Mathematics

◼
  • A field is written as:
    • ϕ(x,t)​And dynamically interpreted by the Lagrangian form:​L(t)=
    ∫
    3
    d
    x
    L (
    φ
    α
    ,
    ∂
    μ
    φ
    α
    )
    with L being the Lagrangian density (or simply Lagrangian)
    ◼
  • It is also important to note the general Klein-Gordon Equation considering the Lagrangian with arbitrary potential V(φ):​​
    ∂
    μ
    μ
    ∂
    ϕ+
    ∂V
    ∂ϕ
    =0

    • Wolfram Model Correlation

    Let’s make a Hypergraph of the Wolfram Model Final state plot for some initial conditions. The goal is to later connect the nodes of the graph with the fields that are described in this theory.
    In[]:=
    ResourceFunction["WolframModel"]
    Out[]=
    [◼]
    WolframModel
    Version (latest): 7.0.0
    Documentation »
    In[]:=
    wm=ResourceFunction["WolframModel"][{{x,y},{x,z}}->{{x,z},{x,w},{y,w},{z,w}},{{0,0},{0,0}},10,"FinalStatePlot"]​​
    Out[]=
    The final state plot of the Hypergraph can be used to associate nodes with QF excitations.

    Bibliography

    [1] Tong, D. (2006). Lectures on quantum field theory. University of Cambridge. https://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf
    [2] Tong, D. (n.d.). What is quantum field theory? (Video)

    CITE THIS NOTEBOOK

    Quantum field theory and the Wolfram model- theoretical framework and introduction​
    by Myrto Terpsiadou​
    Wolfram Community, April 11, 2026
    https://community.wolfram.com/groups/-/m/t/3682254