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This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles.
An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics. However, digital physics considers nature fundamentally discrete at the Planck scale, which imposes upper limit to the density of information , aka Holographic principle .
Traditionally, in theoretical physics, the Planck scale is the highest energy scale and all dimensionful parameters are measured in terms of the Planck scale. There is a great hierarchy between the weak scale and the Planck scale, and explaining the ratio of strength of weak force and gravity / = is the focus of much of beyond-Standard-Model physics.
Examples of toy models in physics include: the Ising model as a toy model for ferromagnetism, or lattice models more generally. It is the simplest model that allows for Euclidean quantum field theory in statistical physics. [2] [3] [4] Newtonian orbital mechanics as described by assuming that Earth is attached to the Sun by an elastic band;
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics , which uses experimental tools to probe these phenomena.
For example, in order to study the geometry of the Euclidean plane, one defines the coordinates x and y as the distances between any point in the plane and a pair of axes. In ordinary geometry, the coordinates of a point are numbers, so they can be multiplied, and the product of two coordinates does not depend on the order of multiplication.
In any case, users of a model need to understand the assumptions made that are pertinent to its validity for a given use. Building a model requires abstraction. Assumptions are used in modelling in order to specify the domain of application of the model. For example, the special theory of relativity assumes an inertial frame of reference.