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'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation.  In the areas of its domain (electromagnetic, weak nuclear, and strong nuclear forces), it is arguably the most precisely verified theory in all of physics.

'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation.  In the areas of its domain (electromagnetic, weak nuclear, and strong nuclear forces), it is arguably the most precisely verified theory in all of physics.

"Field theory" describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.

QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.

The differences between basic QM and Field Theory are these: in QM, the interactions between more than two particles are increasingly difficult to model, and the creation and destruction of particles cannot be modeled at all. In contrast, Field Theory can describe states containing arbitrary numbers of particles of different energies, masses, charges and types. Field Theory also provides an elegant framework for describing the interactions between particles, and the creation of new particles and destruction of old ones-- for example, the emission and absorption of photons by electrons, and vice versa.<ref>Bjorken and Drell. <i>Quantum Field Theory</i> Chapter 3; McGraw Hill Inc. (1980)</ref>

The differences between basic QM and Field Theory are these: in QM, the interactions between more than two particles are increasingly difficult to model, and the creation and destruction of particles cannot be modeled at all. In contrast, Field Theory can describe states containing arbitrary numbers of particles of different energies, masses, charges and types. Field Theory also provides an elegant framework for describing the interactions between particles, and the creation of new particles and destruction of old ones-- for example, the emission and absorption of photons by electrons, and vice versa.<ref>Bjorken and Drell. <i>Quantum Field Theory</i> Chapter 3; McGraw Hill Inc. (1980)</ref>

QFT assumes that relativity is true, and then bases the mathematical work on an assumption that elementary particles can be treated as "point-like objects of zero intrinsic size."<ref>http://theory.caltech.edu/people/jhs/strings/str114.html</ref>

Like all physical theories since the mid-1930's, QFT is "Lorentz invariant".  That is, it is consistent with [[Theory of Relativity|Special Relativity]].  However, as discussed below, it does not explain gravity in a manner consistent with the curvature of spacetime in General Relativity.

 

QFT bases the mathematical work on an assumption that elementary particles can be treated as "point-like objects of zero intrinsic size."<ref>http://theory.caltech.edu/people/jhs/strings/str114.html</ref>

For a given interaction of particles, field theoretical calculations generally cannot be solved in a closed, analytical form-- that is, the predicted probabilities cannot be described by one simple equation; however, physicists have developed numerous approximation methods which produce estimates of ever-increasing precision (compared to experiment), with the precision depending upon how much mathematical work is put into the analysis.<ref>Pierre Ramond. <i>Field Theory: A Modern Primer</i>, Chapter VIII; Benjamin-Cummings Inc. (1981)</ref>

For a given interaction of particles, field theoretical calculations generally cannot be solved in a closed, analytical form-- that is, the predicted probabilities cannot be described by one simple equation; however, physicists have developed numerous approximation methods which produce estimates of ever-increasing precision (compared to experiment), with the precision depending upon how much mathematical work is put into the analysis.<ref>Pierre Ramond. <i>Field Theory: A Modern Primer</i>, Chapter VIII; Benjamin-Cummings Inc. (1981)</ref>