Quantum Field Theory

    The wave-particle duality led to a problem in interpreting the equations. This problem was solved by treating the equations not as functions of a single particle, but as field functions that when quantized give  particles and antiparticles which is an example of symmetry.  The quanta of the field are called fermions and bosons.

 No genral method has been found to solve the coupled set of field equations that result, exept in special cases.

     One of these cases is the interaction of electrons with the electromagnetic field. Quantum electrodynamics (QED) is the resulting theory.

QED - developed (1940's) independantly by Feynman, Dyson, Schwinger, and Tomonaga
           
            Uses Renormalization to get rid of the infities present in the higher order perturbation theory
           
            Is a Gauge theory  an example is gravity where an object has a potential  that can be measured                        from any where. The baseline is un-important. It is the difference that is important.
                Depends on gauge symmetry- the idea that equations of the field don't change when an  
                            operation is performed
                     (the idea of broken symmetry lead to the unification of the electormagnetic and weak                                         forces through the electroweak theory of Weinberg and Salam)


Quantum Chromodynamics (QCD)- developed  (1970's) as a theory describing hadrons as interactions               of quarks with one another mediated by gluons
              "Chromo" comes from the relation of color to electrical charge (convention only)
             
               Last great achievement of the Standard Model 


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