Understand Physics Conveniently Throughout Quantum Field Theory

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Understand Physics Conveniently Throughout Quantum Field Theory
The next contradiction that physicists faced was between quantum mechanics (which had been created over the thirty years following Planck's seminal insight) and the special theory of relativity. Most of the work in quantum mechanics was in the Galilean (or non-relativistic) approximation.
To be sure, Dirac had created a relativistic wave equation for the electron, which was a crucial development, but there was still a basic contradiction that needed to be fixed. The new feature that is required in a successful union of quantum mechanics and special relativity is the possibility of the creation and annihilation of quanta (or'particles'). The non-relativistic theory does not have this feature.
The framework in which quantum mechanics and special relativity are successfully reconciled is called quantum field theory. It is based on three basic principles: two of them, naturally, are quantum mechanics and special relativity. The third one, which I wish to emphasize, is the postulate that elementary particles are point-like objects of zero intrinsic size. In practice, they are smeared over a region of space due to quantum effects, but their descripton in the basic equations is as mathematical points.
Now the general principles on which quantum field theory are based actually allow for lots of different consistent theories to be constructed. (The consistency has not been determined with mathematical severity, but this is not a worry for a lot of physicists.).
Among these various possible theories there is a class of theories, called' gauge theories' or'Yang-Mills theories'that become especially intriguing and crucial. These are identified by a symmetry structure (called a Lie group) and the assignment of various matter particles to particular symmetry patterns (called group representations). There is an infinite set of possibilities for the choice of the symmetry group, and for each group there are lots of possible choices of group representations for the matter particles.
One of this boundless selection of theories has been experimentally singled out. It is called the "common model". It is based on a Lie group called SU(3) X SU(2) X U(1). The matter particles consist of three families of quarks and leptons. (I will not describe the representations that they are appointed to here.) There are also addition matter particles called "Higgs particles", which are required to account for the truth that part of the symmetry is spontaneously broken.
The common model consists of some 20 adjustable parameters, whose values are figured out experimentally. Still, there are lots of more points that can be gauged than that, and the common model is surprisingly successful in accounting for a large range of experiments to really high precision. Without a doubt, at the time this is written, there is only one specific piece of experimental evidence that the common model is not an exactly right theory. This evidence is the truth that the common model does not consist of gravity!


The new feature that is required in a successful union of quantum mechanics and special relativity is the possibility of the creation and annihilation of quanta (or'particles'). The framework in which quantum mechanics and special relativity are successfully reconciled is called quantum field theory. It is based on three basic principles: two of them, of course, are quantum mechanics and special relativity. Among these various possible theories there is a class of theories, called' gauge theories' or'Yang-Mills theories'that turn out to be especially intriguing and crucial.