After Erwin Schrödinger's triumph, physicists, including Schrödinger himself, realised that a relativistic quantum theory was needed. The man behind the first field theory was none other than Paul Dirac. His attempt to quantize the electromagnetic field in the 1920's saw much success and Quantum Electrodynamics (QED) was born. However, Dirac had problems avoiding infinities which his theory produced. It took a brilliant man to solve the problematic infinities Dirac had stumbled upon, and that man was Richard Feynman. This was also done independently by Tomanaga and Schwinger, and all three won the nobel prize in 1965.

Carl Gauss, Georg Riemann, Ricci, Christoffel and Levi-Civita has done essential work the field of differential geometry. This is a field where sets with special properties are examined. We call them manifolds. Einstein's special theory of relativity could not only account for constant speed, but what also varying speed in the flat Minkowski geometry using the corresponding metric. After all, although we are talking about inertial frames, Newton's laws do include acceleration. That being said, the inertial frames themselves must not accelerate. Special relativity deals with kinematics, but when gravitational effects are present we must step into the world of general relativity. His realisation that gravity and accelerated motion are equivalent enabled him to work out a more general theory of relativity in which he made extensive use of Riemannian Geometry.

When an objects travels from a to b it moves in some particular path. But what determines the particular path of the object? How does the object know which path to take? This is where the principle of least action comes in. The classical principle of least action is well understood. However, while the quantum mechanical version is so too, it is harder to grasp because all possible paths contribute in the sum.

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© Vebjørn Gilberg, 2017