By Derek F. Lawden
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Extra info for A Course in Applied Mathematics, Vol.1, 2
Heisenberg felt that there must be discontinuous quantum jumps to represent the photons in the ﬁeld yet wave mechanics was based on continuous waves and this led to a division across physics. The impasse ended in 1926 via the name quantum mechanics and Dirac who showed the similarities between the two perspectives. Dirac used a “second quantization” for the EM ﬁeld with annihilation and creation operators to model the vacuum as an inﬁnite sea of particles that possessed negative energy The resultant theory was compatible with special relativity and introduced spin to quantum mechanics.
He found that the generic solution of a charged surface of ﬁnite radius moving at relativistic speeds was correct within the macroscopic domain The underlying self-ﬁeld problem has remained an unsolved problem until recently, when its modern variant succeeded in solving the hydrogen atom as demonstrated in the next chapter. Yet this open wound on the face of classical electromagnetics did force early 20th-century physicists to think laterally inventing quantum theory, in particular QED. Thus SFT has a pride of place at the start not only of quantum mathematics but of particle physics and the search for exotic particles within the cosmos.
Both hole theory and zero-point energy involve subtracting energies from the overall Lagrangian. The concept arises of eliminating virtual particles that exist temporarily. Thus the discovery of QED and QCD occupied theoretical physicists till the end of the century. The application of the October 13, 2011 16:5 PSP Book - 9in x 6in 26 Introduction statistical methods of QFT to the Standard Model of particle physics was a major achievement for late 20th-century physics. Perhaps the most inﬂuential physicist of the pre- and early quantum era apart from Einstein was Heisenberg, who with Bohr established the basis for the mathematics of QM.