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Université catholique de Louvain
Autumn term 2014
Quantum Field Theory I LPHY2120
Historical development of Quantum Field Theory
ASSIGMENT: Write a short essay or text commentary (∼ 2 pages) elaborating on the
following points:
• According to Weinberg, what is the basic motivation leading to the development of Quantum Field Theory?
Describing particle creation and annihilation in the framework of QM. This is for instance
the necessary ingredient to study matter–radiation interaction.
• Explain in some detail the historical analogy used by Weinberg to compare how the paradigms
of Quantum Mechanics and Quantum Field Theory were established. It will be helpful that
you mention the episode of the Conference at Shelter Island in 1947.
While Quantum Mechanics involves a dramatic change of concepts (uncertainty principle &
probabilistic interpretation radically confront the deterministic nature of classical physics),
quantum field theory represents a smooth evolution: it is not about new concepts or tools
(e.g. it is not about changing the picture e.g. of position and momentum being real
functions to hermitian operators ) – but e.g. to extend the notion of elementary field
excitations from forces (electromagnetic field) to particles (the electron); or assuming that
apparently divergent quantities can be related to physical observables through a suitable
redefinition (renormalization).
Weinberg compares these two changes of scientific paradigm to two salient revolutionary
episodes in Western History. With this analogy in mind, the advent of QM would in a way
resemble the russian revolution of 1917, as the latter represented a radical change of all
political, economical and social structures – leading to the end of the tsarist autocracy and
its replacement by a communist regime. At variance, the assumption of the QFT paradigm
would be closer to the British Glorious Revolution of 1688, with the King James II being
replaced by William III, completing a long–term evolution of the powers of the Chrown,
which had been sustainedly drained onto the parliament. In this sense, the overthrown of
James II and the transition to an absolute to a constitutional monarchy is seen as a natural
evolution.
In this sense, let us recall the episode of the Shelter Island conference. The rather skeptical
attitude towards QFT by part of the theory community back then was somehow calling for
a sharp turnabout – the problem of infinities was interpreted as a deep sign of inconsistency. Instead, the successful description of Lamb shift measurement represented a strong
confirmation that the ground ideas and the methods were indeed on the right track – just
a slight change of perspective was necessary: not substituting a king by another, this time
– but bare by renormalized parameters.
I personally find this analogy very wise, as it nicely brings up an example of a historical
change which is not very apparent at first sight (king replacement, very little violence, no
structure breakdowns – very different with respect to the 1917 case); but which nevertheless represents a major step towards the modern democratic societies. Many examples in
history operate contrariwise: seemingly huge changes are in the end barely scratching the
surface. One very well known episode can be drawn from italian history in the period of the
Risorgimento and lead to a celebrated quote in the novel Il Gattopardo by T. di Lampedusa:
if we want things to stay as they are, things will have to change.
• The author highlights a number of conceptual breakthroughs in the history of Quantum
Field Theory. Identify two of them and explain them in some detail.
Particles, as manifestation of elementary field excitations; interactions between particles,
ultimately described in terms of the exchange of force carriers (these are, elementary excitations of the quantized force fields); Particles and forces having the same fundamental
nature: field excitations; the existence of antiparticles.
• Of decisive importance in the construction of Quantum Field Theory was its ability to
anticipate completely unexpected effects or properties that were soon thereafter confirmed
by experiments. Which of them are identified by Weinberg? Can you point out at least one
more?
The atomic transition rates, in particular for spontaneous emission (which were already
known but from a purely heuristical approach); providing a solid theoretical ground for
Fermi’s theory of β–decay; predicting the existence of antiparticles, later on confirmed by
the discovery of the positron.
Aside from those cited in the text: the Lamb shift measurement, the Casimir force.
• Explain with your own words the meaning of the sentence Thus, the inhabitants of the universe were conceived to be a set of fields – an electron field, a proton field, an electromagnetic
field – and particles were reduced in status to mere epiphenomena.
By epiphenomena we mean a secondary manifestation: a visible aspect of a given reality,
which is not the reality itself. In this sense, Weinberg’s sentence simply means that nature
cannot be described if we consider particles as fundamental entities – fields are the basic
building blocks instead.
• When scientific documents are edited, it is very important that the authors provide a number
of keywords so that they can be easily located by search engines. Which six keywords would
you choose to index Weinberg’s text in databases?
Quantum Field Theory, History of Science, Epistemology, radiation–matter interaction,
Physics of Particles and Fields, Physics of the XXth century,