Review of "The Principles of Quantum Mechanics" by P.A.M. Dirac.
Oxford University Press (1958).

The book is just over 300 pages including the Index. It is of
historical interest, mainly. There are better treatments of the
subject, but this is an original work and stands monumental in
that regard, historically. The originality and its place in
history is this works strength and it stands on its own as a
classic in modern theoretical physics, unmatched in many ways
in that sense.

This book was first published in 1930. In 1928, Dirac's
application of the relativistic treatment of spin-1/2 particles
leads to both positive- and negative-energy solutions to the
electron. This book was made new in paperback in 1981. It has
been reprinted 9 times since. The last reprinting was in 1993.
It has a Preface to the first edition, which you should read
using the Amazon "Look Inside!" feature. You can view the
Contents of the book there, too. There you will find that the
book's contents are made up of twelve Chapters and a small
Index.

Quantum reality places the subject back into the study of the
objective world. Listen to the author in his own words:

"This state of affairs is very satisfactory from a
philosophical point of view, as implying an increasing
recognition of the part played by the observer in himself
introducing the regularities that appear in his observations,
and a lack of arbitrariness in the ways of nature, but it makes
things less easy for the learner of physics."

If, in your enquiry into quantum mechanics, you have read about
these philosophical changes brought about from the discovery of
quantum reality, then reading the words of one of its legends
will reinforce why many modern physicist's sound more like
philosophers than physicists. Here is the author, again, in his
own words:

"The methods of progress in theoretical physics have undergone
a vast change during the present century. The classical
tradition has been to consider the world to be an association
of observable objects (particles, fluids, fields, etc.) moving
about according to definite laws of force, so that one could
form a mental picture in space and time of the whole scheme.
This led to a physics whose aim was to make assumptions about
the mechanism and forces connecting these observable objects,
to account for their behaviour in the simplest possible way. It
has become increasingly evident in recent times, however, that
nature works on a different plan. Her fundamental laws do not
govern the world as it appears in our mental picture in any
very direct way, but instead they control a substratum of which
we cannot form a mental picture without introducing
irrelevancies."

In Chapter X "Theory of Radiation" Dirac derives his theory of
radiation in which he connects bosons to oscillators. Relating
a system "S (say a quantizied atom)to its Hermitian operator
Ho," he was able to identify the states of an assembly of
bosons with the states of a set of oscillators. "This means
that *the dynamical system consisting of an assembly of similar
bosons is equivalent to the dynamical system consisting of a
set of scillators--the two systems are just the same system
looked at from two different points of view.*" (Dirac pg
228-229). Von Neumann, probably the greatest mathematician of
the 20th century, in his book "Mathematical Foundations of
Quantum Mechanics", called Dirac's radiation theory "one of the
most beautiful achievements in the quantum mechanical field."
(Von Neumann, pg. 255)

In the last chapter, the author solves both a positive-energy
and a negative-energy solution for an equation (now called the
"Dirac equation") that applies relativistic solutions to the
problem of particle physics, specifically, that of elementary
spin-1/2 particles like the electron. The positive-energy
solution is the electron. The author doesn't ignore the
negative-energy solution, though! This is one of the
philosophical differences between quantum mechanics and
classical mechanics. Dirac simply allows the mathematical
result of a negative-energy solution to suggest that another
particle actually exists in reality, every way equal to that of
the electron, but opposite in sign. This would be like an
antimatter particle to the electron! This would be unheard of
but perhaps for science fiction writers. Here is the author in
his own words:

"In this way we are lead to infer that the negative-energy
solutions of (56) refer to the motion of' a new kind of
particle having the mass of an electron and the opposite
charge. Such particles have been observed experimentally and
are called *positrons*. We cannot, however, simply assert that
the negative-energy solutions represent positrons, as this
would make the dynamical relations all wrong. For instance, it
is certainly not true that a positron has a negative kinetic
energy. We must therefore establish the theory of the positrons
on a somewhat different footing. We assume that *nearly all the
negative-energy states are occupied*, with one electron in each
state in accordance with the exclusion principle of Pauli. An
unoccupied negative-energy state will now appear as something
with a positive energy, since to make it disappear, i.e. to
fill it up, we should have to add to it an electron with
negative energy. We assume that *these unoccupied
negative-energy states are the. positrons*"

The positron was confirmed by Carl Anderson just two short
years later in 1932.

P.A.M. Dirac was an Englishman. Since he is one of the early
founders and contributors to Quantum Mechanics, I suggest that
you read up on him if you haven't learned that much about him
in the past. I always appreciate a book more if I know a little
bit about the author. In the Wiki on him I just learned that he
married Eugene Wigner's sister. Cool. It is a small world.

I hope I have peaked your interest enough to make a purchase
today.