Textbook： Symmetry and Its Breaking in Quantum Field Theory
The above textbook is published in Nova Science (Nova Science).
This textbook describes the symmetry and its breaking in quantum field theory, and the basic
physics of quantum mechanics and field theory is found in Appendix.
This book may be written with slightly higher than the standard knowledge of physics
for undergraduate students,
but still the textbook may help students understand quantum mechanics in depth. Therefore,
I select some parts of the textbook and put them into the PDF files. The textbook describes
the Schroedinger wave function and its equation in terms of field theoretical point of view.
Further, if one tries to understand quantum mechanics and the Schroedinger equation
by comparing them with the Maxwell equations, then one can enjoy physics and understand it more
in depth.
In this textbook, I describe mainly the symmetry and its breaking in quantum field theory,
but at the same time, I treat some of the basic problems in quantum field theory.
Quantum field theory has infinite degrees of freedom, and therefore it is very difficult
to understand it in depth. Among the field theory models, QED is best studied and most
reliable. In particular, the renormalization scheme in QED is well constructed and
evaluated, and people calculated many physical observables and compared them with experiments.
In this respect, there is no basic problem found in the QED renormalization scheme.
However, there are many serious problems in the study of QCD, renormalization group
equation, lattice field theory and so on. Basically, careful discussions as to what are
physical observables from field theory models
are missing and insufficient, and applications of mathematical formula to physical processes
are not carefully done. In particular, in the treatment of the spontaneous symmetry breaking
physics, one finds a theoretical argument which is almost mysterious to physicists. But physics
must be studied always with sufficiently critical attitude, and this is missing in this field
of research.
In this textbook, I stress an important point in physics as to what should be physical
observables in quantum field theory, and try to write it in terms of simple physics
terminology. Therefore, if one understands the basic quantum mechanics properly,
then one can understand this textbook to a reasonably good standard.
At the same time in this textbook, I presented many unsolved problems in quantum field theory,
and therefore I believe some researchers may find a good theme for their investigations
in fundamental field theory. Physics is always difficult, and one can understand it
in depth only after one spends much time for physics. I hope that students may read
this textbook and understand quantum mechanics in depth.