
Book Nr. 12
PARTICLES AND QUANTUM FIELDS

Book 12
Hagen Kleinert
PARTICLES AND QUANTUM FIELDS
pp. 11549, World Scientific, Singapore 2015
Hardcover: ISBN 9789814740890 GBP 111.00
Paperback: ISBN 9789814740906 GBP 40.00
[large cover with blurbs]

This is an introductory book on elementary particles and their interactions. It starts out with manybody SchrÃ¶dinger theory and
second quantization and leads, via its generalization, to relativistic fields of various spins and to gravity. The text begins with
the best known quantum field theory so far, the quantum electrodynamics of photon and electrons (QED). It continues by developing
the theory of strong interactions between the elementary constituents of matter (quarks). This is possible due to the property
called asymptotic freedom. On the way one has to tackle the problem of removing various infinities by renormalization. The divergent
sums of infinitely many diagrams are performed with the renormalization group or by variational perturbation theory (VPT). The
latter is an outcome of the FeynmanKleinert variational approach to path integrals discussed in two earlier books of the author,
one representing a comprehensive treatise on path integrals, the other dealing with critial phenomena. Unlike ordinary perturbation
theory, VPT produces uniformly convergent series which are valid from weak to strong couplings, where they describe critical
phenomena.
The present book develops the theory of effective actions which allow to treat quantum phenomena with classical formalism. For
example, it derives the observed anomalous power laws of strongly interacting theories from an extremum of the action. Their
fluctuations are not based on Gaussian distributions, as in the perturbative treatment of quantum field theories, or in
asymptoticallyfree theories, but on deviations from the average which are much larger and which obey powerlike distributions.
Exactly solvable models are discussed and their physical properties are compared with those derived from general methods. In the
last chapter we discuss the problem of quantizing the classical theory of gravity.
