The concepts of noncommutative space-time and quantum groups have found
growing attention in quantum field theory and string theory. The mathematical
concepts of quantum groups have been far developed by mathematicians and
physicists of the Eastern European countries. Especially, V. G. Drinfeld from
Ukraine, S. Woronowicz from Poland and L. D. Faddeev from Russia have been
pioneering the field. It seems to be natural to bring together these scientists with
researchers in string theory and quantum field theory of the Western European
This new and updated deals with all aspects of Monte Carlo simulation of
complex physical systems encountered in condensed-matter physics and statistical
mechanics as well as in related fields, for example polymer science,
lattice gauge theory and protein folding.
After briefly recalling essential background in statistical mechanics and probability
theory, the authors give a succinct overview of simple sampling methods.
The next several chapters develop the importance sampling method,
both for lattice models and for systems in continuum space....
In this book I present diﬀerential geometry and related mathematical topics with
the help of examples from physics. It is well known that there is something
strikingly mathematical about the physical universe as it is conceived of in
the physical sciences. The convergence of physics with mathematics, especially
diﬀerential geometry, topology and global analysis is even more pronounced in
the newer quantum theories such as gauge ﬁeld theory and string theory. The
amount of mathematical sophistication required for a good understanding of
modern physics is astounding.
The divergence of the photon self-energy diagram in spinor quantum electrodynamics
in (2 + 1) dimensional space time- (QED3 ) is studied by the Pauli-Villars regularization and dimensional regularization. Results obtained by two different methods are coincided if the gauge invariant of theory is considered carefully step by step in these calculations