Setting ourselves free from these popular, primitive, anti-progressive biases, and following the deeper versatile trajectory (geometry) of the theory of space-time-matter established by Albert Einstein, no doubt certain researchers could arrive at new instruments of observation based on the geometric resurgence of the long-range action (in parallel with certain gravitational and gauge field instantons
of the Plebanski type).
His topics include the octahedral group and the octahedral double group, Lie groups and Lie algebras, Coxeter's reflection groups, ALE spaces and gravitational instantons
, knots and links and braids, elliptic curves and the monster group, sphere packing and error-correcting codes, the holographic principle, Calabi-Yau spaces and mirror symmetry, and Heisenberg algebras.
Among the topics are elusive worldsheet instantons
in heterotic string compactifications, the Witten equation and the geometry of the Landau-Ginzburg model, algebraic topological string theory, the fibrancy of symplectic homology in cotangent bundles, and the theory of higher rank stable pairs and virtual localization.
Oh, Floer cohomology and disc instantons
of Lagrangian torus fibers in Fano toric manifolds, Asian J.
Rajaraman, Solitons and Instantons
: An Introduction to Solitons and Instantons
in Quantum Field Theory, North-Holland, Amsterdam (1989).
of Michigan) and their contributors cover a wide range of subjects, including Gromov-Witten theory, mirror symmetry in complex and symplectic geometry, and important ramifications in enumerative geometry, with specific papers addressing strong coupling, brane-induced gravity, heterotic geometry influxes, pure Yang-Mills theory, black hole microstates, gravitational singularity, recent developments in heterotic compactifications, instantons
and torsion curves.
The qualitative understanding of many aspects of the QCD vacuum and lattice simulations in terms of helicity-flipping, quark-quark interactions induced by instantons
or other nontrivial gluon field configurations is another intriguing possibility.
For example, creation of the universe in cosmology, generation of gauge bosons, Higgs particles, t'Hooft monopoles, instantons
and solitons in high energy elementary particle physics, and phenomena of laser action, superradiance, superconductivity, superfluidity, phase transition, magnetism and electret behavior in condensed matter physics are all well understood in terms of SBS.
Among the topics are the group theory of twist eating solutions, the algebraic characterization of Witten's topological Yang-Mills theory, instantons
from over-improved cooling, calorons on the lattice, exact Fermion zero-mode for the new calorons, and higher charge calorons with non-trivial holonomy.
describe fuzzy spaces, including the Holstein-Primakoff construction, star products, scalar fields on the fuzzy sphere, instantons
, monopoles, projective modules, fuzzy nonlinear sigma models, fuzzy gauge theories, the Dirac operator and axial anomaly, fuzzy super-symmetry, SUSY anomalies on the fuzzy supersphere, and fuzzy spaces as Hopf algebras.
Table 1: Main features of the solutions of WDW equation, Classical Trajectories (CT) and Instantons
(I), for different values of parameter [LAMBDA], k, D, [gamma].
These are followed by nine cutting-edge articles with topics including n-flat connections, Dirac equations in a black hole background, homological matrices, quantitative properties of stratified flows, property (T) and tensor products by certain irreducible finite dimensional representations, Painleve equations for invariant instantons
, quantum statistical mechanics and class field theory, Kashiwara's quantization of complex contact manifolds and K-theoretic labeling for quasicrystals.