Quantum Fields and Off-Shell Sciences

Intensive studies on light–matter interactions and technological breakthroughs, especially conducted in the field of dressed photon research, have led to a growing concern regarding unsettled off-shell quantum field interactions. The Special Issue, entitled “Quantum Fields and Off-Shell Sciences”, was organized to promote the progress of such research activities from a wider perspective, not limited to dressed photon studies. This book contains excellent papers that were published in this Special Issue. It will provide scientific and technical information on the quantum fields and off-shell sciences to scientists, engineers, and students who are and will be engaged in this field

Polycyclic monoids and their generalisations

EPSRC Doctoral Training Account EP/P503647/

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group