**Preface to "Quantum Fields and Off-Shell Sciences"**

Intensive experimental studies on light–matter interactions and their associated technological breakthroughs, especially conducted in the field of dressed photon research, have led to a growing concern regarding unsettled off-shell quantum field interactions. In order to respond to the demand of this new tide of scientific progress, a new initiative has been recently launched. The Special Issue, entitled "Quantum Fields and Off-Shell Sciences", was organized in the academic journal *Symmetry* to promote the progress of such research activities from a wider perspective, not necessarily limited to dressed photon studies. The scope of the Special Issue covered quantum probability theory, quantum walk modeling, quantum measurement theory, micro–macro duality, category theory, the vortex structure of spacetime, off-the-mass-shell property of quantum field and symmetry, and symmetry breaking in quantum fields.

Eleven excellent original papers were successfully accepted for publication via an impartial peer-review process. This book contains these published papers. 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.

> **Motoichi Ohtsu** *Editor*
