Space-time symmetry and quantum Yang-Mills gravity. How space-time translational gauge symmetry enables the unification of gravity with other forces (Q2857274)

In the present book, the authors introduce a different way to describe the gravitational interaction than Einstein's general relativity theory. As described by the authors this book is based on their research on this area for over the past two decades. Before the present book, one of the authors, Professor Jong-Ping Hsu published two books where some of the ideas described here had already been introduced. The first book is a collection of articles entitled ``100 Years of Gravity and Accelerated Frames, The Deepest Insight of Einstein and Yang-Mills'' [the first author (ed.) and \textit{D. Fine} (ed.), Adv. Ser. Theor. Phys. Sci. 9, 623 p. (2005; Zbl 1106.83002)]. It was edited along with Professor Dana Fine and published by World Scientific in 2005. The second book entitled ``A Broader View of Relativity, General Implications of Lorentz and Poincaré Invariance'' was co-authored by Professor Leonard Hsu and published by World Scientific in 2006, see [\textit{J.-P. Hsu} and \textit{L. Hsu}, Adv. Ser. Theor. Phys. Sci. 10, 516 p. (2006; Zbl 1104.83006)].NEWLINENEWLINEThe main idea of this new description of the gravitational interaction, named by the authors Yang-Mills gravity (YMG), is to consider a theory in flat spacetime rather than in a curved one, differently from Einstein's general relativity theory. The motivation for that is trying to find a gauge symmetry for gravity, described in flat spacetime, such that one could, in a natural way, unify this interaction with the other three interactions through a Yang-Mills scheme. The authors choose as the gauge symmetry for the YMG, the global spacetime translations in flat spacetime. It is an abelian subgroup of the Poincaré group, called \(T_4\). In fact, the global transformations generated by \(T_4\) are inadequate for the formulation of a gauge theory. Therefore, the authors consider also the local translations in flat spacetime. Although the spacetime in this theory is flat, the authors show that the gauge curvature associated with the \(T_4\) subgroup gives rise to an effective curved spacetime for the motion of classical physical systems. Using that result the authors evaluate the experimental predictions of the classical version of the YMG for three physical phenomena: the perihelion shift of planet Mercury, the deflection of light rays in a gravitational field and the emission of gravitational quadrupole radiation from gravitational systems.NEWLINENEWLINEThe book is divided in two parts. In the first part, the authors introduce the notion of \textit{taiji spacetime} which is the maximally symmetric spacetime with zero curvature. Then, for this spacetime, they explicitly derive coordinate transformations between inertial frames and non-inertial frames. They show that in the limit of zero acceleration, the transformations reduce to the Lorentz transformations and the effective metric of non-inertial frames reduce to the Minkowski metric. In the second part of the book, the authors construct the classical (CYMG) and quantum (QYMG) versions of the YMG. They introduce the gauge invariant action and evaluate the experimental predictions of CYMG. They show that the S-matrix of QYMG satisfies both the conditions of unitarity and gauge invariance. They also derive the rules for the Feynman diagrams, compute the graviton self-energy at one-loop level and study the renormalizability of QYMG. Finally, they construct unified models for gravity and the electroweak interactions and for gravity and the strong interaction using the YMG.