Massless Representations of the Poincaré Group: electromagnetism, gravitation, quantum mechanics, geometry by Ronald Mirman (PDF)

Description

Geometry through its fundamental transformations, the Poincaré group, requires that wavefunctions belong to representations. Massless and massive representations are very different and their coupling almost impossible. Helicity-1 gives electromagnetism, helicity-2 gives gravitation; no higher helicities are possible. Basis states, thus the fundamental fields, are the potential and connection. General relativity is derived and is the unique theory of gravity, thus the only possible quantum theory of gravity. It is explained why it is. Because of transformations trajectories must be geodesics. Momenta are covariant derivatives and must commute. Covariant derivatives of the metric are zero.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Mirman’s book expands on the sort of discussion that is found in Chapter 2 of Weinberg’s

⭐, in which the differences between the representations of massive particles (like the electron) and massless particles (like the photon) are elucidated. The problem, with this book, however, is that the notation used (e.g. the Lorentz generators of the Poincare group on p.15) is often not defined within the confines of this book. Instead the reader is directed to other difficult to obtain books or journal articles (e.g. Kim and Noz

⭐) for these definitions. Such an approach to defining essential features such as notation is what you might expect from journal articles–though even most review articles define basic notation. Nevertheless, Mirman deserves credit for presenting the reader with helpful intuitive insights that are expressed verbally rather than being couched solely in equations. For example, the equation-free discussion of Section 3.6 (pp.49-50), “How are massless representations obtained from massive ones,” is both brief and insightful.

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