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This advanced course, a sequel to the first volume of this lecture series on topos quantum theory, delves deeper into the theory, addressing further technical aspects and recent advances. These include, but are not limited to, the development of physical quantities and self-adjoint operators; insights into the quantization process; the description of an alternative, covariant version of topos quantum theory; and last but not least, the development of a new concept of spacetime. The book builds on the concepts introduced in the first volume (published as Lect. Notes Phys. 868), which presents the main building blocks of the theory and how it could provide solutions to interpretational problems in quantum theory, such as: What are the main conceptual issues in quantum theory? And how can these issues be solved within a new theoretical framework of quantum theory? These two volumes together provide a complete, basic course on topos quantum theory, offering a set of mathematical tools to readers interested in tackling fundamental issues in quantum theory in general, and in quantum gravity in particular. From the reviews of the first volume: The book is self-contained and can be used as a textbook or self-study manual teaching the usage of category theory and topos theory, in particular in theoretical physics or in investigating the foundations of quantum theory in mathematically rigorous terms. [The] book is a very welcome contribution. Frank Antonsen, Mathematical Reviews, December, 2013
In the last five decades various attempts to formulate theories of
quantum gravity have been made, but none has fully succeeded in
becoming "the "quantum theory of gravity. One possible explanation
for this failure might be the unresolved fundamental issues in
quantum theory as it stands now. Indeed, most approaches to quantum
gravity adopt standard quantum theory as their starting point, with
the hope that the theory's unresolved issues will get solved along
the way. However, these fundamental issues may need to be solved
before attempting to define a quantum theory of gravity.
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