Quantum Field Theory: completing the "A Bridge between Mathematicians and Physicists" series

Question

I decided to read the series "A Bridge between Mathematicians and Physicists" written by Eberhard Zeidler. But when I read the preface of the first book I realized that at first this series should be composed of six volumes, namely:

1. Quantum Field Theory I: Basics in Mathematics and Physics
2. Quantum Field Theory II: Quantum Electrodynamics
3. Quantum Field Theory III: Gauge Theory
4. Quantum Field Theory IV: Quantum Mathematics
5. Quantum Field Theory V: The Physics of the Standard Model
6. Quantum Field Theory VI: Quantum Gravity and String Theory

I have only the first three books. Searching for the last three I discovered that Eberhard Zeidler died and therefore the last three volumes will never be published.

For this reason I ask: could someone please indicate me books that cover the subject of the last three books and that focus a lot on the mathematical part?

Thank you for your attention.

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Quotes from the prologue of the first volume to clarify the proposed contents of Volume IV:

Volume IV. Quantum physics differs from classical relativistic field theories by adding the process of quantization. From the physical point of view, there appear additional quantum effects based on random quantum fluctuations. From the mathematical point of view, one has to deform classical theories in an appropriate way. Volume IV is devoted to the mathematical methods of quantization. For this, we coin the term Quantum Mathematics. This is a branch of mathematics. Volume IV represents the first systematic textbook on Quantum Mathematics. This volume will be divided into the following parts

1. Part I: Quantization
2. Part II: Quantum Information
3. Part III: Symmetry, Groups, and Hopf Algebras
4. Part IV: Observables and Operator Algebras
5. Part V: Cohomology and Homology VI: Physical Fields, Fiber Bundles, and Sheaves.

...

(i). Rigorous methods: We first develop quantum mathematics in finite dimensional spaces. In this case, we can use rigorous methods based on the theory of Hilbert spaces, operator algebras, and discrete functional integrals.

(ii). Formal methods. The formulas from (i) can be generalized in a straightforward, but formal way to infinite-dimensional systems.

Answer 1

The volume number 4 has a vague title. 2 volumes of "Quantum fields and strings: a course for mathematicians" probably cover whatever that term is supposed to mean (there is also a partial QFT-mathematics dictionary in the books, very nice). The books are outdated by this point, but they should be enough to get you started (then you should be able to read physical mathematics papers without too much pain).