Any suggestion for a book that includes quantum mechanics principles and smoothly introduces you to QED (quantum electrodynamics)? I am not a physicist but I am into quantum mechanics and statistical mechanics.
In my department, the quantum mechanics we do include only Schroedinger's equation and problems, some approximation methods like perturbation theory. I would like to learn more about Dirac, Feynman diagrams, quantum electrodynamics and chromodynamics -quantum field theory in general-.
I am searching for a book that is easy to follow and has the facts in chronological order in order to have a complete understanding about the problems that appeared in each theory that arose in that times. Without cutting off the mathematical background of all those.
Maybe all these are not in one book. In the books I have found, different theories appear here and there without any linkage between them.
 A: I'd like to add a few other worthy titles:


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*G. Esposito, G. Marmo, G. Sudarshan, "From Classical to Quantum Mechanics" (2004): modern presentation starting from a detailed discussion of the "Experimental foundations of quantum theory", through "Wave mechanics", "Weyl quantization", up to a brief intro to the Dirac equation.

*A. Messiah, "Quantum Mechanics", vols.1-2 (2014, Dover ed): excellent oldie-but goodie books covering everything you need for a good start, from the "End of the classical period" and a detailed historical account of the origins of quantum theory, to mathematical formalism and methods of solution, simple systems, symmetries and invariance, and elements of relativistic quantum mechanics, including the quantization of the electromagnetic field. Notation is modern enough to remain current to this day.

*M. Plenio, "Quantum Mechanics" (2002): excellent presentation following Dirac's "Principles of Quantum Mechanics", only modern in spirit and notation (unlike Dirac's). It is especially useful for getting acquainted with the Hilbert space formalism, up to an introduction to quantum computing. 

*W. Greiner, "Quantum Mechanics - An Introduction" (2001, 4th ed): first volume of an extensive series in theoretical physics. Other volumes include "Quantum Mechanics - Symmetries", "Relativistic Quantum Mechanics", "Field Quantization", "Quantum Electrodynamics", "Quantum Chromodynamics", "Statistical Mechanics", and many others. One of my favorites. The distinguishing feature of the series is an emphasis on worked-out examples and proofs. Some are hard to find elsewhere, especially compiled in the same book. This first volume in Quantum Mechanics begins with a pretty detailed historical overview and works its way through the formalism up to an introduction to quantum many-body systems. The Symmetries volume continues with a look at angular momentum and an introduction to symmetry groups (Lie groups) and representation theory. There is also a volume on "Quantum Mechanics - Special Chapters" that introduces quantum field theory (free and interacting electromagnetic fields), non-relativistic quantum field theory, quantum statistics, superfluidity, plasmons, special topics in the structure of atoms and molecules. If you'd like to continue with fields, then the "Field Quantization" volume provides a great introduction in the same spirit.   
A: There is one book which fits your requirements and background very well, it is called "Relativistic Quantum Mechanics" by Bjorken and Drell.
In it you will find focus on the Dirac equation and its solutions (chapter 1), followed by a practical introduction to QED and Feynman diagrams (chapter 6), without having to set up the whole of quantum field theory for general fields. 
It should serve as an excellent introduction and could prepare you for the well-known textbook by Peskin and Schroeder, for example, if you wish to delve into the subject further!
PS: Another one that can save you a lot of time is A. Sudbery: "Quantum mechanics and the particles of nature". Very interesting and specific, and you won't get stuck in hundreds of pages of machinery.
A: I have heard that Matthew Schwartz's Quantum Field Theory and the Standard Model is pretty good. It covers more than what you asked, but in a very accessible manner. According to your description, you have enough background to study this book. (I probably have less background than you do. Even for me, the first several chapters was a pretty comfortable read. So you will definitely be fine). 
Another interesting book is Richard Feynman and Albert Hibbs' Quantum Mechanics and Path Integrals. It introduces the Path integral method (quintessential to QFT) very comprehensively. Could be a great supplement.
