What is the best book to learn relativistic quantum mechanics at first time? I would like a book that also talk about the representations of the Lorentz group and the Poincaré group.
3 Answers
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Note that it is inevitable to go to quantum field theory, that is, many-particle theory, if you want relativistic extension. A book giving the complete answer to what you asked is Weinberg, vol. 1. However an accessible book would be Peskin and Schroeder. A particle theory book like Halzen and Martin would be also a good starting point.
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Relativistic extension of quantum mechanics will extend naturally into quantum field theory and on a beginner level, my suggestions would be to follow the book by Lewis H. Ryder and Mark Srednicki. A more theoretical approach can be found in the book named "Quantum Field Theory in a nutshell" by Anthony Zee. QFT books of Peskin and Schroeder, and Weinberg Volume 1 are the ultimate books to go to in the end.
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Previous posts highlighted that it proved to be difficult to design a relativistic quantum theory that is not a quantum field theory. As a reference to why that is the case, maybe the book by Strocchi is helpful. It is mostly about quantum field theory, but the first chapter deals with attempts to formulate relativistic wave equations that have a probabilistic interpretation.