Saturday, 17 November 2018

resource recommendations - Rigorous approaches to quantum field theory



I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles.



I was wondering if anyone familiar with the book knows any equally elegant presentation for quantum field theory. Weinberg's books start off nice with the irreducible representations of the Poincare group/algebra but the later chapters lose me with the notation. Also, most books I've read on QFT (Srednicki, Peskin and Schroeder, Mandl and Shaw) make a valiant initial attempt at a nice consistent framework but end up being a big collection of mathematical recipes and intuitive insights that seem to work but the overall structure of the theory seems to be sewn up. The relativistic equations crop out of rather flimsy arguments, the canonical anti/commutation relations are imposed out of density indeterminate air, functional methods are developed cause we know no better, infinities come about with renormalization theory to the rescue but it seems very alien from the initial context.


Is there any approach that ties all these things together in an elegant mathematical framework which accounts for all the patch up work that is needed? I am not talking about axiomatization just a global point of view that encompasses all the issues.




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