In single-particle quantum mechanics, particles are replaced by wave-functions -- which are functions from the space of possible particle positions to the complex numbers. It seems that the most 'natural' definition of a quantum field would be as a functional from the space of field configurations to the complex numbers. Reading QFT textbooks, it often seems that this viewpoint is lurking in the background but rarely made explicit. Are there any textbooks (or lecture notes, papers etc.) that spell out as explicitly as possible the connection between this viewpoint and the usual formulation with creation and annihilation operators, feynman diagrams etc?
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3It is the states that are functionals over the space of fields, not the fields themselves – coconut Dec 27 '16 at 08:35
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related: Is there any theorem that suggests that QM+SR has to be an operator theory? – AccidentalFourierTransform Dec 27 '16 at 10:03
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Around p.6 in the review article: A Perspective on Constructive Quantum Field Theory, Stephen J. Summers. – Keith McClary Dec 27 '16 at 17:00
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This approach is discussed in details in "Quantum Field Theory of Point Particles and Strings" by Hatfield. It can be found on the net.
Andrey Feldman
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