Integrating over all possible fields

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Discussion Overview

The discussion revolves around the integration over all possible fields in the Path integral formulation of quantum field theory (QFT) and its implications for understanding field quanta. Participants also explore whether newcomers to QFT should begin with the traditional second quantization approach or directly engage with the path integral method.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant questions the meaning of integrating over all possible fields in the Path integral formulation and how this relates to describing field quanta.
  • Another participant suggests reading "Field Theory" by Ashok Das for a good deduction of path integrals, emphasizing the connection between different approaches in QFT.
  • A third participant notes that practicing Quantum Field Theorists typically use path-integral quantization, highlighting its natural fit for modern concepts like Effective Field Theory and RG analysis.
  • There is a correction regarding the author's name of a recommended book, clarifying it should be "Ashok Das" instead of "Ashko Das."
  • A later reply recommends "Quantum Field Theory in a Nutshell" by A. Zee as a good pedagogical introduction that starts from the path integral approach.

Areas of Agreement / Disagreement

Participants express various viewpoints on the best approach to learning QFT, with some advocating for the path integral method while others suggest starting with second quantization. The discussion remains unresolved regarding which approach is preferable for newcomers.

Contextual Notes

Some participants acknowledge the complexity of conveying the power of Feynman's view in a brief format, indicating that deeper understanding may require more extensive study.

quantumfireball
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What does it really mean to integrate over all possible fields in the Path integral formulation of quantum field theory,and how does such a formalism goes out to decribe
field quanta?

Another question is
im new to Quantum field theory
i was wondering whether i should stick to the old second quantization approach of QFT or would it be better to directly jump to path integral method of doing QFT
 
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I suggest you to read the book "field theory" Ashko Das. ther is areal good deduction of path integrals... starting from Q.M. and then discretizing the Minkoskwy space time. before there is an introduction to path untegral approach an then you will get the idea of pertirbation theory and Feynman diagrams. If you want a canonical approach i suggest u QFT Itzykinson Zuber. this Book use the operator algebra not the Feynman Integral..
Buty show also the connection...
Quantum and statistical field theorie from LE BELLAC is a really good one also...

It is not so easy to transmit the power of Feynman view in a post.
but trust me... he invinted a new area and a new conception of QM. There was another INTERPRETATION (a new explanation). In DAS bookk u can find an euristic equivalence of feynman QM and Heisenberg/Schrödinger one...

bye
have a good time
 
Practicing Quantum Field Theorists almost always use path-integral quantization when deriving things. The modern concept of Effective Field Theory and RG analysis, as well as Yang-Mills quantization, are much more natural in this formalism. You should be sure to understand 2nd Quantization, but then you should try to get comfortable with Feynman - his formalism is what you'll most likely be using when doing research.
 
Not "Ashko Das" but "Ashok Das"
 
quantumfireball said:
What does it really mean to integrate over all possible fields in the Path integral formulation of quantum field theory,and how does such a formalism goes out to decribe
field quanta?

Another question is
im new to Quantum field theory
i was wondering whether i should stick to the old second quantization approach of QFT or would it be better to directly jump to path integral method of doing QFT
A good pedagogic intro to QFT that starts from the path integral approach and explains it in a nice way is
A. Zee, Quantum field theory in a Nutshell (2003)
 

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