Where Can I Find Rigorous Developments of the Path Integral Formulation?

[ghotra]

Hi, I'm wondering if someone can point me to "rigorous" developments of the path integral formulation. I've mostly seen arguments based on chopping up a line into a discrete set of points and then taking the limit as the number of points goes to infinity and integrating over all possible values of the infinite number of points.

I am convinced by these arguments, but I am interested in some of the formalities...particularly some of the intermediate steps. It seems like quite a big jump to the final result, and and I am interested in some of the justifications. Surely this must have been done rigorously at some point...though it doesn't seem that many QFT books describe the details (with good reason).

Thanks.

 

[Perturbation]

I thought the treatment of the path integral in "An Introduction To Quantum Field Theory"-Schroeder & Peskin was great and pretty comprehensive. They give the one dimensional classical derivation and then extend that to general quantum mechanical systems with higher degrees of freedom. The explanations you've had, did they involve discussions of classical paths, least action etc.?
http://arxiv.org/abs/hep-th/9302097"

 

[Perturbation]

The development by Dirac and Feynman built on work already performed in mathematics.

 

[samalkhaiat]

Hi, I'm wondering if someone can point me to "rigorous" developments of the path integral formulation. I've mostly seen arguments based on chopping up a line into a discrete set of points and then taking the limit as the number of points goes to infinity and integrating over all possible values of the infinite number of points.
I am convinced by these arguments, but I am interested in some of the formalities...particularly some of the intermediate steps. It seems like quite a big jump to the final result, and and I am interested in some of the justifications. Surely this must have been done rigorously at some point...though it doesn't seem that many QFT books describe the details (with good reason).
Thanks.

Start by reading Ch2 of J. Sakurai's book; Modern Quantum Mechanics.(my rating;*****)
Next read Ch11 & Ch12 of the book; Field Quantization, by Greiner & Reinhardt.(rating****)
Then Ch12,Ch13 & Ch14 of B. Hatfield's book; Quantum Field Theory Of Point Particles And Strings.(rating******)
After reading the above, Now go and read L.S.Schulman's book;
Techniques and Applications of Path Integration
(rating***************************)

regards

sam