
#1
Apr408, 01:12 PM

P: 962

Does anyone know what the Feynman Path Integral would look like in a space that has a curved geometry? I'm NOT talking about expressing the path integral in curvilinear coordinates that merely parameterize the cartesian coordinates of flat space. I'm talking about a space with curvature, like in general relativity, etc. Thanks.




#2
Apr408, 02:13 PM

Sci Advisor
P: 1,663

Actually it looks exactly like the path integral you normally see, with two subleties.
One, the normalization is different. So Z(0) = <out, 00, in> =<00> = 1 no longer applies. Two, You need to include a source function J( ), that in general will not vanish, even if you insist (it will reappear upon renormalization). The hard part though are intepretational issues, as well as the renormalization/regularization subleties for curved space. That requires a full textbooks treatment though and is lengthy.. 



#3
Apr408, 06:59 PM

P: 962





#4
Apr408, 10:28 PM

P: 478

Path Integral for curved spacetime
Birrell and Davies is pretty good, from what I hear:
http://www.amazon.com/QuantumCambri.../dp/0521278589 It actually looks pretty affordable. 



#5
Apr508, 09:39 AM

P: 962

So I'm also considering another book by Stephen A. Fulling, entitled, "Aspects of Quantum Field Theory in Curved Spacetime". See more info at: http://www.amazon.com/AspectsQuantu...684/ref=sr_1_1 It start with the Path Integral, and it is geared more for mathematicians without knowledge of QFT. Does anyone have an opinion on this book or its author? Thanks. 



#6
Apr508, 10:44 AM

Mentor
P: 6,037

I don't have Fulling with me, but, if I remember correctly (I'll check tomorrow or Monday), Fulling doesn't treat path integrals at all. Fulling is a math text, and I don't think there is (what mathematicians would call) a mathematically rigorous general formulation of path integrals (What is the measure?) in Minkowski spacetime, let alone curved spacetime.
Maybe you should have a look at this book. Read the review by smallphi on this page. 



#7
Apr508, 11:13 AM

Mentor
P: 6,037




#8
Apr508, 11:34 AM

P: 478

If you want a free book, one is here: http://www.physics.ucsb.edu/~mark/qft.html If you want to pay for a book, try Zee, ``QFT in a nutshell''. Any book you buy about QFT in a curved spacetime is going to assume that you already are pretty good at regular QFT. You gotta wak before you can run. 


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