Register to reply

Path Integral for curved spacetime

by friend
Tags: curved, integral, path, spacetime
Share this thread:
friend
#1
Apr4-08, 01:12 PM
P: 968
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.
Phys.Org News Partner Physics news on Phys.org
First in-situ images of void collapse in explosives
The first supercomputer simulations of 'spin?orbit' forces between neutrons and protons in an atomic nucleus
Magnets for fusion energy: A revolutionary manufacturing method developed
Haelfix
#2
Apr4-08, 02:13 PM
Sci Advisor
P: 1,677
Actually it looks exactly like the path integral you normally see, with two subleties.

One, the normalization is different. So Z(0) = <out, 0|0, in> =<0|0> = 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..
friend
#3
Apr4-08, 06:59 PM
P: 968
Quote Quote by Haelfix View Post
Actually it looks exactly like the path integral you normally see, with two subleties.

One, the normalization is different. So Z(0) = <out, 0|0, in> =<0|0> = 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..
Is there a book that you know of that treats this subject in a complete and modern way? Does this book develop the subject from scratch, or does it generalize on the flat spacetime version? Thanks.

BenTheMan
#4
Apr4-08, 10:28 PM
P: 478
Path Integral for curved spacetime

Birrell and Davies is pretty good, from what I hear:

http://www.amazon.com/Quantum-Cambri.../dp/0521278589

It actually looks pretty affordable.
friend
#5
Apr5-08, 09:39 AM
P: 968
Quote Quote by BenTheMan View Post
Birrell and Davies is pretty good, from what I hear:

http://www.amazon.com/Quantum-Cambri.../dp/0521278589

It actually looks pretty affordable.
Yes, thank you. But the book you refer to by Birrel and Davies assumes a "working knowledge" of QFT in flat spacetime, which I do not have. I've read up on QFT a couple of time a couple years ago, but I never really worked with it.

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/Aspects-Quantu...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.
George Jones
#6
Apr5-08, 10:44 AM
Mentor
George Jones's Avatar
P: 6,226
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.
George Jones
#7
Apr5-08, 11:13 AM
Mentor
George Jones's Avatar
P: 6,226
Quote Quote by George Jones View Post
Maybe you should have a look at this book
Detailed table of contents.
BenTheMan
#8
Apr5-08, 11:34 AM
P: 478
Yes, thank you. But the book you refer to by Birrel and Davies assumes a "working knowledge" of QFT in flat spacetime, which I do not have. I've read up on QFT a couple of time a couple years ago, but I never really worked with it.
Ahh. Well...I would suggest that you read up on QFT again, and this time work with it ;)

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 space-time is going to assume that you already are pretty good at regular QFT. You gotta wak before you can run.


Register to reply

Related Discussions
Re: Renormalized Curved Spacetime Feynman Path Integrals by Epstein-Glaser General Physics 1
Re: Renormalized Curved Spacetime Feynman Path Integrals by Epstein-Glaser General Physics 0
Motion Along a Curved Path Introductory Physics Homework 2
Motion along curved path Introductory Physics Homework 10