# Wick rotation and imaginary number

1. Dec 5, 2006

### touqra

Can you use Wick rotation to turn any real variable to an imaginary one, not necessary time, such that your integration converges, and then, return back to the real? I'm not really sure how to use Wick rotation.

2. Dec 9, 2006

### marlon

You are not sure to "use" a Wick rotation ? Well, what is the problem ? In any self respecting intro QFT study book, you will find a nice illustration of the Wick rotation and how/why it is used. Knowing that, will also answer your first question.

marlon

3. Jan 9, 2007

can you give the name of a "self-respecting" intro QFT book please?

4. Jan 9, 2007

### marlon

"QFT in a Nutshell" by Anthony Zee

marlon

5. Jan 10, 2007

### AlphaNumeric

If memory serves, it crops up in relativity now and again since it's essentially a way of 'Euclideanising' a metric. In some general relativity cases, it's not the time coordinate which is time-like so you'd perform a Wick rotation on the radial coordinate perhaps.

It's nothing more than a change of variables to allow you to compute the integral. Some people have reservations about it because they question what physical meaning $$\tau = it$$ has, but that might be trying to give physical meaning to too many things when you're just wanting to crunch some numbers.
"An Introduction to Quantum Field Theory" - Peskin & Schroeder gets my vote. It's the beginners QFT bible in plenty of UK unis. :)

6. Jan 10, 2007

### humanino

7. Jan 10, 2007

### MeJennifer

It seems to me that such a rotation changes the results when space-time is no longer flat. Am I perhaps mistaken in that?

8. Jan 10, 2007

### marlon

Err, a non flat space time is not an ingredient of QFT, which is the formalism where this Wick rotation is very often used and which is indeed the context withint which the OP was asking the question.

The main reason why this rotation is used in QFT is that it connects quantum (field) theory to statistical mechanics. So the equations from both formalisms are linked to each other and one of the two formalisms can be used to describe a fenomenon in the other.

marlon

Last edited: Jan 10, 2007
9. Jan 11, 2007

### humanino

I agree that "Wick rotation" refers usually to QFT in flat spacetime. There are however interesting studies in GR using the "Wick rotation". See for instance : From Euclidean to Lorentzian General Relativity: The Real Way

10. Jan 11, 2007