Where Are the Poles of the Integrand for Δ<0 in Wick Rotation?

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Thread starter july21
Start date Aug 7, 2021
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In summary, Wick rotation is a mathematical technique used in theoretical physics to transform problems in four-dimensional Minkowski space into problems in four-dimensional Euclidean space. It simplifies calculations by converting non-Euclidean space into Euclidean space and is often used in quantum field theory and the study of black holes. However, it has limitations and must be used carefully to avoid errors.

Aug 7, 2021

july21

TL;DR Summary: Hi I would like to ask why we can still do Wick rotations even if \Delta<0
it's from Schwartz qft

Last edited: Aug 7, 2021

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Aug 7, 2021

vanhees71

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Just think about where the poles of the integrand are for ##\Delta<0##.

Related to Where Are the Poles of the Integrand for Δ<0 in Wick Rotation?

1. What is Wick rotation?

Wick rotation is a mathematical technique used in theoretical physics to relate real-time dynamics to imaginary-time dynamics. It involves a rotation of the time coordinate in a complex plane, which simplifies certain calculations and allows for the use of techniques from complex analysis.

2. Why is Wick rotation used in theoretical physics?

Wick rotation is used because it allows for the calculation of physical quantities that are difficult or impossible to calculate in real time. It also has applications in quantum field theory, statistical mechanics, and other areas of theoretical physics.

3. How does Wick rotation relate to quantum mechanics?

Wick rotation is closely related to quantum mechanics because it allows for the calculation of quantum mechanical systems in imaginary time, which is equivalent to calculating the thermodynamic properties of a system at finite temperature. This is useful for studying systems that are not in equilibrium.

4. What are some examples of problems that can be solved using Wick rotation?

Wick rotation can be used to solve problems such as calculating the partition function of a system, determining the behavior of particles in a potential, and studying the properties of black holes. It is also used in the study of phase transitions and critical phenomena.

5. Are there any limitations to using Wick rotation?

While Wick rotation is a useful tool in theoretical physics, it does have some limitations. It can only be applied to systems that are in equilibrium, and it may not always give accurate results for systems with strong interactions. Additionally, the rotation of time can lead to complex values, which may require additional mathematical techniques to interpret.