Peskin equ(2.51)and(2.52)

[sunkesheng]

Homework Statement

can we use the Steepest descent method,formula is in the picture

Homework Equations

for the case of picture one it has AN APPROXIMATE EXPRESSION in picture two.

The Attempt at a Solution

for (2.51),h(z)=-iz,z_{0}=m(mass),m=1,n=0;it caulate e^{-imt}/t,take the limit
t->\infty,the result is 0
for (2.52),h(z)=-z,z_{0}=m(mass),m=1,n=0;it caulate e^{-imt}/t,take the limit
t->\infty,the result is 0
where is wrong?

 

[mark726]

I would like to clarify a few things before addressing your question. Firstly, please provide the pictures or equations you are referring to for better understanding. Secondly, it would be helpful to know the context and background of your problem. What is the problem you are trying to solve using the Steepest descent method? Is it related to a specific field or theory in science? This information will help in providing a more accurate response.

That being said, let me try to address your question based on the information provided. The Steepest descent method is a mathematical technique used to find the stationary points or minima of a function. It involves taking small steps in the direction of steepest descent until the minimum is reached. This method is commonly used in optimization problems and has applications in various fields such as physics, engineering, and economics.

In regards to your attempt at solving the problem, I am unable to provide a specific answer as I do not have enough information about the equations and context. However, it is important to note that the Steepest descent method is an iterative process and requires multiple steps to reach the minimum. It is possible that your calculations for (2.51) and (2.52) are correct, but the limit you are taking may not be the final step in the process.

Additionally, the Steepest descent method may not always give the exact solution, but an approximate one. This could be due to the complexity of the function or other factors. Without more information, it is difficult to determine where the error may lie.

In conclusion, please provide more context and information about your problem for a better understanding and accurate response. The Steepest descent method is a useful tool in solving optimization problems, but it is important to use it correctly and in the right context.