- #1

- 970

- 3

## Main Question or Discussion Point

On page 68, equation (8.13) of Srednicki's QFT book is the equation for the scalar propagator:

[tex]\Delta(x-x')=i\theta(t-t') \int \frac{d^3k}{2(2\pi)^3E_k}e^{ik(x-x')}

+i\theta(t'-t) \int \frac{d^3k}{2(2\pi)^3E_k}e^{-ik(x-x')}

[/tex]

where the exponential is the product of 4-vectors and k is on-shell.

My question is to evaluate the integrals, can you set t'=t in the exponential by choosing a frame where the two events happen simultaneously?

Because Srednicki says that these integrals are the same ones as in equation (4.12) on page 46, which turn out to be modified Bessel functions. However, equation (4.12) assumed space-like separations by evaluating the integral in a frame where t=t', thereby simplifying the expression. However, when you do this, isn't the expression only correct for space-like separations, and not time-like separations?

[tex]\Delta(x-x')=i\theta(t-t') \int \frac{d^3k}{2(2\pi)^3E_k}e^{ik(x-x')}

+i\theta(t'-t) \int \frac{d^3k}{2(2\pi)^3E_k}e^{-ik(x-x')}

[/tex]

where the exponential is the product of 4-vectors and k is on-shell.

My question is to evaluate the integrals, can you set t'=t in the exponential by choosing a frame where the two events happen simultaneously?

Because Srednicki says that these integrals are the same ones as in equation (4.12) on page 46, which turn out to be modified Bessel functions. However, equation (4.12) assumed space-like separations by evaluating the integral in a frame where t=t', thereby simplifying the expression. However, when you do this, isn't the expression only correct for space-like separations, and not time-like separations?