Gaussian integral over the rindler wedge
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I'm trying to evaluate analytically, if it's possible, the Gaussian integral over the Rindler wedge, meaning:
$int^infty_0dx_1int_-x_1^x_1dx_0e^-b(x_1+a_1)^2e^b(x_0+a_0)^2$
Where $a_1,a_0$ are just real constants.
As you can see this is an integral over the infinite cone with an angle that goes from $theta=-pi/4 $ to $theta=pi/4$, where $theta=0$ placed on the $x_1$ axis.
I tried to integrate first $x_0$ and I got Erfi functions but after I tried to integrate the second parameter Mathematica couldn't figure out the answer.
Is there a way to solve this analytically?
gaussian-integral
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up vote
0
down vote
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I'm trying to evaluate analytically, if it's possible, the Gaussian integral over the Rindler wedge, meaning:
$int^infty_0dx_1int_-x_1^x_1dx_0e^-b(x_1+a_1)^2e^b(x_0+a_0)^2$
Where $a_1,a_0$ are just real constants.
As you can see this is an integral over the infinite cone with an angle that goes from $theta=-pi/4 $ to $theta=pi/4$, where $theta=0$ placed on the $x_1$ axis.
I tried to integrate first $x_0$ and I got Erfi functions but after I tried to integrate the second parameter Mathematica couldn't figure out the answer.
Is there a way to solve this analytically?
gaussian-integral
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm trying to evaluate analytically, if it's possible, the Gaussian integral over the Rindler wedge, meaning:
$int^infty_0dx_1int_-x_1^x_1dx_0e^-b(x_1+a_1)^2e^b(x_0+a_0)^2$
Where $a_1,a_0$ are just real constants.
As you can see this is an integral over the infinite cone with an angle that goes from $theta=-pi/4 $ to $theta=pi/4$, where $theta=0$ placed on the $x_1$ axis.
I tried to integrate first $x_0$ and I got Erfi functions but after I tried to integrate the second parameter Mathematica couldn't figure out the answer.
Is there a way to solve this analytically?
gaussian-integral
I'm trying to evaluate analytically, if it's possible, the Gaussian integral over the Rindler wedge, meaning:
$int^infty_0dx_1int_-x_1^x_1dx_0e^-b(x_1+a_1)^2e^b(x_0+a_0)^2$
Where $a_1,a_0$ are just real constants.
As you can see this is an integral over the infinite cone with an angle that goes from $theta=-pi/4 $ to $theta=pi/4$, where $theta=0$ placed on the $x_1$ axis.
I tried to integrate first $x_0$ and I got Erfi functions but after I tried to integrate the second parameter Mathematica couldn't figure out the answer.
Is there a way to solve this analytically?
gaussian-integral
gaussian-integral
asked Sep 8 at 10:44
Noam Chai
1094
1094
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