/sci/ - Science & Math

[Anonymous No.10498457]

Why is a berezin integral defined the way it is.

I understand that [math]\int d\theta_{a}\theta_{b} = \delta_{ab} [/math] but I lack a good physical understanding of why this should be or even of what this represents physically. I hasten to add that I understand how it follows from certain formal requirements of an integral of grassmann variables, but I have no physical sense for any of this.

[Anonymous No.10498948]

>>10498457
>i need the physical interpretation
Just drop academia and go work a factory job

[Anonymous No.10499414]

>>10498948
My thought is that there should be a nicer way of motivating the berezin integral, to ask for some physical significance really isn't that egregious considering that this is physics afterall

[Anonymous No.10499467]

You kind of have to feel around to understand these types of things. A physical, visceral understanding of the math does not necessarily translate to a physical explanation of it.
Try doing transformations and plugging in odd and even variables so you can feel out how it changes the shape. Get a good grasp on how it can warp around depending on what polynomials/variables you pick and where the vanishing point is.
There. You have a visceral, "physical" model of it that you can feel in your hands and play with.
You can draw it out in your head with coordinates if you really need to, but really you're just treating it like a machine and seeing what inputs yield what outputs. Don't even worry about what it represents in regards to fermions or physics or whatever. Just understand the math and that yields understanding of the physical behavior.