Is this lamda abstraction created as a generator of a recursive function?

In Lambda calculus, a recursive function $ f$ is obtained by

$ $ f = Y g $ $

where $ Y$ is the Y combinator and $ g$ is the generator of $ f$ i.e. $ f$ is a fixed point of $ g$ i.e. $ f == g f$ .

In The Scheme Programming Language, I saw an example implementing a recursive function $ f$ that sums the integers in a list:

(let ([sum (lambda (f ls)                   (if (null? ls)                      0                      (+ (car ls) (f f (cdr ls)))))]) (sum sum '(1 2 3 4 5)))  => 15 

What is the mathematical derivation that drives to create the lambda abstraction

 lambda (f ls)      (if (null? ls)          0         (+ (car ls) (f f (cdr ls)))) 

? It looks like a generator of $ f$ , but not entirely.

Thanks.

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