02 | October | 2015 | Physics Town

You Could Have Invented Monads! (And Maybe You Already Have.)

Show that lift f * lift g = lift (f.g)

——————————

The meaning of f' * g' should be (bind f') . (bind g') instead.

f' * g' = (bind f') . (bind g') lift f = unit . f f' = lift f

(lift f * lift g) (x, xs) = (bind (lift f)) . (bind (lift g)) (x, xs) = bind (lift f) (bind (lift g) (x, xs)) = bind (lift f) (gx, xs++gs) where (gx, gs) = (lift g) x


= bind (lift f) (gx, xs++gs)
  where
    (gx, gs) = (g x, "")
= bind (lift f) (g x, xs)
= (fx, xs++fs)
  where
    (fx, fs) = (lift f) gx
  
= (fx, xs++fs)
  where
    (fx, fs) = (f gx, "")
= (fx, xs)
  where
    (fx, fs) = (f (g x), "")

= (f (g x), xs)

bind f' (gx,gs) = (fx, gs++fs) where (fx,fs) = f' gx


bind (lift (f.g)) (x, xs)
= (hx, xs++hs)
  where
    (hx, hs) = (lift (f.g)) x
= (hx, xs++hs)
  where
    (hx, hs) = ((f.g) x, "")

= ((f (g x)), xs)

— Me@2015.07.19 11:04 PM

A First Course in String Theory

14.3 Massive level in the open superstring.

~~~

What is the difference between “open bosonic string” and “open superstring”?

p.320 “With our conventions, these are world-sheet fermionic states that are now recognized to be states of spacetime fermions. The resulting, truncated sector is called the R- sector.”

NS(+): Equation (14.38) $\left(\alpha' M^2 = 1, N^\perp = \frac{3}{2}\right)$ :