then
QUANTUM STRINGS AND RANDOM SURFACES
.
^
.
4n^n^
dr =
/l„
=
n^O
^
1 65
^ x(t) = dflo n d«„
n# 0
From this we derive:
I
^ J^I2 det' - dr
-SI/2
(9.53)
(where det'(x) is defined as the product of the nonzero eigenvalues).
Using the representation of the preceding section we get:
00
-lo g D e t'^ - ^ ^ =
L e\p(-4n^n^s/T^
ds
^ exp( —47r^n^s/T^) — 1
00
= j* —
exp( —47T^n^x) — 1
(e/T)2
= J —
exp( —47c^n^x) — 1
dx
— j Y, exp( — 47T^n^x) — 1
dx f
1
(£/T)2
_____
X [27(7TX)
- 1 -I- 0 ( e x p (- c /x )) l 4- const
T
T
=
- 2 log -
Syjn
e
(9.54)
QUANTUM STRINGS AND RANDOM SURFACES
.
^
.
4n^n^
dr =
/l„
=
n^O
^
1 65
^ x(t) = dflo n d«„
n# 0
From this we derive:
I
^ J^I2 det' - dr
-SI/2
(9.53)
(where det'(x) is defined as the product of the nonzero eigenvalues).
Using the representation of the preceding section we get:
00
-lo g D e t'^ - ^ ^ =
L e\p(-4n^n^s/T^
ds
^ exp( —47r^n^s/T^) — 1
00
= j* —
exp( —47T^n^x) — 1
(e/T)2
= J —
exp( —47c^n^x) — 1
dx
— j Y, exp( — 47T^n^x) — 1
dx f
1
(£/T)2
_____
X [27(7TX)
- 1 -I- 0 ( e x p (- c /x )) l 4- const
T
T
=
- 2 log -
Syjn
e
(9.54)