IL NUOVO CISIENT0 VoL. 93 A, N. 3 1 Giugno 1986

Quantum Corrections in Kaluza-Klein Theory.

R. D~LB0V~0 and R. 0. WJ~B~

Department o] Physics, University o/ Tasmania - Hobart, Australia, 7005

(Nuovo Gimento A, 92, 347 (1986))

The factor of 2E 2 in eq. (16a) is incorrect and should be replaced by 64E a. This effects eqs. (16b), (17) and the equation for V~(r, ~ ) in the long-range limit and the ex- pression given for the gravitational potential in the following paragraph, all of which should have 32E 4 in place of E ~.

In equation (30), the factor 238 should be changed to 2380 and in (32) 970 replaced by 961.

Due to an incorrect interaction Lagrangian given in appendix B, namely (B.2), which should be omitted entirely, the vertex rule given in (B.3) should read

Hence the scattering corrections, eqs. (33), are modified to read

(33)

(33')

(33")

-h I d~q (p. q)~(k" q)~(4 ~ + p" 4)~(q ~ -- k" 4) 2 T['] ~ -- i ~ (3M~) v'(~-~4 (42_ M~)2(q~ ~_ 2p'q -- M~)(42- 2k 'q- - M~) '

f daq (p. q)~(~, q)S(q2 -- p . q)~(4 ~ - k" q)2 T'~o~- iZ, (3~:)-, (2~)~-- (4~- ~ : 2 - V . ~ - ~,~)~-- 2~.q -- ~:)

T"[ ' ] , - - - i Z (3M~)-'- n

�9 ~_ddq (p.q)(k.q)(q2_~_ p.q)(q2_ k . q ) ( p . k _ p . q ) 2 ( p . k Jr k.q)2

j(2.). (q~- ~)~(4 ~- 2~.q- ~) (~u ~ . q : ~ ~ ~::~-- ~)"

Then, in the following sentence, which reads (~ The leading part of the result is of order (k.p) lo ... ,, (k.p) 1~ should be replaced by (k.p) ~. Finally eq. (34) and the following line should be changed to

468617 ]Ss](2gR) s ( p ' k ) ' l 1 A (34) e T,o,~ 105 8! (36.)2 ~ 2 - l ] , ~ 2 '

where B s comes from the sum over massive modes,

(n2) ~-e as l -~2~) . n

288