Los Vínculos e Intercambios de Favores.

and work only with the rest of variables, This new Poisson bracket coincides with Dirac bracket for the physically significant variables X^.Pi (1=1,2).

Dirac’s scheme can be applied to any well-behaved hyper- N

surface ( not necessarily of constant curvature ) in F , Also, it

is applicable to cases in which more than one geometrical constraint are involved. The applicability of Dirac’s scheme to V ^ and to the other cases indicated to in this paragraph constitutes a verification of Dirac’s "non-rigorous" rules,

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GENERAL REMARKS

We have c o n fin e d our c o n s id e r a t io n s in t h i s t h e s i s to Riemannian m a n ifo ld s . I t i s e a s y , h ow ever, to show th a t m ost o f our r e s u l t s can fo r m a lly b e ex ten d e d to m a n ifo ld s w ith i n d e f i n i t e m e t r i c s . Examples o f such a re th e de S i t t e r s p a c e s . T hese a re 4 -d im e n s io n a l sp a c e s o f c o n s ta n t cu r v a tu r e K b u t o f i n d e f i n i t e

m e tr ic ds^ = (dx^dx^ - dx^dx^)/Cl + ^ (x^x^ - x^ x^ )]^ ( i =1,2,3) [ 4 8 ] , The i n f i n i t e s i m a l g e n e r a to r s o f th e de S i t t e r groups (th e

i n f i n i t e s i m a l m otion s o f th e de S i t t e r s p a c e s ) a re e a s i l y deduced. T hese ten d to th e g e n e r a to r s o f th e P o in c a r e group i n th e l i m i t K 0 , The form al v a l i d i t y o f most o f our r e s u l t s f o r th e de S i t t e r s p a c e s s u g g e s t s th a t i t m igh t be p o s s i b l e to m od ify and e x te n d our tr e a tm e n t to t a c k l e th e problem, o f q u a n t iz a t io n in th e de S i t t e r c o s m o lo g ic a l m odels o f th e u n iv e r s e .

A nother problem t o p u rsu e i s th e e v a lu a t io n o f th e s p e c t r a l

N . . '

f u n c t io n s o f p h y s i c a l o b s e r v a b le s in CC . T hese p r o v id e th e d i r e c t l i n k b etw een th e th e o r y and e x p e r im e n ta lly m easurab le q u a n t i t i e s such as e x p e c t a t io n v a lu e s and p r o b a b i l i t y d i s t r i b u t i o n s o f p h y s ic a l

o b s e r v a b le s .

F i n a l l y , we would l i k e t o draw th e r e a d e r ’s a t t e n t i o n to some u s e f u l papers w hich d e a l w it h q u a n t iz a t io n i n Riem annian mani­ f o l d s or w ith r e l a t e d a s p e c t s . T hese a re r e f e r e n c e s [ 4 9 - 5 7 ] .