TRZY DROGI DO
KWANTOWEJ GRAWITACJI.
Literatura
naukowa.
Niemal cała
powstała po roku 1991 literatura naukowa ważna dla fizyki teoretycznej dostępna
jest w archiwum internetowym http://xxx.lanl.gov/. Warto
podkreślić, że podczas gdy trzeba mieć wystarczające naukowe kwalifikacje, by
móc cokolwiek na tej stronie opublikować, to dostęp do niej jest praktycznie
nieograniczony. Artykuły ważne ze względy na zagadnienia poruszane w mojej
książce znaleźć można głównie w archiwach hep-th i gr-qc.
Odszukanie prac autorów, których wymieniam poniżej, pozwoli również prześledzić
rozwój dziedziny.
Kolejnym ważnym
źródłem wiedzy o fizycznych i matematycznych podstawach kwantowej grawitacji
jest strona internetowa Johna Baeza „This Week's Finds in Mathematical
Physics”, którą można znaleźć pod adresem http://math.ucr.edu/home/baez/TWF.html. Baez przygotował
również doskonałe wprowadzenie do ogólnej teorii względności, dostępne pod
adresem http://math.ucr.edu/home/baez/gr/gr.html.
Czytelnik zainteresowany historią i podstawowymi problemami kwantowej
grawitacji zapewne zainteresuje się również pracami Carlo Rovelliego 'Notes for
a brief history of quantum gravity' (gr-qc/0006061), 'Quantum spacetime - what do
we know?' (gr-qc/9903045) oraz moim artykułem 'The new universe around the next
corner' w Physics World, grudzień 1999
Większość prac
wymienianych niżej znaleźć można w archiwum xxx.lanl.gov. Bardziej
szczegółowa lista lektur dostępna jest na stronie Johna Baeza.
[od wydawcy –
ponieważ znajomość języka angielskiego jest i tak niezbędna do zapoznania się z
przywoływanymi niżej publikacjami, resztę bibliografii pozostawiamy w języku
angielskim]
Rozdział 2.
The discussion of the logic of observers inside the
universe is based on F. Markopoulou, 'The internal description of a causal set:
What the universe looks like from the inside', gr-qc/9811053, Commun. Math Phys. 211 (2000) 559-583
Rozdział 3.
The consistent histories interpretation is described
in R.B. Griffiths, Journal of Statistical Physics 36 (1984) 219;
R. Omnes, Journal of Statistical Physics 53 (1988) 893;
and M. Gell-Mann and J.B. Hartle in Complexity, Entropy, and the Physics of
Information, SFI Studies in the Sciences of Complexity, Vol. VIII, edited
by W. Zurek (Addison Wesley, Reading, MA, 1990). The criticisms of Kent and
Dowker are found in Fay Dowker and Adrian Kent, 'On the consistent histories
approach to quantum mechanics', Journal of Statistical Physics. 82 (1996)
1575. Gell-Mann and Hartle comment in 'Equivalent sets of histories and
multiple quasiclassical realms', gr-qc/9404013; J. B. Hartle, gr-qc/9808070.
The reformulation of the consistent histories formulation in terms of topos
theory, which emphasizes its relational aspects, is found in C.J. Isham and J.
Butterfield, 'Some possible roles for topos theory in quantum theory and
quantum gravity', gr-qc/9910005. Other relational approaches to quantum
cosmology are found in L. Crane, Journal of Mathematical Physics 36 (1995)
6180; L. Crane, in Knots and Quantum Gravity, edited by J. Baez (Oxford
University Press, New York, 1994); L. Crane, 'Categorical physics',
hep-th/9301061; F. Markopoulou, 'Quantum causal histories', hep-th/9904009, Class.
Quan. Grav. 17 (2000) 2059-2072; F. Markopoulou, ‘An insider's
guide to quantum causal histories', hep-th/9912137, Nucl. Phys. Proc. Suppl.
88 (2000) 308-313; C. Rovelli, 'Relational quantum
mechanics', quant-ph/9609002. International Journal of Theoretical Physics 35 (1996)
1637; L. Smolin, 'The Bekenstein bound, topological field theory and
pluralistic quantum cosmology', gr-qc/950806.
Rozdział 4.
The process formulation of quantum theory was
developed first by David Finkelstein, whose work is the main inspiration for
this chapter. It is described in David Ritz Finkelstein, Quantum Relativity:
A Synthesis of the ideas of Einstein and Heisenberg (Springer-Verlag,
1996). Rafael Sorkin has also pioneered the exploration of the role of
causality in quantum gravity.
Rozdziały 5-8.
This is all standard material in classical general
relativity and quantum field theory. Good introductions are N .D. Birrell and P
.C. W . Davies, Quantum Fields in Curved Spacetime (Cambridge
University Press, 1982); and Robert M. Wald, Quantum Field Theory in Curved
Space- time and Black Hole Thermodynamics (University of Chicago Press,
1994).
Rozdziały 9 i 10.
There are several expositions of loop quantum gravity
at a semi-popular or semi-technical level. They include Carlo Rovelli, 'Loop
quantum gravity', gr-qc/9710008, Carlo Rovelli, 'Quantum spacetime; what do we
know?', gr-qc/9903045; L. Smolin in Quantum Gravity and Cosmology, edited
by Juan Perez-Mercader et al. (World Scientific, 1992); L. Smolin, 'The
future of spin networks', in The Geometric Universe (1997), edited by
S.A. Huggett et al. (Oxford University Press, 1998), gr-qc/9702030. The
book by Rodolfo Gambini and Jorge Pullin, Loops, Knots, Gauge Theories and
Quantum Gravity (Cam- bridge University Press, 1996) describes their
approach to the subject.
The mathematically rigorous approach to loop quantum
gravity is presented in Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, Jose
Mourao and Thomas Thiemann, 'Quantization of diffeomorphism invariant theories
of connections with local degrees of freedom " Journal of Mathematical
Physics 36 (1995) 6456, gr-qc/9504018; Abhay Ashtekar,
Jerzy Lewandowski, 'Quantum field theory of geometry', hep-th/9603083; and T.
Thiemann, 'Quantum spin dynamics I and II', gr-qc/9606089, gr-qc/9606090, Classical
and Quantum Gravity 15 (1998) 839, 875 The original references for the
Ashtekar-Sen formalism are in A. Sen, Physics. Letters 8119 (1982) 89; International
Journal; of Theoretical Physics 21 (1982) 1;
A. Ashtekar, Physical Review Letters 57 (1986)
2244; A. Ashtekar, Physical. Review D36 (1987) 1587.
Rozdział 11.
This is all standard material in string theory, to
which Brian Greene's The Elegant Universe (Norton, 1999) is an excellent
introduction. The best textbook is J. Polchinksi, String Theory (Cambridge
University Press 1998).
Rozdział 12.
The original references for the holographic principle
are Gerard 't Hooft, 'Dimensional reduction in quantum gravity', gr-qc/9310006.
in Salan-festschrift, edited by A. Alo, J. Ellis, S. Randjbar-Daemi (World
Scientific, 1993); and Leonard Susskind, 'The world as a hologram',
hep-th/9409089, Journal of Mathematical Physics 36 (1995)
6377. Ideas closely related to the holographic principle were presented earlier
by L. Crane in 'Categorical physics', hep-th/9301061 and hep-th/9308126 in Knots'
and Quantum Gravity, edited by J. Baez (Oxford University Press, 1994) L.
Crane, 'Clocks and categories: is quantum gravity of Mathematical Physics 36 (1995)
6180, gr-qc/algebraic?' Journal 9504038.
The Bekenstein bound was proposed in J.D. Bekenstein Lettere
Nuovo Cimento 4 (1972) 737, Physical Review D7 2333 (1973),
Physical Review D9 (1974) 3292. Ted Jacobsons paper
deriving general relativity from the Bekenstein bound and
the laws of thermodynamics is “Thermodynamics of spacetime: the Einstein equation of
state' gr-qc/9504004 Physical Review Letters 75(1995). The
derivation of the Bekenstein bound in loopquantum gravity is in L. Smolin 'Linking
topological quantum field theory and nonperturbative quantum gravity',
gr-qc/9505028, Journal of Mathematical Physics 36 (1995)
6417. Another very promising version of the holographic principle was proposed
by Rafael Bousso in' A covariant entropy conjecture', hep-th/9905177, Journal
of High-Energy Physics, 9907 (1999) 0004; R.
Bousso, 'Holography in general space-times', hep-th/9906022, Journal of
High-Energy Physics 9906 (1999) 028. A related
theorem was proved in E. Flanagan, D. Marolf and R. Wald, hep-th/ 9908070. F.
Markopoulou and I proposed a background independent version in 'Holography in a
quantum spacetime', hep-th/9910146. In strong and weak holographic principles',
hep-th/0003056 I review the arguments for and against the different versions of
the principle.
Rozdział 13.
The view of the relationship between loop quantum
gravity and string theory is based on L. Smolin, 'Strings as perturbations of
evolving spin networks', hep-th/9801022; L. Smolin ,’A candidate for a
background independent formulation of M-theory', hep-th/9903166; L. Smolin,
'The cubic matrix model and a duality between strings and loops', hep-th/
006137.
There is an extensive literature on black holes in
both string theory and loop quantum gravity. A sample of string theory
papers is a A. Strominger and C. Vafa, Physics Letters 8379 (1996) 99,
hep-th/9601029; C.V. Johnson, R.R. Khuri and R.C. Myers, Physics Letters 8378 (1996) 78,
hep-th/9603061; J.M. Maldacena and A. Strominger, Physical Review Letters 77 (1996) 428,
hep-th/9603060; C.G. Callan and Maldacena, Nuclear Physics 8472 (1996) 591,
hep-th/9602043 Horowitz and A. Strominger, Physical Review Letters 77 (1996)
hep-th/9602051.
A sample of papers on black holes in loop quantum
gravity is: Carlo Rovelli, 'Black hole entropy from loop quantum gravity',
gr-qc/9603063, Physical Review Letters 77 (1996)
3288; Marcelo Barreira, Mauro Carfora and Carlo Rovelli, 'Physics with
nonperturbative quantum gravity: radiation from a quantum black hole',
gr-qc/9603064, General Relativity and Gravity 28 (1996)
1293; Kirill Krasnov, 'On quantum statistical mechanics of a Schwarzschild
black hole', gr-qc/9605047, General Relativity and Gravity 30 (1998) 53;
Kirill Krasnov, 'Quantum geometry and thermal radiation from black holes',
gr-qc/9710006, Classical and Quantum Gravity 16 (1999) 563;
A. Ashtekar, J. Baez and K. Krasnov, 'Quantum geometry of isolated horizons and
black hole entropy', gr-qc/0005126; A. Ashtekar, J. Baez, A. Corichi and K.
Krasnov, 'Quantum geometry and black hole entropy', gr-qc/9710007, Physical
Review Letters 80 (1998) 904.
Non-commutative geometry is introduced in the book by
Alain Non-commutative Geometry (Academic Press, 1994).
Rozdział 14.
The material described here is mostly related to my
book, Life of the Cosmos. The discussion of space is drawn from S. Kauffman
and L. Smolin, 'Combinatorial dynamics in quantum gravity', hep-th/9809161.