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Volumn 39, Issue 2, 1989, Pages 438-451

Schrödinger-picture field theory in Robertson-Walker flat spacetimes

Author keywords

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Indexed keywords

EID: 0000477744 PISSN: 05562821 EISSN: None Source Type: Journal
DOI: 10.1103/PhysRevD.39.438 Document Type: Article

Times cited : (56)

References (13)

1
- 84927403541
- See, for example, R. Jackiw, in Current Algebra and Anomalies, edited by S. Treiman, R. Jackiw, B. Zumino, and E. Witten (World Scientific, Singapore/Princeton University Press, Princeton, NJ, 1985); R. Jackiw, in Theories and Experiments in High Energy Physics, edited by B. Kursunoglu, A. Perlmutter, and S. Widmayer (Plenum, New York, 1975).

2
- 0000988829
- (1985) Nucl. Phys. , vol.255 B , pp. 693
- Freese, K.¹ Hill, C.² Muller, M.³

3
- 0000535493
- The following references contain summaries of much of the existing work on field theories in curved-space backgrounds. The second also includes an extensive bibliography.
- (1975) Phys. Rep. , vol.19 C , pp. 297
- DeWitt, B.¹

4
- 0003517035
- Cambridge University Press, Cambridge, England
- (1982) Quantum Fields in Curved Space
- Birrell, N.D.¹ Davies, P.C.W.²

6
- 84927403539
- Although the time dependence of the oscillator frequencies makes it impossible to define a physical state | 0 > which is annihilated by the scrA ( k ; t ) for all times, we do expect the high-k modes to behave as in Minkowski space. More precisely, we should be able to define our vacuum state such that scrA (k; t ) | 0 > approx 0 for a-1k >>ȧ/ a. This condition on k ensures that the oscillator's frequency is large compared to the expansion rate, or equivalently, that the frequency varies adiabatically. For this range of k, we can sensibly define a state containing n particles of momentum k by operating on a vacuum state PSI n times with scrAdag(k): PSInapp Hn[ α (k) ] PSI, where Hn[ α ] denotes the Hermite polynomial of order n in α (k).

9
- 0000192757
- Quantum Field Theory in De Sitter Space: Renormalization by Point-Splitting
- (1978) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , vol.360 A , pp. 117
- Bunch, T.¹ Davies, P.C.W.²

10
- 33646044994
- (1977) Phys. Rev. D , vol.15 , pp. 2738
- Gibbons, G.¹ Hawking, S.²

11
- 0003864328
- edited by, A. Erdélyi, McGraw-Hill, New York
- (1954) Higher Transcendental Functions (Bateman Manuscript Project)

12
- 84927403538
- Strictly speaking, de Sitter space belongs to that class of spacetimes with no static in region, and hence without a well-defined | 0 , in > . However, as was shown in Sec. III, when working in Robertson-Walker flat coordinates, for fixed k, the space becomes quasi-Minkowski in the limit t -> - inf. Hence, a unique choice of positive and negative frequencies can be made, mode by mode, in the asymptotic past, thus defining an effective in a vacuum.

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