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Volumn 71, Issue 4, 2005, Pages

On the physical Hilbert space of loop quantum cosmology

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COSMOS; KINEMATICS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; QUANTUM MECHANICS; QUANTUM THEORY;

EID: 84927765452     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.044025     Document Type: Article
Times cited : (36)

References (37)
  • 1
    • 1842855789 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, England
    • C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2004), p. 480.
    • (2004) Quantum Gravity , pp. 480
    • Rovelli, C.1
  • 2
    • 84927757872 scopus 로고    scopus 로고
    • Thomas Thiemann, gr-qc/0110034
    • Thomas Thiemann, gr-qc/0110034.
  • 4
    • 84927757871 scopus 로고    scopus 로고
    • unpublished
    • Alejandro Perez (unpublished).
    • Perez, A.1
  • 7
    • 33646624346 scopus 로고
    • C. Rovelli and L. Smolin, Nucl. Phys. B442, 593 (1995); B456, 753(E) (1995).
    • (1995) Nucl. Phys. , vol.B456
  • 15
  • 20
    • 84927757870 scopus 로고    scopus 로고
    • note
    • This remains an open issue in the full theory of LQG. The master constraint approach [20] and the spin foam formulation [21] are current proposals to solve this problem.
  • 21
    • 84927757869 scopus 로고    scopus 로고
    • T. Thiemann, gr-qc/0305080
    • T. Thiemann, gr-qc/0305080.
  • 23
    • 84927757868 scopus 로고    scopus 로고
    • Donald Marolf, gr-qc/0011112
    • Donald Marolf, gr-qc/0011112.
  • 27
    • 84927757867 scopus 로고    scopus 로고
    • note
    • According to the general analysis of symmetric connections for arbitrary symmetry groups [25] the time component of the connection is a connection on a symmetry-reduced principal fiber bundle. This fiber bundle has as its gauge group the centralizer Zλ := ZG[λ(F)] where G is the gauge group of the theory, F is the isotropy group, and λ is a homomorphism from F to G. For our model the gauge group as well as the isotropy group is SU(2). The homomorphism λ is thus the identity map and the centralizer Zλ only contains the identity. The time component of the connection thus vanishes.
  • 30
    • 84927757866 scopus 로고    scopus 로고
    • note
    • The factor of 1/√E is added such that Hmatter agrees with the standard form of the matter Hamiltonian used in other formulations. Note that the constraint used here does not have units of energy hence the need for the extra factor.
  • 31
    • 84927757865 scopus 로고    scopus 로고
    • note
    • Halliwell [31] has considered the path integral for actions that are reparametrization invariant such as the action presented here. Starting with the path integral P = ∫ DADEDB exp[i ∫t′ t″ dt3EȦ + BH] the one form component B is gauge fixed to be constant in time and after including ghost terms to make the path integral independent of the gauge choice the path integral becomes P = ∫ dB(t″ - t′) ∫ DADE exp[i ∫t′t″ dt3EȦ + BH] which with the redefinition T = B(t″ - t′) and t = B(t - t′) takes on the form equivalent to the group averaging one P = ∫ dT ∫ DADE exp[i ∫0T dt̄3EȦ + H] = ∫ dT〈v″|e-iĤT|v′〉.
  • 33
    • 84927757864 scopus 로고    scopus 로고
    • note
    • Notice that the effect of the cosmological constant term depends on the orientation of the triad which is dynamical for our action.
  • 35
    • 17044436179 scopus 로고    scopus 로고
    • Ph.D. thesis, Pennsylvania State University
    • Joshua Willis, Ph.D. thesis, Pennsylvania State University, 2004.
    • (2004)
    • Willis, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.