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1

Landsman, N. P. "Against the Wheeler - DeWitt equation." Classical and Quantum Gravity 12, no. 12 (December 1, 1995): L119—L123. http://dx.doi.org/10.1088/0264-9381/12/12/003.

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2

Kruglov, Sergey I., and Mir Faizal. "Wave function of the universe from a matrix-valued first-order formalism." International Journal of Geometric Methods in Modern Physics 12, no. 04 (April 2015): 1550050. http://dx.doi.org/10.1142/s0219887815500504.

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In this paper, the Wheeler–DeWitt equation in full superspace formalism will be written in a matrix-valued first-order formalism. We will also analyze the Wheeler–DeWitt equation in minisuperspace approximation using this matrix-valued first-order formalism. We will note that this Wheeler–DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyze the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler–DeWitt equation in this matrix-valued first-order formalism. This will lead to a possible solution for the cosmological constant problem.
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3

Barvinsky, Andrei O., and Claus Kiefer. "Wheeler-DeWitt equation and Feynman diagrams." Nuclear Physics B 526, no. 1-3 (August 1998): 509–39. http://dx.doi.org/10.1016/s0550-3213(98)00349-6.

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4

Faizal, Mir. "Deformation of the Wheeler–DeWitt equation." International Journal of Modern Physics A 29, no. 20 (August 6, 2014): 1450106. http://dx.doi.org/10.1142/s0217751x14501061.

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In this paper, we will analyze the consequences of deforming the canonical commutation relations consistent with the existence of a minimum length and a maximum momentum. We first generalize the deformation of first quantized canonical commutation relation to second quantized canonical commutation relation. Thus, we arrive at a modified version of second quantization. A modified Wheeler–DeWitt equation will be constructed by using this deformed second quantized canonical commutation relation. Finally, we demonstrate that in this modified theory the big bang singularity gets naturally avoided.
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5

Pavšič, Matej. "Klein–Gordon–Wheeler–DeWitt–Schrödinger equation." Physics Letters B 703, no. 5 (September 2011): 614–19. http://dx.doi.org/10.1016/j.physletb.2011.08.041.

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6

Andrzej Glinka, Lukasz. "Novel Solution of Wheeler-DeWitt Theory." Applied Mathematics and Physics 2, no. 3 (June 6, 2014): 73–81. http://dx.doi.org/10.12691/amp-2-3-3.

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7

BELINCHÓN, JOSÉ ANTONIO. "WHEELER–DEWITT EQUATION WITH VARIABLE CONSTANTS." International Journal of Modern Physics D 11, no. 04 (April 2002): 527–44. http://dx.doi.org/10.1142/s0218271802001871.

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In this paper we study how all the physical "constants" vary in the framework described by a model in which we have taken into account the generalize conservation principle for its stress-energy tensor. This possibility enable us to take into account the adiabatic matter creation in order to get rid of the entropy problem. We try to generalize this situation by contemplating multi-fluid components. To validate all the obtained results we explore the possibility of considering the variation of the "constants" in the quantum cosmological scenario described by the Wheeler–DeWitt equation. For this purpose we explore the Wheeler–DeWitt equation in different contexts but from a dimensional point of view. We end by presenting the Wheeler–DeWitt equation in the case of considering all the constants varying. The quantum potential is obtained and the tunneling probability is studied.
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8

Chakraborty, Subenoy. "Solutions of the Wheeler-DeWitt equation." International Journal of Theoretical Physics 31, no. 2 (February 1992): 289–302. http://dx.doi.org/10.1007/bf00673259.

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9

BISWAS, S., A. SHAW, and D. BISWAS. "SCHRÖDINGER–WHEELER–DEWITT EQUATION IN MULTIDIMENSIONAL COSMOLOGY." International Journal of Modern Physics D 10, no. 04 (August 2001): 585–93. http://dx.doi.org/10.1142/s0218271801001372.

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We study multidimensional cosmology to obtain the wavefunction of the universe using wormhole dominance proposal. Using a prescription for time we obtain the Schrödinger–Wheeler–DeWitt equation without any reference to WD equation and WKB ansatz for WD wavefunction. It is found that the Hartle–Hawking or wormhole-dominated boundary conditions serve as a seed for inflation as well as for Gaussian type ansatz to Schrödinger–Wheeler–DeWitt equation.
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10

BISWAS, S., A. SHAW, and B. MODAK. "TIME IN QUANTUM GRAVITY." International Journal of Modern Physics D 10, no. 04 (August 2001): 595–606. http://dx.doi.org/10.1142/s0218271801001384.

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The Wheeler–DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting from Wheeler–DeWitt equation and WKB ansatz for the WD wavefunction. The approach has some drawbacks. In this work, we obtain the time-contained Schrödinger–Wheeler–DeWitt equation without using the WD equation and the WKB ansatz for the wavefunction. We further show that a Gaussian ansatz for SWD wavefunction is consistent with the Hartle–Hawking or wormhole dominance proposal boundary condition. We thus find an answer to the small scale boundary conditions.
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11

Cianfrani, Francesco, and Jerzy Kowalski-Glikman. "Wheeler–DeWitt equation and AdS/CFT correspondence." Physics Letters B 725, no. 4-5 (October 2013): 463–67. http://dx.doi.org/10.1016/j.physletb.2013.07.034.

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12

Kubota, Takahiro, Tatsuya Ueno, and Naoto Yokoi. "Wheeler–DeWitt equation in AdS/CFT correspondence." Physics Letters B 579, no. 1-2 (January 2004): 200–204. http://dx.doi.org/10.1016/j.physletb.2003.10.085.

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13

POLLOCK, M. D. "GRAVITATIONAL THERMODYNAMICS AND THE WHEELER–DEWITT EQUATION." International Journal of Modern Physics D 20, no. 01 (January 2011): 23–42. http://dx.doi.org/10.1142/s0218271811018603.

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In a previous paper, we have derived the Hawking temperature T H = 1/8πM for a Schwarzschild black hole of mass M, starting from the Wheeler–DeWitt for the wave function Ψ on the apparent horizon, due to Tomimatsu. Here we discuss the derivation of this result in greater detail, with particular regard to the Euclideanization procedure involved and the boundary conditions on the horizon. Further, analysis of the de Sitter space-time generated by a cosmological constant Λ yields the temperature [Formula: see text] found by Gibbons and Hawking, which thus vindicates the method. The emission of radiation occurs with preservation of unitarity, and hence entropy, which is substantiated by a global thermodynamical argument in the case of the black hole.
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14

BENINI, RICCARDO, and GIOVANNI MONTANI. "MIXMASTER DYNAMICS IN THE WHEELER-DEWITT FRAMEWORK." International Journal of Modern Physics A 23, no. 08 (March 30, 2008): 1244–47. http://dx.doi.org/10.1142/s0217751x08040159.

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In this work we present an analysis of the Mixmaster model in the Wheeler-DeWitt framework. After a brief review of the classical evolution, several aspects of the semi-classical and of the quantum dynamics are discussed: the most important results we will present are a possible operator ordering obtained from the semi-classical analysis and the full characterization of the quantum dynamics in Misner-Chitré like variables.
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15

Pavlov, A. E. "Intrinsic time in Wheeler–DeWitt conformal superspace." Gravitation and Cosmology 23, no. 3 (July 2017): 208–18. http://dx.doi.org/10.1134/s0202289317030124.

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16

Bojowald, Martin. "Loop quantum cosmology: III. Wheeler-DeWitt operators." Classical and Quantum Gravity 18, no. 6 (February 27, 2001): 1055–69. http://dx.doi.org/10.1088/0264-9381/18/6/307.

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17

ANADA, HAJIME, TETSURO KITAZOE, and YOSHIHIKO MIZUMOTO. "PERTURBATIVE APPROACH TO THE WHEELER-DEWITT EQUATION." Modern Physics Letters A 08, no. 01 (January 10, 1993): 45–52. http://dx.doi.org/10.1142/s0217732393000052.

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A perturbation method is introduced to solve the Wheeler-DeWitt equation approximately. The chaotic inflationary model is used to demonstrate how the perturbative solutions approximate the numerical ones calculated with the aid of a computer.
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18

McGuigan, Michael. "Third quantization and the Wheeler-DeWitt equation." Physical Review D 38, no. 10 (November 15, 1988): 3031–51. http://dx.doi.org/10.1103/physrevd.38.3031.

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19

Yurov, Artyom V., Artyom V. Astashenok, and Valerian A. Yurov. "The big trip and Wheeler-DeWitt equation." Astrophysics and Space Science 342, no. 1 (August 29, 2012): 1–7. http://dx.doi.org/10.1007/s10509-012-1211-6.

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20

Adi, E., and S. Solomon. "The solution to Wheeler-DeWitt is eight." Physics Letters B 336, no. 2 (September 1994): 152–56. http://dx.doi.org/10.1016/0370-2693(94)01001-3.

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21

Faizal, Mir, Ahmed Farag Ali, and Saurya Das. "Discreteness of time in the evolution of the universe." International Journal of Modern Physics A 32, no. 10 (April 6, 2017): 1750049. http://dx.doi.org/10.1142/s0217751x1750049x.

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In this paper, we will first derive the Wheeler–DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended structure, their extended structure will limits the resolution to which this generalized geometry can be defined. We will demonstrate that this will deform the Wheeler–DeWitt equation for the generalized geometry. We analyze such a deformed Wheeler–DeWitt equation in the minisuperspace approximation, and observe that this deformation can be used as a solution to the problem of time. This is because this deformation gives rise to time crystals in our universe due to the spontaneous breaking of time reparametrization invariance.
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22

Fernandes, Alexandre Da Silva. "Cosmologia quântica de Wheeler-DeWitt: suas tentativas e falhas." e-Boletim da Física 6, no. 1 (April 17, 2017): 1–3. http://dx.doi.org/10.26512/e-bfis.v6i1.9797.

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A cosmologia quântica de Wheeler-DeWitt é descrita a partir da formulação hamiltoniana da Relatividade Geral (RG) proposta em 1962 por Arnowitt, Deser e Misner (ADM) e utilizando a interpretação da física quântica de Everett-Wheeler. Ao longo das décadas muita pesquisa foi feita com essa teoria. Contudo, ela apresenta alguns problemas, como falta de evidências da física quântica de Everett-Wheeler e interpretação da função de onda cosmológica, dentre outras. Um breve histórico da RG e da cosmologia é feito, com foco na formulação de Wheeler e DeWitt, apresentando suas dificuldades e citando algumas soluções que foram entregues à comunidade científica com o passar do tempo.
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23

Ghosh, Saumya, Sunandan Gangopadhyay, and Prasanta K. Panigrahi. "Anisotropic quantum cosmology with minimally coupled scalar field." Modern Physics Letters A 34, no. 34 (November 5, 2019): 1950283. http://dx.doi.org/10.1142/s0217732319502833.

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In this paper, we perform the Wheeler–DeWitt quantization for Bianchi type I anisotropic cosmological model in the presence of a scalar field minimally coupled to the Einstein–Hilbert gravity theory. We also consider the cosmological (perfect) fluid to construct the matter sector of the model whose dynamics plays the role of time. After obtaining the Wheeler–DeWitt equation from the Hamiltonian formalism, we then define the self-adjointness relations properly. Doing that, we proceed to get a solution for the Wheeler–DeWitt equation and construct a well-behaved wave function for the universe. The wave packet is next constructed from a superposition of the wave functions with different energy eigenvalues together with a suitable weight factor which renders the norm of the wave packet finite. It is then concluded that the Big-Bang singularity can be removed in the context of quantum cosmology.
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24

POLLOCK, M. D. "ERRATUM: "GRAVITATIONAL THERMODYNAMICS AND THE WHEELER–DEWITT EQUATION"." International Journal of Modern Physics D 20, no. 12 (November 25, 2011): 2447–48. http://dx.doi.org/10.1142/s0218271811020494.

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25

Pollock, M. D. "Erratum: "Gravitational thermodynamics and the Wheeler-DeWitt equation"." International Journal of Modern Physics D 24, no. 07 (May 27, 2015): 1592002. http://dx.doi.org/10.1142/s0218271815920029.

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26

POLLOCK, M. D. "ON THE WHEELER-DEWITT EQUATION FOR BLACK HOLES." International Journal of Modern Physics D 03, no. 03 (September 1994): 579–91. http://dx.doi.org/10.1142/s0218271894000721.

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Integration over the angular coordinates of the evaporating, four-dimensional Schwarzschild black hole leads to a two-dimensional action, for which the Wheeler-DeWitt equation has been found by Tomimatsu, on the apparent horizon, where the Vaidya metric is valid, using the Hamiltonian formalism of Hajicek. For the Einstein theory of gravity coupled to a massless scalar field ζ, the wave function Ψ obeys the Schrödinger equation [Formula: see text], where M is the mass of the hole. The solution is [Formula: see text], where k2 is the separation constant, and for k2>0 the hole evaporates at the rate Ṁ=−k2/4M2, in agreement with the result of Hawking. Here, this analysis is generalized to the two-dimensional theory [Formula: see text], which subsumes the spherical black holes formulated in D≥4 dimensions, when A = ½ (D - 2) (D - 3)ϕ2 (D - 4)/(D - 2), B=2(D−3)/(D−2), C=1, and also the twodimensional black hole identified by Witten and by Gautam et al., when A=4/α′, B=2, C=1/8π, c=+8/α′ being (minus) the central charge. In all cases an analogous Schrödinger equation is obtained. The evaporation rate is [Formula: see text] when D≥4 and [Formula: see text] when D=2. Since Ψ evolves without violation of unitarity, there is no loss of information during the evaporation process, in accord with the principle of black-hole complementarity introduced by Susskind et al. Finally, comparison with the four-dimensional, cosmological Schrödinger equation, obtained by reduction of the ten-dimensional heterotic superstring theory including terms [Formula: see text], shows in both cases that there is a positive semi-definite potential which evolves to zero, this corresponding to the ground state, which is Minkowski space.
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27

Seo, Min-Seok. "Eternal inflation in light of Wheeler-DeWitt equation." Journal of Cosmology and Astroparticle Physics 2020, no. 11 (November 5, 2020): 007. http://dx.doi.org/10.1088/1475-7516/2020/11/007.

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28

Mostafazadeh, Ali. "Two-component formulation of the Wheeler–DeWitt equation." Journal of Mathematical Physics 39, no. 9 (September 1998): 4499–512. http://dx.doi.org/10.1063/1.532522.

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29

Mazzitelli, Francisco D. "Midisuperspace-induced corrections to the Wheeler-DeWitt equation." Physical Review D 46, no. 10 (November 15, 1992): 4758–60. http://dx.doi.org/10.1103/physrevd.46.4758.

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30

Barrett, John W., and Louis Crane. "An algebraic interpretation of the Wheeler - DeWitt equation." Classical and Quantum Gravity 14, no. 8 (August 1, 1997): 2113–21. http://dx.doi.org/10.1088/0264-9381/14/8/011.

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31

Anada, Hajime, Tetsuro Kitazoe, and Yoshihiko Mizumoto. "ERRATA: PERTURBATIVE APPROACH TO THE WHEELER-DEWITT EQUATION." Modern Physics Letters A 08, no. 11 (April 10, 1993): 1065–66. http://dx.doi.org/10.1142/s0217732393002555.

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32

HORIGUCHI, TSUTOMU. "QUANTUM POTENTIAL INTERPRETATION OF THE WHEELER-DeWITT EQUATION." Modern Physics Letters A 09, no. 16 (May 30, 1994): 1429–43. http://dx.doi.org/10.1142/s021773239400126x.

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We apply Bohm’s quantum potential interpretation to quantum cosmology. We study closed, flat and open minisuperspace models by introducing “extended” Robertson-Walker time which exists not only in classically allowed region but also in classically forbidden region. It is shown that how the classical universe emerges from the quantum area. We also discuss briefly quantum potential interpretation of quantum geometrodynamics based on the Arnowitt-Deser-Misner canonical formalism.
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33

Woodard, R. P. "Enforcing the Wheeler-DeWitt constraint the easy way." Classical and Quantum Gravity 10, no. 3 (March 1, 1993): 483–96. http://dx.doi.org/10.1088/0264-9381/10/3/008.

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34

Norbury, John W. "From Newton's laws to the Wheeler-DeWitt equation." European Journal of Physics 19, no. 2 (March 1, 1998): 143–50. http://dx.doi.org/10.1088/0143-0807/19/2/007.

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35

Giulini, Domenico, and Claus Kiefer. "Wheeler-DeWitt metric and the attractivity of gravity." Physics Letters A 193, no. 1 (September 1994): 21–24. http://dx.doi.org/10.1016/0375-9601(94)00651-2.

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36

Carroll, R. "Metric fluctuations, entropy, and the Wheeler-deWitt equation." Theoretical and Mathematical Physics 152, no. 1 (July 2007): 904–14. http://dx.doi.org/10.1007/s11232-007-0076-2.

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37

ISHIKAWA, ATUSHI, and TOSHIKI ISSE. "THE STABILITY OF THE MINISUPERSPACE." Modern Physics Letters A 08, no. 36 (November 30, 1993): 3413–27. http://dx.doi.org/10.1142/s0217732393003834.

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The stability of the minisuperspace model of the early universe is studied by solving the Wheeler-DeWitt equation numerically. We consider a system of Einstein gravity with a scalar field. When we solve the Wheeler-DeWitt equation, we pick up some inhomogeneous wave modes from infinite wave modes adequately: degrees of freedom of the superspace are restricted to finite. We show that the minisuperspace is stable when a scale factor (a) of the universe is a few times larger than the Planck length, while it becomes unstable when a is comparable to the Planck length.
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38

SAVCHENKO, V. A., T. P. SHESTAKOVA, and G. M. VERESHKOV. "QUANTUM GEOMETRODYNAMICS OF THE BIANCHI-IX MODEL IN EXTENDED PHASE SPACE." International Journal of Modern Physics A 14, no. 28 (November 10, 1999): 4473–90. http://dx.doi.org/10.1142/s0217751x99002098.

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A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noninvariant and thus consistent with the observation conditions of a closed universe, by that being considerably distinguished from the traditional Wheeler–DeWitt one. For the Bianchi-IX cosmological model it is shown that a normalizable wave function of the universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Schrödinger equation. The Wheeler–DeWitt quantum geometrodynamics is represented a singular, BRST-invariant solution to the Schrödinger equation having no property of normalizability.
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39

Vázquez-Báez, V., and C. Ramírez. "Quantum Cosmology of Quadratic f(R) Theories with a FRW Metric." Advances in Mathematical Physics 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/1056514.

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We study the quantum cosmology of a quadratic fR theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.
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40

VISSER, MATT. "WHEELER WORMHOLES AND TOPOLOGY CHANGE: A MINISUPERSPACE ANALYSIS." Modern Physics Letters A 06, no. 29 (September 21, 1991): 2663–67. http://dx.doi.org/10.1142/s0217732391003109.

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Wheeler's wormholes are analyzed within the context of a particular minisuperspace approximation. In this approximation the Wheeler-DeWitt equation describing a wormhole is exactly solvable and the quantum mechanical wavefunction of a wormhole can be explicitly exhibited. Calculation shows that the throat of a minisuperspace Wheeler wormhole is stabilized against collapse by quantum mechanical effects: The radius of the throat has an expectation value of order the Planck length. Implications of this result with respect to the process of quantum gravitational topology change are discussed. In particular it is argued that the putative stability of minisuperspace Wheeler wormholes—if it persists beyond the minisuperspace approximation—might serve to suppress fluctuations in topology.
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41

Pavšič, Matej. "Wheeler–DeWitt equation in five dimensions and modified QED." Physics Letters B 717, no. 4-5 (October 2012): 441–46. http://dx.doi.org/10.1016/j.physletb.2012.09.034.

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42

Dias, J. P., and M. Figueira. "The Cauchy problem for a nonlinear Wheeler-DeWitt equation." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 10, no. 1 (January 1993): 99–107. http://dx.doi.org/10.1016/s0294-1449(16)30223-2.

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43

CAPOZZIELLO, SALVATORE, and RUGGIBRO DE RITIS. "MINISUPERSPACE AND WHEELER-DEWITT EQUATION FOR STRING DILATON COSMOLOGY." International Journal of Modern Physics D 02, no. 03 (September 1993): 373–79. http://dx.doi.org/10.1142/s021827189300026x.

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In connection with the string-dilaton cosmology, we construct a bidimensional mini-superspace model in which we write down and integrate the Wheeler-DeWitt equation. The solution and its probabilistic interpretation contains the feature of the scale factor duality.
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44

Pollock, M. D. "The Wheeler–Dewitt Equation for the Superstring World Sheet." International Journal of Modern Physics D 06, no. 01 (February 1997): 91–105. http://dx.doi.org/10.1142/s0218271897000078.

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The Wheeler–DeWitt equation for the wave function ψ is obtained from the two-dimensional world-sheet action for the bosonic string and the superstring, including higher-derivative terms, as the Schrödinger equation i ∂ ψ/ ∂τ = V(τ)ψ. The potential is given by the rate at which the world-sheet area is swept out, V(τ) = dA(τ)/dτ, and is positive semi-definite, allowing the existence of a ground state, corresponding to the absence of the string, with a non-vanishing probability density ψ ψ*. Integration of this equation yields the solution [Formula: see text], where [Formula: see text] is the action, minus the higher-derivative terms [Formula: see text] (and terms involving ∊ab in the case of the superstring), which, however, are constrained to vanish semi-classically, being constructed from the square of the equation of motion for the bosonic coordinates XA derived from [Formula: see text] alone. This path-integral expression for ψ is consistent with the operator replacements for the canonical momenta used in its derivation, and forms the basis of the approach due to Polyakov of summing over random surfaces. Comparison is made with the Schrödinger equations derived previously from the reduced, four-dimensional effective action for the heterotic superstring, and for the Schwarzschild black hole (by Tomimatsu), where the potential is also positive semi-definite, being (twice) the total mass of the Universe and the mass of the black hole, respectively, showing the unity of the method.
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45

Parentani, R. "Interpretation of the solutions of the Wheeler-DeWitt equation." Physical Review D 56, no. 8 (October 15, 1997): 4618–24. http://dx.doi.org/10.1103/physrevd.56.4618.

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46

Lü, H., J. Maharana, S. Mukherji, and C. N. Pope. "Cosmological solutions,p-branes, and the Wheeler-DeWitt equation." Physical Review D 57, no. 4 (February 15, 1998): 2219–29. http://dx.doi.org/10.1103/physrevd.57.2219.

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47

Brotz, Thorsten. "Quantization of black holes in the Wheeler-DeWitt approach." Physical Review D 57, no. 4 (February 15, 1998): 2349–62. http://dx.doi.org/10.1103/physrevd.57.2349.

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48

Soo, C. "Three-geometry and reformulation of the Wheeler–DeWitt equation." Classical and Quantum Gravity 24, no. 6 (March 6, 2007): 1547–55. http://dx.doi.org/10.1088/0264-9381/24/6/011.

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49

Garattini, Remo. "Extracting the Maxwell charge from the Wheeler–DeWitt equation." Physics Letters B 666, no. 2 (August 2008): 189–92. http://dx.doi.org/10.1016/j.physletb.2008.06.070.

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50

Kim, Sang Pyo. "New asymptotic expansion method for the Wheeler-DeWitt equation." Physical Review D 52, no. 6 (September 15, 1995): 3382–91. http://dx.doi.org/10.1103/physrevd.52.3382.

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