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On the Schroedinger Representation for a Scalar Field on Curved Spacetime
General Relativity and Quantum Cosmology · Submitted 24 Jul 2002
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown that in this case, the measure is also Gaussian.
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The abstract, sentence by sentence
It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the usual Fock representation is described by a Gaussian measure. In this paper, arbitrary globally hyperbolic space-times and embeddings of the Cauchy surface are considered. The classical structures relevant for quantization are used for constructing the Schroedinger representation in the general case. It is shown that in this case, the measure is also Gaussian. Possible implications for the program of canonical quantization of midisuperspace models are pointed out.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s1 | In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the usual Fock representation is described by a Gaussian measure. | background 1.00 | 0.04 | 0.04 | asserted 1.00 |
| s2 | In this paper, arbitrary globally hyperbolic space-times and embeddings of the Cauchy surface are considered. | contribution 0.87 | 0.59 | 0.02 | asserted 0.89 |
| s3 | The classical structures relevant for quantization are used for constructing the Schroedinger representation in the general case. | method 0.94 | 0.86 | 0.05 | asserted 0.96 |
| s4 | It is shown that in this case, the measure is also Gaussian. | result 1.00 | 0.93 | 0.79 | asserted 1.00 |
| s5 | Possible implications for the program of canonical quantization of midisuperspace models are pointed out. | interpretation 0.94 | 0.73 | 0.06 | hedged possibility 0.93 |
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Original abstract
It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the usual Fock representation is described by a Gaussian measure. In this paper, arbitrary globally hyperbolic space-times and embeddings of the Cauchy surface are considered. The classical structures relevant for quantization are used for constructing the Schroedinger representation in the general case. It is shown that in this case, the measure is also Gaussian. Possible implications for the program of canonical quantization of midisuperspace models are pointed out.
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3 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 2 papers
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It leads [ref] ) to the description of the corresponding quantum field in terms of the Schrödinger wave functional $([ϕ()],t)$ satisfying the
Precanonical structure of the Schr\"odinger wave functional in curved space-time · Quantum scalar field on a curved space-time: canonical and precanonical description · 0.81
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The canonical ization of scalar theory in curved using the functional picture of QFT [ref] ) leads to the description of the ing um in s of the wave al $([ϕ()],t)$ which satisfies the al ive ħ∂_t = ∫ d √(-g) (ħ^2/2 g_00/g^2/ϕ()^2 - 1/2 g^ij ∂_iϕ()∂_jϕ() + V(ϕ) ) , where $g [equation] _μν(x)$ s the metric tensor, $g$ is the deinant of $g [equation] √(g_00)$ $N_i [equation] ^μ(x)$ are the Dirac matrices in curved space time which factorize the metric tensor $g [equation] ω_μ(x)$ is the covariant ive acting on -algebra-valued wave s, $ω_μ(x) = ω_μ_AB(x)^AB$ are the spin- matrices $$ (Fock–Ivanenko coefficients [ref] ), $_A$ are the constant tangent space Dirac matrices: $_A _B + _B _A [equation] ...$.
Schr\"odinger Functional of a Quantum Scalar Field in Static Space-Times from Precanonical Quantization · Introduction · 0.92
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