Quantum Scalar-Field Propagator in a Stochastic Gravitational-Plane Wave
A stochastic metric can appear in classical as well as in quantum gravity. We show that if the linearized stochastic Gaussian gravitational-plane wave has the frequency spectrum <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><sema...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/12/648 |
| Summary: | A stochastic metric can appear in classical as well as in quantum gravity. We show that if the linearized stochastic Gaussian gravitational-plane wave has the frequency spectrum <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>ω</mi><mrow><mn>4</mn><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>γ</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>), then the equal-time propagator of the scalar field behaves as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>p</mi><mrow><mo>−</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi>γ</mi></mrow></mfrac></mrow></msup></semantics></math></inline-formula> for large momenta. We discuss models of quantum-field theory where such anomalous behavior can appear. |
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| ISSN: | 2218-1997 |