{"title":"标量场在黎曼和伪黎曼扩展度量中的薛定谔演化","authors":"Z. Haba","doi":"arxiv-2312.07677","DOIUrl":null,"url":null,"abstract":"We study the quantum field theory (QFT) of a scalar field in the\nSchr\\\"odinger picture in the functional formulation. We derive a formula for the evolution kernel in a flat expanding metric. We\ndiscuss a transition between Riemannian and pseudoRiemannian metrics (signature\ninversion). We express the real time Schr\\\"odinger evolution by the Brownian\nmotion (Feynman-Kac formula). We discuss the Feynman integral for a scalar\nfield in a radiation background. We show that the unitary Schr\\\"odinger\nevolution for positive time can go over for negative time into a dissipative\nevolution described by diffusive paths.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Schrödinger evolution of a scalar field in Riemannian and pseudoRiemannian expanding metrics\",\"authors\":\"Z. Haba\",\"doi\":\"arxiv-2312.07677\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the quantum field theory (QFT) of a scalar field in the\\nSchr\\\\\\\"odinger picture in the functional formulation. We derive a formula for the evolution kernel in a flat expanding metric. We\\ndiscuss a transition between Riemannian and pseudoRiemannian metrics (signature\\ninversion). We express the real time Schr\\\\\\\"odinger evolution by the Brownian\\nmotion (Feynman-Kac formula). We discuss the Feynman integral for a scalar\\nfield in a radiation background. We show that the unitary Schr\\\\\\\"odinger\\nevolution for positive time can go over for negative time into a dissipative\\nevolution described by diffusive paths.\",\"PeriodicalId\":501275,\"journal\":{\"name\":\"arXiv - PHYS - Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2312.07677\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2312.07677","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Schrödinger evolution of a scalar field in Riemannian and pseudoRiemannian expanding metrics
We study the quantum field theory (QFT) of a scalar field in the
Schr\"odinger picture in the functional formulation. We derive a formula for the evolution kernel in a flat expanding metric. We
discuss a transition between Riemannian and pseudoRiemannian metrics (signature
inversion). We express the real time Schr\"odinger evolution by the Brownian
motion (Feynman-Kac formula). We discuss the Feynman integral for a scalar
field in a radiation background. We show that the unitary Schr\"odinger
evolution for positive time can go over for negative time into a dissipative
evolution described by diffusive paths.
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