Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2308.01190

Bogoliubov Transformation and Schrodinger Representation on Curved Space

Musfar Muhamed Kozhikkal·Arif Mohd
View original source ↗Read source document ↗Export metadata ↓

Abstract

It is usually accepted that quantum dynamics described by Schrodinger equation that determines the evolution of states from one Cauchy surface to another is unitary. However, it has been known for some time that this expectation is not borne out in the conventional setting in which one envisages the dynamics on a fixed Hilbert space. Indeed it is not even true for linear quantum field theory on Minkowski space if the chosen Cauchy surfaces are not preserved by the flow of a timelike Killing vector. This issue was elegantly addressed and resolved by Agullo and Ashtekar who showed that in a general setting quantum dynamics in the Schrodinger picture does not take place in a fixed Hilbert space. Instead, it takes place on a non-trivial bundle over time, the Hilbert bundle, whose fibre at a given time is a Hilbert space at that time. In this article, we postulate a Schrodinger equation that incorporates the effect of change in vacuum during time evolution by including the Bogoliubov transformation explicitly in the Schrodinger equation. More precisely, for a linear (real) Klein-Gordon field on a globally hyperbolic spacetime we write down a Schrodinger equation that propagates states between arbitrary chosen Cauchy surfaces, thus describing the quantum dynamics on a Hilbert bundle. We show that this dynamics is unitary if a specific tensor on the canonical phase space satisfies the Hilbert-Schmidt condition. Generalized unitarity condition of Agullo-Ashtekar follows quite naturally from our construction.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Musfar Muhamed Kozhikkal, Arif Mohd. 2023-08-02. Bogoliubov Transformation and Schrodinger Representation on Curved Space. https://doi.org/10.1103/physrevd.108.085028

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

gr-qc↗
arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗