# Dr. Onirban Islam

### Postdoktorand

Kontakt
Raum:
2.09.3.05
Telefon:
+49 331 977-1248

#### Publications

2021 | A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime | Onirban IslamZeitschrift: to appear in The Journal of Geometric AnalysisLink zum Preprint

### A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime

#### Autoren: Onirban Islam (2021)

A Duistermaat-Guillemin-Gutzwiller trace formula for Dirac-type operators on a globally hyperbolic spatially compact standard stationary spacetime is achieved by generalising the recent construction by A. Strohmaier and S. Zelditch to a vector bundle setting. We have analysed the spectrum of the Lie derivative with respect to a global timelike Killing vector field on the solution space of the Dirac equation and found that it consists of discrete real eigenvalues. The distributional trace of the time evolution operator has singularities at the periods of induced Killing flow on the space of lightlike geodesics. This gives rise to the Weyl law asymptotic at the vanishing period.

Zeitschrift:
to appear in The Journal of Geometric Analysis

2020 | On microlocalization and the construction of Feynman propagators for normally hyperbolic operators | Onirban Islam, Alexander StrohmaierZeitschrift: to appear in Communications in Analysis and GeometryLink zum Preprint

### On microlocalization and the construction of Feynman propagators for normally hyperbolic operators

#### Autoren: Onirban Islam, Alexander Strohmaier (2020)

This article reviews the microlocal construction of Feynman propagators for normally hyperbolic operators acting on vector bundles over globally hyperbolic spacetimes and its consequences. It is shown that for normally hyperbolic operators that are selfadjoint with respect to a hermitian bundle metric, the Feynman propagators can be constructed to satisfy a positivity property that reflects the existence of Hadamard states in quantum field theory on curved spacetimes. We also give a more direct construction of the Feynman propagator for the Dirac operator on a globally hyperbolic spacetime. Even though the natural bundle metric on spinors is not positive-definite, in this case we can give a direct microlocal construction of a Feynman propagator that satisfies positivity.

Zeitschrift:
to appear in Communications in Analysis and Geometry

2020 | Relative entanglement entropy of thermal states of Klein-Gordon and Dirac quantum field theories | Onirban IslamLink zum Preprint

### Relative entanglement entropy of thermal states of Klein-Gordon and Dirac quantum field theories

#### Autoren: Onirban Islam (2020)

An upper bound of the relative entanglement entropy of thermal states at an inverse temperature $$\beta$$  of linear, massive Klein-Gordon and Dirac quantum field theories across two regions, separated by a nonzero distance $$d$$ in a Cauchy hypersurface of an ultrastatic (spin-)spacetime has been computed. This entanglement measure is bounded by a negative constant times $$\mathrm{ln}|\tanh(\pi d/2\beta)|$$ which signifies power law decay for asymptotic $$d$$ where the exponent depends on $$\beta < \infty$$.

2018 | Relative entanglement entropy for widely separated regions in curved spacetime | Stefan Hollands, Onirban Islam, Ko SandersZeitschrift: Journal of Mathematical PhysicsBand: 59Link zur Publikation , Link zum Preprint

### Relative entanglement entropy for widely separated regions in curved spacetime

#### Autoren: Stefan Hollands, Onirban Islam, Ko Sanders (2018)

We give an upper bound of the relative entanglement entropy of the ground state of a massive Dirac-Majorana field across two widely separated regions $$A$$ and $$B$$ in a static slice of an ultrastatic Lorentzian spacetime. Our bound decays exponentially in $$\mathrm{dist}(A,B)$$ at a rate set by the Compton wavelength and the spatial scalar curvature. The physical interpretation of our result is that, on a manifold with positive spatial scalar curvature, one cannot use the entanglement of the vacuum state to teleport one classical bit from $$A$$ to $$B$$ if their distance is of the order of the maximum of the curvature radius and the Compton wavelength or greater.

Zeitschrift:
Journal of Mathematical Physics
Band:
59

#### Arbeitsgebiete

• Global Analysis is the investigation of differential operators on manifolds and on vector bundles. Broadly speaking, I am interested in differential operators and their generalisations (pseudodifferential operators and Fourier integral operators) naturally arising in the context of quantum field theory, general relativity, and their interplay. Often these operators are non-elliptic and their analysis requires tools from microlocal analysis, functional analysis, and Lorentzian geometry. At the moment, I am working on a Lorentzian generalisation of the Atiyah-Patodi-Singer index theorem.
• Semi-classical Gravity is the study of quantum field theory interacting with classical gravity, also known as quantum field theory in curved spacetime. In this context, my current focus is on constructing Hadamard states on globally hyperbolic spacetimes (with timelike boundary).
• Spectral Geometry explores the bridge between spectral invariants of differential operators and the underlying manifolds (vector bundles). At present, I am investigating a relativistic generalisation of the Duistermaat-Guillemin-Gutzwiller trace formula for wave-type and for Dirac-type operators on a stationary spacetime admitting compact Cauchy hypersurface with boundary. On the physics side, my interest is to employ this trace formula to explore semi-classical manifestation of horizon-induced instability.

#### Talks

• Feynman propagators for wave-type and for Dirac-type operators on a curved spacetime, AQFTUK (York, UK: 7 July 2022)
• h-principle for Open Ample Partial Differential Relation, Block Seminar: Convex Integration (Chiemsee, Germany: 4 May 2022)
• A Gutzwiller trace formula for Dirac operators on a stationary spacetime, Microlocal and Global Analysis, Interactions with Geometry (Potsdam, Germany: 24 February, 2022)
• On the microlocalisation of normally hyperbolic operators, Young Functional Analysts' Workshop (Lanchaster, UK: 12 August 2021)
• Existence of Feynman propagators of a normally hyperbolic operator, London Mathematical Society Virtual Graduate Student Meeting(UK: 16 November 2020)
• Relative entanglement entropy of thermal states in a static spacetime, Hamilton School on Mathematical Physics (Dublin, UK: 24 August 2020)
• On the construction of Feynman parametrices for a normally hyperbolic operator, LQP 45: Foundations and Constructive Aspects of QFT (Cardiff, UK: 18 June 2020)
• Entanglement entropy of the Dirac field in a static spacetime, LQP 40: Foundations and Constructive Aspects of QFT (Leipzig, Germany: 24 June 2017)