Abstract: As gravitational-wave detectors become more sensitive to lower frequencies, they will increasingly detect binaries with smaller mass ratios, larger spins, and higher eccentricities. In this talk I describe how gravitational self-force theory, when combined with a recently developed method of multiscale expansions, provides an ideal framework for modelling these systems. The framework proceeds from first principles while simultaneously enabling rapid generation of waveforms on a timescale of milliseconds. I present the first waveforms calculated at second perturbative order in this framework. While self-force methods were originally motivated by extreme-mass-ratio inspirals with mass ratios $\sim 10^4–10^7$, these new results show that multiscale self-force models can be highly accurate for all mass ratios above $\sim 10$.   

Abstract:  As emphasised in the seminal 1964 Haag-Kastler paper, elements of local algebras in AQFT may be regarded as quantum operations. However, as argued in Sorkin’s 1993 “impossible measurements” paper, quantum operations induced by typical elements enable superluminal signaling. In this talk I will argue for the interpretation of (self-adjoint) elements as observables. In particular, I will review the notion of a measurement scheme from quantum measurement theory, Fewster and Verch’s adaption to AQFT and I will introduce asymptotic measurement schemes. Then, for the example of a linear real scalar field on a globally hyperbolic spacetime, I will show how to construct asymptotic measurement schemes for every quantum observable. This talk is based on arXiv:2203.09529, joint work with C. J. Fewster and I. Jubb.

Abstract: Bayes’ theorem is a fundamental tool in classical (i.e. commutative) probability theory, so it is of interest to find generalised instances of it in noncommutative probability. Among the most stimulating directions of research in this sense is the attempt to algebraically “synthesize” the axioms of probability theory, looking for categorical formulations of them. In this talk, after an overview of the aforementioned approach, which will lead us directly to (a) definition of “Bayesian inversion”, I will discuss its connections with the field of operator algebras, in particular with Tomita-Takesaki’s modular theory.

Abstract: The Cauchy slicings for globally hyperbolic spacetimes are surveyed and revisited, including techniques and adaptive possibilities of the slicings. Simple counterexamples on $R^2$ will be constructed showing a variety of possibilities: (a) logical independence (for normalized sliced spacetimes) between the completeness of the slices and global hyperbolicity, (b) necessity of uniform bounds on the slicings in order to ensure global hyperbolicity, or (c) non convexity of the space of all the (normalized, conformal classes of) globally hyperbolic metrics on a manifold. Further possibilities for globally hyperbolic spacetimes-with-timelike-boundary and causal boundaries will be also pointed out. Based on arXiv:2110.13672.

Abstract: Geometric quantization is a natural way to construct the quantum algebra starting from classical data given as a symplectic manifold. When the quantization admits an adjoint operation, referred to as dequantization, we may use this operation to equip the quantum algebra with a distinguished state determined by dequantization. As an example, I show the construction for the free scalar field over a (finite) causal set (locally finite, partially ordered set), where the starting point is a symplectic vector space with an inner product. I compare the result with the construction due to Sorkin, which starts from the same input data, and I show that the distinguished state coincides with the Sorkin-Johnson state, provided the inner product is chosen appropriately. This talk is based on joint work with Eli Hawkins and Kasia Rejzner.

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Abstract: Gaussian quantum states play a central role in many branches of physics – from quantum optics, to condensed matter and quantum field theory. In this talk, I aim to showcase the strength of the Kähler structure formalism for Gaussian states by discussing a recent result on the entanglement structure of supersymmetric (SUSY) bosonic and fermionic Gaussian states [1]. Mathematically, Gaussian states can be defined in terms of Kähler structures on classical phase space. In fact, this approach has proven to be very powerful: It yields a formalism which is both practical for applications, clearly captures the structure and geometry of Gaussian states, adapts to discrete and continuous settings and, moreover, can treat bosons and fermions simultaneously. To exemplify this, we will consider the basic example of a free SUSY system. This is a pair of one bosonic and one fermionic quadratic hamiltonian which is generated by a supercharge and, therefore, is isospectral. Not only does the Kähler structure formalism parallelly capture the Gaussian ground states and their entanglement structure of both the bosonic and the fermionic part. Moreover, it allows us to derive an appealing entanglement duality between bosonic and fermionic subsystems [1], and to interpret it in terms of phase space geometry and its physical implications. Time permitting, as a special application, we consider topological insulators and superconductors and their SUSY partners, discussing the recently derived classification of supercharges in this context [2]. [1] Jonsson, Robert H., Lucas Hackl, and Krishanu Roychowdhury. “Entanglement Dualities in Supersymmetry.” Physical Review Research 3, no. 2 (June 16, 2021): 023213. [2] Gong, Zongping, Robert H. Jonsson, and Daniel Malz. “Supersymmetric Free Fermions and Bosons: Locality, Symmetry, and Topology.” Physical Review B 105, no. 8 (February 24, 2022): 085423.

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Abstract: The Adler-Bardeen theorem states that if gauge anomalies are absent at the one-loop level, then they are absent to all orders. It is crucial for establishing the consistency of quantised gauge theories, such as the Standard Model or extensions thereof. I present a proof which is based on background independence, as formalised in the concept of perturbative agreement.

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