Thomas-Paul Hack

Thomas-Paul Hack
University of Leipzig · Institute of Theoretical Physics

PhD

About

31
Publications
2,780
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603
Citations
Additional affiliations
May 2015 - present
University of Leipzig
Position
  • PostDoc Position
May 2013 - April 2015
Università degli Studi di Genova
Position
  • PostDoc Position
March 2007 - April 2013
University of Hamburg
Position
  • PostDoc Position

Publications

Publications (31)
Article
Full-text available
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first ord...
Article
Full-text available
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology and a fundamental study of the perturbations in Inflation. The two central...
Article
The Principle of Perturbative Agreement, as introduced by Hollands and Wald, is a renormalisation condition in quantum field theory on curved spacetimes. This principle states that the perturbative and exact constructions of a field theoretic model given by the sum of a free and an exactly tractable interaction Lagrangean should agree. We develop a...
Article
Full-text available
We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to spacetimes with Lorentzian signature, manifestly generally covariant, invari...
Article
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We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, t...
Preprint
Full-text available
We present a method that "meta" classifies whether segments (objects) predicted by a semantic segmentation neural network intersect with the ground truth. To this end, we employ measures of dispersion for predicted pixel-wise class probability distributions, like classification entropy, that yield heat maps of the input scene's size. We aggregate t...
Preprint
Full-text available
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering states, thermal states). Project C7 of the SFB 676 was focused on characterisations of states by asymptotic cond...
Preprint
Full-text available
Non-equilibrium steady states (NESS) describe particularly simple and stationary non-equilibrium situations. A possibility to obtain such states is to consider the asymptotic evolution of two infinite heat baths brought into thermal contact. In this work we generalise corresponding results of Doyon~et.~al. (J.\ Phys.\ A 18 (2015) no.9) for free Kle...
Article
Full-text available
We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflationary cosmologies. We give explicit, covariant and mutually invertible transformations between the two sets of observables, thus resolving any doubts about their equival...
Article
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We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) l...
Chapter
In this chapter, we review all background material on algebraic quantum field theory on curved spacetimes which is necessary for understanding the cosmological applications discussed in the next chapter. Starting with a brief account of globally hyperbolic curved spacetimes and related geometric notions, we then explain how the algebras of observab...
Chapter
In this chapter we discuss two cosmological applications of algebraic quantum field theory in curved spacetimes. In the Standard Model of Cosmology—the \(\varLambda \)CDM-model—the matter-energy content of the universe on large scales is modelled by a classical stress-energy tensor of perfect fluid form. Motivated by the fact that this matter-energ...
Article
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sect...
Article
Full-text available
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor \({{\mathfrak{A}}}\) :...
Article
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We quantise the massless vector potential A of electromagnetism in the presence of a classical electromagnetic (background) current, j, in a generally covariant way on arbitrary globally hyperbolic spacetimes M. By carefully following general principles and procedures we clarify a number of topological issues. First we combine the interpretation of...
Article
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We quantize the linearised Einstein-Klein-Gordon system on arbitrary on-shell backgrounds in a manifestly covariant and gauge-invariant manner. For the special case of perturbations in Inflation, i.e. on-shell backgrounds of Friedmann-Lema\^itre-Robertson-Walker type, we compare our general quantization construction with the standard approach to th...
Article
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The aim of this review is to outline a full route from the fundamental principles of algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with experimental data. We give a brief account on the quantization of the free scalar field and its Wick powers in terms...
Article
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The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections. The C*-algebra...
Article
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In the standard model of cosmology, the universe is described by a Robertson-Walker spacetime, while its matter/energy content is modeled by a perfect fluid with three components corresponding to matter/dust, radiation and a cosmological constant. On the other hand, in particle physics matter and radiation are described in terms of quantum field th...
Article
Full-text available
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a suitable algebra of observables is assigned to a physical system, which is meant to encode all algebraic relatio...
Article
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We review a few rigorous and partly unpublished results on the regularisation of the stress-energy in quantum field theory on curved spacetimes: 1) the symmetry of the Hadamard/Seeley-DeWitt coefficients in smooth Riemannian and Lorentzian spacetimes 2) the equivalence of the local $\zeta$-function and the Hadamard-point-splitting procedure in smoo...
Article
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We construct and discuss Hadamard states for both scalar and Dirac spinor fields in a large class of spatially flat Friedmann–Robertson–Walker spacetimes characterised by an initial phase either of exponential or of power-law expansion. The states we obtain can be interpreted as being in thermal equilibrium at the time when the scale factor a has a...
Article
Full-text available
It is well-known that coupling a spin $\frac32$-field to a gravitational or electromagnetic background leads to potential problems both in the classical and in the quantum theory. Various solutions to these problems have been proposed so far, which are all restricted to a limited class of backgrounds. On the other hand, negative results for general...
Article
Full-text available
First, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of observables of the Dirac field is constructed in the algebraic framework. This algebra contains normal-ordered Wick pol...
Article
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We study the backreaction of free quantum fields on a flat Robertson-Walker spacetime. Apart from renormalization freedom, the vacuum energy receives contributions from both the trace anomaly and the thermal nature of the quantum state. The former represents a dynamical realisation of dark energy, while the latter mimics an effective dark matter co...
Article
Full-text available
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a cov...
Article
Full-text available
Using $\star$-calculus on the dual of the Borchers-Uhlmann algebra endowed with a combinatorial co-product, we develop a method to calculate a unitary transformation relating the GNS representations of a non-quasifree and a quasifree state of the free hermitian scalar field. The motivation for such an analysis and a further result is the fact that...
Article
Full-text available
Wightman functions for interacting quantum fields on curved space times are cal- culated via the perturbation theory of the Yang-Feldman equations, where the incoming field is a free field in a quasifree representation. We show that these Wightman functions that are ob- tained as a sum over extended Feynman graphs fulfill the basic axioms of hermit...
Article
We first introduce a set of conditions which assure that a free spin $\frac32$ field with $m\ge 0$ can be consistently ('unitarily') quantized on all curved spacetimes, i.e. also on spacetimes which are not assumed to be solutions of the Einstein equations. We discuss a large -- and, as we argue, exhaustive -- class of spin $\frac32$ field equation...

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