# Thomas-Paul HackUniversity of Leipzig · Institute of Theoretical Physics

Thomas-Paul Hack

PhD

## About

31

Publications

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603

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Introduction

Additional affiliations

May 2015 - present

May 2013 - April 2015

March 2007 - April 2013

## Publications

Publications (31)

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 \({{\mathfrak{A}}}\) :...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

Dissertation & Ph. D. thesis Temporary entry (new)