Publikationen - Institut für Theoretische Physik (ab 2018) - Jahr 2020

Beginning with results for the leading-twist two-particle distribution amplitudes of π- and K-mesons, each of which exhibits dilation driven by the mechanism responsible for the emergence of hadronic mass, we develop parameter-free predictions for the pointwise behaviour of all π and K distribution functions (DFs), including glue and sea. The large-x behaviour of each DF meets expectations based on quantum chromodynamics; the valence-quark distributions match extractions from available data, including the pion case when threshold resummation effects are included; and at ζ5=5.2GeV, the scale of existing measurements, the light-front momentum of these hadrons is shared as follows: ⟨xvalence⟩π=0.41(4), ⟨xglue⟩π=0.45(2), ⟨xsea⟩π=0.14(2); and ⟨xvalence⟩K=0.42(3), ⟨xglue⟩K=0.44(2), ⟨xsea⟩K=0.14(2). The kaon’s glue and sea distributions are similar to those in the pion, although the inclusion of mass-dependent splitting functions introduces some differences on the valence-quark domain. This study should stimulate improved analyses of existing data and motivate new experiments sensitive to all π and K DFs. With little known empirically about the structure of the Standard Model’s (pseudo-) Nambu-Goldstone modes and analyses of existing, limited data being controversial, it is likely that new generation experiments at upgraded and anticipated facilities will provide the information needed to resolve the puzzles and complete the picture of these complex bound states.

With discovery of the Higgs boson, science has located the source for ≲2% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining ≳98%. The instruments at work here must be capable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.

A Poincaré-covariant quark+diquark Faddeev equation is used to compute nucleon elastic form factors on 0≤Q2≤18m2N (mN is the nucleon mass) and elucidate their role as probes of emergent hadronic mass in the Standard Model. The calculations expose features of the form factors that can be tested in new generation experiments at existing facilities, e.g. a zero in GpE/GpM; a maximum in GnE/GnM; and a zero in the proton's d-quark Dirac form factor, Fd1. Additionally, examination of the associated light-front-transverse number and anomalous magnetisation densities reveals, inter alia: a marked excess of valence u-quarks in the neighbourhood of the proton's centre of transverse momentum; and that the valence d-quark is markedly more active magnetically than either of the valence u-quarks. The calculations and analysis also reveal other aspects of nucleon structure that could be tested with a high-luminosity accelerator capable of delivering higher beam energies than are currently available.

We study the trident process in laser pulses. We provide exact numerical results for all contributions, including the difficult exchange term. We show that all terms are in general important for a short pulse. For a long pulse, we identify a term that gives the dominant contribution even if the intensity is only moderately high, a0≳1, which is an experimentally important regime where the standard locally constant field (LCF) approximation cannot be used. We show that the spectrum has a richer structure at a0∼1, compared to the LCF regime a0≫1. We study the convergence to LCF as a0 increases and how this convergence depends on the momentum of the initial electron. We also identify the terms that dominate at high energy.

Higher-order tree-level processes in strong laser fields, i.e., cascades, are in general extremely difficult to calculate, but in some regimes the dominant contribution comes from a sequence of first-order processes, i.e., nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. At high intensity the field can be treated as locally constant, which is the basis for standard particle-in-cell codes. However, the locally-constant-field (LCF) approximation and these particle-in-cell codes cannot be used when the intensity is only moderately high, which is a regime that is experimentally relevant. We have shown that one can still use a sequence of first-order processes to estimate higher orders at moderate intensities provided the field is sufficiently long. An important aspect of our new “gluing” approach is the role of the spin and polarization of intermediate particles, which is more nontrivial compared to the LCF regime.

We study nonlinear trident in laser pulses in the high-energy limit, where the initial electron experiences, in its rest frame, an electromagnetic field strength above Schwinger’s critical field. At lower energies the dominant contribution comes from the “two-step” part, but in the high-energy limit the dominant contribution comes instead from the one-step term. We obtain new approximations that explain the relation between the high-energy limit of trident and pair production by a Coulomb field, as well as the role of the Weizsäcker-Williams approximation and why it does not agree with the high-χ limit of the locally-constant-field approximation. We also show that the next-to-leading order in the large-a0 expansion is, in the high-energy limit, nonlocal and is numerically very important even for quite large a0. We show that the small-a0 perturbation series has a finite radius of convergence, but using Padé-conformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the large-a0 approximation. We use Borel-Padé-conformal methods to resum the small-χ expansion and obtain a high precision up to very large χ. We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions.

We study the photon trident process, where an initial photon turns into an electron-positron pair and a final photon under a nonlinear interaction with a strong plane-wave background field. We show that this process is very similar to double Compton scattering, where an electron interacts with the background field and emits two photons. We also show how the one-step terms can be obtained by resumming the small- and large-\chiχ expansions. We consider a couple of different resummation methods, and also propose new resummations (involving Meijer-G functions) which have the correct type of expansions at both small and large \chiχ. These new resummations require relatively few terms to give good precision.

In the firrst-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics (QED) in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons in configuration as well as in momentum space.

Many phenomena described in relativistic quantum field theory are inaccessible to direct observations, but analogue processes studied under well-defined laboratory conditions can present an alternative perspective. Recently, we demonstrated an analogy of particle creation using an intrinsically robust motional mode of two trapped atomic ions. Here, we substantially extend our classical control techniques by implementing machine-learning strategies in our platform and, consequently, increase the accessible parameter regime. As a proof of methodology, we present experimental results of multiple quenches and parametric modulation of an unprotected motional mode of a single ion, demonstrating the increased level of real-time control. In combination with previous results, we enable future experiments that may yield entanglement generation using a process in analogy to Hawking radiation. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.

Quantum electrodynamics predicts the vacuum to behave as a nonlinear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly nonlinear measurement schemes--while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.

By a generalization of the Hopfield model, we construct a microscopic Lagrangian describing a dielectric medium with dispersion and dissipation. This facilitates a well-defined and unambiguous ab initio treatment of quantum electrodynamics in such media, even in time-dependent backgrounds. As an example, we calculate the number of photons created by switching on and off dissipation in dependence on the temporal switching function. This effect may be stronger than quantum radiation produced by variations of the refractive index Δn(t) since the latter are typically very small and yield photon numbers of order (Δn)². As another difference, we find that the partner particles of the created medium photons are not other medium photons but excitations of the environment field causing the dissipation (which is switched on and off).

Off-shell Ward identities in non-abelian gauge theory continue to be a subject of active research, since they are, in general, inhomogeneous and their form depends on the chosen gauge-fixing procedure. For the three-gluon and four-gluon vertices, it is known that a relatively simple form of the Ward identity can be achieved using the pinch technique or, equivalently, the background-field method with quantum Feynman gauge. The latter is also the gauge-fixing underlying the string-inspired formalism, and here we use this formalism to derive the corresponding form of the Ward identity for the one-loop N - gluon amplitudes.

Electron-positron pair production for inhomogeneous electric and magnetic fields oscillating in space and time is investigated. By employing accurate numerical methods (Furry-picture quantization and quantum kinetic theory), final particle momentum spectra are calculated and analyzed in terms of effective models. Furthermore, criteria for the applicability of approximate methods are derived and discussed. In this context, special focus is placed on the local density approximation, where fields are assumed to be locally homogeneous in space. Eventually, we apply our findings to the multiphoton regime. Special emphasis is on the importance of linear momentum conservation and the effect of its absence in momentum spectra within approximations based on local homogeneity of the fields.

Electron-positron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the Dirac-Heisenberg-Wigner formalism (quantum kinetic theory) through computing the corresponding Wigner functions. The focus is on discussing the particle momentum spectrum regarding signatures of Schwinger and multiphoton pair production. Special emphasis is put on studying the impact of a strong dynamical magnetic field on the particle distribution functions. As the equal-time Wigner approach is formulated in terms of partial integro-differential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.

We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbard model that is induced by fermionic baths. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the reduced density matrix. An improvement on the commonly-used secular approximation, referred to as coherent approximation, is presented. We analyze the spectrum of relaxation rates and identify different time scales that are involved in the equilibration of the Hubbard dimer after a quantum quench.

Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium.The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z-expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation time scales strongly depend on the type of excitations (particles or holes or both) that are initially present.

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a tree replacement rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N.