Hugo Münsterberg: a German Jew (?) in America

An historical account by Jan-Christopher Horak of Hugo Münsterberg's life and work in America – or, more exactly, upon the nature and consequences of being a German Jew at work within Harvard University during the first decades of the 20th-century

Realtime properties of QCD

We present a novel technique for the calculation of fundamental realtime correlation functions in functional approaches to quantum field theory, the spectral functional approach, and demonstrate its potential for the calculation of observables in quantum chromodynamics (QCD). The approach builds on spectral representations for correlation functions, such as the K\"all\'en-Lehmann representation of the propagator, and facilitates dimensional regularisation as well as on-shell renormalisation. We apply the spectral functional approach to the two most prominent functional frameworks for the calculation of non-perturbative fundamental correlation functions in QCD, which are Dyson-Schwinger equations and the functional renormalisation group. Building on this conceptual development, we calculate the spectral functions of all fundamental QCD fields, i.e., quark, gluon and ghost. We complement these results with data from spectral reconstruction with Gaussian process regression, inferring gluon and ghost spectral functions from Euclidean lattice QCD data in a Bayesian, non-parametric manner. Finally, as use cases for the spectral functional approach, we present direct computations of several QCD observables, facilitated by realtime correlator data. These include the shear viscosity of the quark-gluon plasma, the non-perturbative, timelike strong coupling constant, a crucial ingredient for scattering amplitudes, and the hadronic vacuum polarisation in the complex momentum plane, the leading QCD contribution to g-2

On the quark spectral function in QCD

We calculate the spectral function of light quark flavours in 2+1 flavour vacuum QCD in the isospin-symmetric approximation. We employ spectral Dyson-Schwinger equations and compute the non-perturbative quark propagator directly in real-time, using recent spectral reconstruction results from Gaussian process regression of gluon propagator data in 2+1 flavour lattice QCD. Our results feature a pole-like peak structure at time-like momenta larger than the propagator's gapping scale as well as a negative scattering continuum, which we exploit assuming an analytic pole-tail split during the iterative solution. The computation is augmented with a general discussion of the impact of the quark-gluon vertex and the gluon propagator on the analytic structure of the quark propagator. In particular, we investigate under which conditions the quark propagator shows unphysical complex poles. Our results offer a wide range of applications, encompassing the ab-initio calculation of transport as well as resonance properties in QCD.Comment: 17 pages, 7 figure

On the complex structure of Yang-Mills theory

We consider the coupled set of spectral Dyson-Schwinger equations in Yang-Mills theory for ghost and gluon propagators, which gives us access to the ghost and gluon spectral functions. The set-up is used for a systematic analytic evaluation of the constraints on generalised spectral representations in Yang-Mills theory that are most relevant for informed spectral reconstructions. We also provide numerical results for the coupled set of spectral functions for a large range of potential mass gaps of the gluon, and discuss the limitations and extensions of the present work.Comment: 30 pages, 16 figure

Spectral properties and observables in ultracold Fermi gases

We calculate non-perturbative self-consistent fermionic and bosonic spectral functions of ultra-cold Fermi gases with the spectral functional approach. This approach allows for a direct real-time computation of non-perturbative correlation functions, and in the present work we use spectral Dyson-Schwinger equations. We focus on the normal phase of the spin-balanced Fermi gas and provide numerical results for the full fermionic and bosonic spectral functions. The spectral functions are then used for the determination of the equation of state, the Tan contact and ejection rf spectra at unitarity. These results are compared to experimental data, the self-consistent T-matrix approach and lattice results. Our approach offers a wide range of applications, including the ab initio calculation of transport and spectral properties of the superfluid phase in the BCS-BEC crossover

Ghost spectral function from the spectral Dyson-Schwinger equation

We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.Comment: 15 pages, 11 figure

Scalar spectral functions from the spectral fRG

We compute non-perturbative spectral functions in a scalar $\phi^4$-theory in three spacetime dimensions via the spectral functional renormalisation group. This approach allows for the direct, manifestly Lorentz covariant computation of correlation functions in Minkowski spacetime, including a physical on-shell renormalisation. We present numerical results for the spectral functions of the two- and four-point correlation functions for different values of the coupling parameter. These results agree very well with those obtained from another functional real-time approach, the spectral Dyson-Schwinger equation.Comment: 22 pages, 13 figure