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We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
We investigate the dynamical generation of fermion mass in quantum electrodynamics (QED). This non-perturbative study is performed using a truncated set of Schwinger-Dyson equations for the fermion and the photon propagator. First, we study…
An attempt is made to present modern hopes to find manifestation of supersymmetry, a new symmetry that relates bosons and fermions, in particle physics from the point of view of renormalization group flow. The Standard Model of particle…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter ingredients only truly microscopically and it…
In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by…
Monitored quantum systems undergo Measurement-induced Phase Transitions (MiPTs) stemming from the interplay between measurements and unitary dynamics. When the detector readout is post-selected to match a given value, the dynamics is…
Non-perturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster…
We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles…
We carry out a detailed study of the three-point fermion-photon interaction vertex at one loop order for massive fermions in reduced quantum electrodynamics. This calculation is carried out in arbitrary covariant gauges and space-time…
We analyze a system of fermions in a one-dimensional harmonic trap with attractive delta-interactions between different fermions species, as an approximate description of experiments involving atomic dimers. We solve the problem of two…
One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization…
The computation of dynamical response functions is central to many problems in condensed matter physics. Owing to the rapid growth of quantum correlations following a quench, classical methods face significant challenges even if an…
We derive the relativistic quantum kinetic equation for massless fermions with vector and axial vector interaction using the Wigner function formalism. The vector and axial vector currents are self-consistently treated with corresponding…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type…