Related papers: Ward-Schwinger-Dyson equations in $\phi^3_6$ Quant…
We take the first steps in a systematic study of Group Field Theory renormalization, focusing on the Boulatov model for 3D quantum gravity. We define an algorithm for constructing the 2D triangulations that characterize the boundary of the…
Four-dimensional field equations are determined for perturbations of the quotient seven-sphere size and squashing parameter in eleven-dimensional supergravity. The quotient seven-sphere is a S^1-bundle over the CP^3 which is regarded as a…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
The renormalised quark Dyson-Schwinger equation is studied in the limit of the renormalised current heavy quark mass m_R --> infinity. We are particularly interested in the analytic pole structure of the heavy quark propagator in the…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
This thesis is concerned with the development of a general method to compute renormalised local observables for quantum matter fields, in a given quantum state, on a rotating black hole spacetime. The rotating black hole may be surrounded…
This paper examines the effectiveness of the Dyson-Schwinger (DS) equations as a calculational tool in quantum field theory. The DS equations are an infinite sequence of coupled equations that are satisfied exactly by the connected Green's…
We construct the gauge invariant three-photon decay amplitude of particle-antiparticle bound states modeled by the Dyson-Schwinger and Bethe-Salpeter equations. Application to the quark-antiquark ($q\bar{q}$) bound states is emphasized. An…
We present a relation which connects the propagator in the radial (Fock-Schwinger) gauge with a gauge invariant Wilson loop. It is closely related to the well-known field strength formula and can be used to calculate the radial gauge…
Within the framework of the Dyson-Schwinger equations in the axial gauge, we study the effect that non-perturbative glue has on the quark propagator. We show that Ward-Takahashi identities, combined with the requirement of matching…
We investigate the phase structure and the infrared properties of higher-derivative quantum gravity (QG) with matter, in $4-\varepsilon$ dimensions. The renormalization group (RG) equations in $4-\varepsilon$ dimensions are analysed for the…
We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative GFT (spin foam)…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
We study the dimensionally regularized fermion propagator Dyson-Schwinger equation in quenched nonperturbative QED. We work in arbitrary covariant gauge and perform nonperturbative renormalization numerically. The nonperturbative fermion…
We show how to derive relativistic, unitary, gauge invariant, and charge conserving three-dimensional scattering equations for a system of hadrons interacting with an electromagnetic field. In the method proposed, the spectator equations…
A system of generalized coherent states for the de Sitter group obeying Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar…
The problem of renormalization in perturbative quantum field theory (pQFT) can be described in a rigorous way through the theory of extension of distributions. In the framework of pQFT a certain type of distribution appears, given by…
I revue the so called Wilson loop approach to bound state problem in QCD. I shall show how using appropriate path integral representations for the quark propagator in an external field it is possible to obtain corresponding path integral…
Calculation of the vacuum polarization, $<\phi^2(x)>$, and expectation value of the stress tensor, $<T_{\mu\nu}(x)>$, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done…