Related papers: CORE 2.1 (COmpendium of RElations, Version 2.1)
We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $\phi ^4$ theory. We eventually give evidence…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
We argue that calculations in QED at finite temperature are more conveniently carried out in the Coulomb gauge, in which only the physical photon degrees of freedom play a rol and are thermalized. We derive the photon propagator in this…
We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
We decompose renormalized Feynman rules according to the scale and angle dependence of amplitudes. We use parametric representations such that the resulting amplitudes can be studied in algebraic geometry.
The system of N scalar particles with Grassmann-valued color charges plus the color SU(3) Yang-Mills field is reformulated on spacelike hypersurfaces. The Dirac observables are found and the physical invariant mass of the system in the…
The dynamics of $N\geq 3$ interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element.…
We construct a first order Lagrangian formalism for bimetric theories with an interaction which is a general function of metrics and their derivatives, including non-analytic functions. The first-order actions are fully equivalent to the…
A confined quark model study in a couple of chirally anomalous processes is presented in comparison with effective meson Lagrangian approaches of various kind. The processes considered are \pi^0 \to \gamma \gamma and \gamma \to \pi^+ \pi^-…
We construct a new model for relativistic particle on the noncommutative surface in $(2+1)$ dimensions, using the symplectic formalism of constrained systems and embedding the model on an extended phase space. We suggest a short cut to…
Diagrammatic approaches to perturbation theory transformed the practicability of calculations in particle physics. In the case of extended theories of gravity, however, obtaining the relevant diagrammatic rules is non-trivial: we must…
A novel strong interaction beyond the standard model could provide a dynamical explanation of electroweak symmetry breaking. Experimental results strongly constrain properties of models that realise this mechanism. Whether these constraints…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a…
We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in $1/c$. Using a Lagrangian approach, we obtain the self-consistent charge and…
Class lecture notes at a beginning graduate level on the mathematical background needed to understand classical gauge theory. Covers group actions, fiber bundles, principal bundles, connections, gauge transformations, parallel transport,…
The three-dimensional complexified exteriour bundle $C \otimes \Lambda(R^3)$ is proposed as a geometric interpretation of electroweak doublets of Dirac fermions. The Dirac equation on this bundle allows a staggered discretization on a…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…