Related papers: Quantum Fields on the Light Front, Formulation in …
The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis avoiding the over-completeness arising from Mandelstam relations. We short-cut this problem using Harmonic analysis on…
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
After a brief introduction to the statistical description of data, these lecture notes focus on quantum field theories as they emerge from lattice models in the critical limit. For the simulation of these lattice models, Markov chain…
We clarify a few conceptual problems of quantum field theory on the level of exactly solvable models with fermions. The ultimate goal of our study is to gain a deeper understanding of differences between the usual ("spacelike") and…
The issue of defining discrete light-cone quantization (DLCQ) in field theory as a light-like limit is investigated. This amounts to studying quantum field theory compactified on a space-like circle of vanishing radius in an appropriate…
We describe a new approach to the problem of putting supersymmetric theories on the lattice. The basic idea is to discretize a {\it twisted} formulation of the supersymmetric theory. For certain theories with extended supersymmetry these…
We recall the special features of quantum dynamics on a light-front (in an infinite momentum frame) in string and field theory. The reason this approach is more effective for string than for fields is stressed: the light-front dynamics for…
Large-N field systems are considered from an unusual point of view. The Hamiltonian is presented in a third-quantized form analogously to the second-quantized formulation of the quantum theory of many particles. The semiclassical…
The analogy between quantum chemistry and light-front quantum field theory, first noted by Kenneth G. Wilson, serves as motivation to develop light-front quantum simulation of quantum field theory. We demonstrate how calculations of hadron…
This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency…
The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the…
I review a new treatment of an old idea for light-front quantization of lattice gauge theories and give new results from some illustrative calculations: [I] transverse lattice gauge theory; [II] pure glue; [III] heavy sources and winding…
We investigate quark matter at finite temperature and finite chemical potential as an example for a relativistic many-particle quantum system. Special relativity is realized through the front form that allows for a Hamiltonian formulation…
We develop methods for computing the effective action at infinite momentum for $1+1d$ QFTs at finite volume which do not rely on the theory having a Lagrangian description. We do this by taking the infinite momentum limit of equal-time…
In this contribution we give an introduction to the foundations and methods of lattice gauge theory. Starting with a brief discussion of the quantum mechanical path integral, we develop the main ingredients of lattice field theory:…
We study the gauge fixing of lattice QCD in 2+1 dimensions, in the Hamiltonian formulation. The technique easily generalizes to other theories and dimensions. The Hamiltonian is rewritten in terms of variables which are gauge invariant…
This dissertation presents the first theoretical investigation of the Lamb shift in a light-front hamiltonian approach: the dominant part of the splitting between the 2S(1/2) and 2P(1/2) energy levels in hydrogen is calculated. Also…
At finite lattice spacing, Lagrangian and Hamiltonian predictions differ due to discretization effects. In the Hamiltonian limit, i.e. at vanishing temporal lattice spacing $a_t$, the path integral approach in the Lagrangian formalism…
Improvement of the Hamiltonian in lattice gauge theory is considered. We give explicit expressions for classical improvement and discuss also quantum corrections.
We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…