Related papers: Poincar\'e Invariant Quantum Mechanics based on Eu…
We discuss a formulation of exactly Poincar\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the…
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear…
We discuss preliminary work on a formulation of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or their generating functionals as phenomenological input. We discuss the construction of a Poincare…
We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert…
A Euclidean formulation of relativistic quantum mechanics is discussed. Representations of the Hilbert space inner product and Poincar\'e generators are all expressed in terms of Euclidean space-time variables. The formulation does not…
It is by now well known that the Poincar\'e group acts on the Moyal plane with a twisted coproduct. Poincar\'e invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a…
Relativistic invariance in Euclidean formulations of quantum mechanics is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. Euclidean formulations of relativistic…
In this paper I discuss a formulation of relativistic few-particle scattering theory where the dynamical input is a collection of reflection-positive Euclidean covariant Green functions. This formulation of relativistic quantum mechanics…
In this paper we study the relativistic quantum mechanical interpretation of the solution of the inhomogeneous Euclidean Bethe-Salpeter equation. Our goal is to determine conditions on the input to the Euclidean Bethe-Salpeter equation so…
Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We…
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's…
Light-front quantization has important advantages for describing relativistic statistical systems, particularly systems for which boost invariance is essential, such as the fireball created in a heavy ion collisions. In this paper we…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees…
There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we…
The formulation of statistical physics using light-front quantization, instead of conventional equal-time boundary conditions, has important advantages for describing relativistic statistical systems, such as heavy ion collisions. We…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant…
We construct a generalisation of the three-dimensional Poincar\'e algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincar\'e gravity in three space-time dimensions as well as to study…