Related papers: Condensed matter many-body theory in relativistic …
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
We discusse a relativistic Hamiltonian for an n-body problem in which all the masses are equal and all spins take value 1/2. In the frame of reference in which the total momentum $\v{P}=0$, the Foldy-Wouthuysen transformation is applies and…
The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant…
We consider a classical condensed matter theory in a Newtonian framework where conservation laws \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) + \partial_i(\rho v^i v^j + p^{ij}) = 0 are related with the Lagrange…
We give here a field-theoretical derivation of the Hamiltonian of the non-relativistic quantum electrodynamics in the Coulomb gauge using the Lagrange formalism. It leads to the same result as the usual derivation, where one just replaces…
This paper concerns the quantisation of a rigid body in the framework of ``covariant quantum mechanics'' on a curved spacetime with absolute time. The basic idea is to consider the multi-configuration space, i.e. the configuration space for…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…
In this article we construct a relativistic extended metric theory of gravity, for which its weak field limit reduces to the non-relativistic MOdified Newtonian Dynamics regime of gravity. The theory is fully covariant and the way to…
Recent developments in the study of shape-invariant Hamiltonians are briefly summarized. Relations between certain exactly solvable problems in many-body physics and shape-invariance are explored. Connection between Gaudin algebras and…
We study properties of classical reparametrization-invariant matter systems, mainly the relativistic particle and its d-brane generalization. The corresponding matter Lagrangian naturally contains background interaction fields, such as a…
A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion,…
Collective center-of-mass variables are introduced in the Lagrangian formalism of the relativistic classical mechanics of directly interacting particles. It is shown that the transition to the Hamiltonian formalism leads to the…
Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing light-front gauge and adopting a basis function…
From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor…
The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These…
We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on…
I discuss different formulations of the relativistic few-body problem with an emphasis on how they are related. I first discuss the implications of some of the differences with non-relativistic quantum mechanics. Then I point out that the…
A simple argument is presented which, based on the minimal coupling Lagrangian for a many-body system, keeps the gauge invariance of the many-body Schr\"odinger equation with explicit Coulomb potential. The elimination of longitudinal…
The many-body theory of degenerate systems is described in detail. More generally, this theory applies to systems with an initial state that cannot be described by a single Slater determinant. The double-source (or closed-time-path)…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…