Related papers: Representations of U(2\infty) and the Value of the…
In constrast to discretized space-time approximations to continuum quantum field theories, discretized velocity space approximations to continuum quantum field theories are investigated. A four-momentum operator is given in terms of bare…
A system of two fermions with different masses and interacting by the Coulomb potential is presented in a completely covariant framework. The spin-spin interaction, including the anomalous magnetic moments of the two fermions, is added by…
The spinor representation of the quantum group $U_q(su(N))$ is given in terms of a set of fermion creation and annihilation operators. It is shown that the $q$-fermion operators introduced earlier can be identifi ed with the conventional…
We present a theoretical framework called Lorentz quantum mechanics, where the dynamics of a system is a complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary…
Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of…
We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form $x_\mu x^\mu = \tau^2$. This choice of quantization surface implies that all components of the 4-momentum…
In relativistic quantum constraint mechanics the state of a physical system is constrained to a 3-dimensional subspace of Minkowski 4-space. Fourier transformation can be used to relate this state between constraint spaces in 4-position and…
We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system…
Quantum Algebras (q-algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and…
Four-fermion operators may have large anomalous scaling and become relevant operators in some strongly interacting gauge theories. We present a detailed model which illustrates some of the implications of such operators for the generation…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
We study the quantum fermions+gravity system, that is, the gravitational counterpart of QED. We start from the standard Einstein-Weyl theory, reformulated in terms of Ashtekar variables; and we construct its non- perturbative quantum theory…
A light-front Hamiltonian reproducing the results of two-dimensional quantum electrodynamics in the Lorentz coordinates is constructed using the bosonization procedure and an analysis of the bosonic perturbation theory in all orders in the…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
In this article we are concerned with finite dimensional Fermions, by which we mean vectors in a finite dimensional complex space embedded in the exterior algebra over itself. These Fermions are spinless but possess the characterizing…
The restricted solid-on-solid models in the anti-ferromagnetic regime is studied in the framework of quantum affine algebras. Following the line developed recently for vertex models, a representation theoretical picture is presented for the…
We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using…
The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.