Related papers: Euclidean Relativistic Quantum Mechanics
Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…
Einstein's program of the unified field theory transformed nowadays to the TOE requiring new primordial elements and relations between them. Definitely, they must be elements of the quantum nature. One of most fundamental quantum elements…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincar\'e invariant quantum mechanics. In the case of the bound state, and for a wide variety of model…
In previous work, the author extended the Poincare Lie algebra to include a four position operator as a natural extension to a large fifteen parameter Lie algebra of operators. We here propose to generalize the metric contained in those…
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases…
The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
Different approaches have been applied to the calculation of form factors of various hadronic systems within relativistic quantum mechanics. In a one-body current approximation, they can lead to results evidencing large discrepancies.…
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\mathcal{PT}$.…
A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…
We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard…
In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…
We examine Hamiltonian formalism on Euclidean Snyder space. The latter corresponds to a lattice in the quantum theory. For any given dynamical system, it may not be possible to identify time with a real number parametrizing the evolution in…