Related papers: Covariant relativistic quantum theory
We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of…
The logical inference approach to quantum theory, proposed earlier [Ann. Phys. 347 (2014) 45-73], is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
The relativistic quantum mechanics equations for the electromagnetic interaction are propososed.
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
A new synthesis of the principles of relativity and quantum mechanics is developed by replacing the Poincar\'e group for the de Sitter one. The new relativistic quantum mechanics is an indefinite mass theory which is reduced to the standard…
A novel perspective on relativistic transformation recently-proposed provides an insight into the very meaning of the principle of relativity. With this novel perspective and Bell's theorem, we argue that special relativity, instead of…
We describe the twisted space-time symmetries which imply the quantum Poincar\'{e} covariance of noncommutative Minkowski spaces, with constant, Lie algebraic and quadratic commutators. Further we present the relativistic and…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…
A Lorentz covariant quantization of membrane dynamics is defined, which also leaves unbroken the full three dimensional diffeomorphism invariance of the membrane. Among the applications studied are the reduction to string theory, which may…
The following two papers form a natural development of a previous series of three articles on the foundations of quantum mechanics; they are intended to take the theory there developed to its utmost logical and epistemological consequences.…
A complete solution to the long standing problem of basing Schroedinger quantum theory on standard stochastic theory is given. The solution covers all "single" particle three-dimensional Schroedinger theory linear or nonlinear and with any…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current…