Related papers: Generally covariant Quantum Mechanics
The standard formalism of quantum mechanics is extended to describe a total system including the reference system (RS), with respect to which the total system is described. The RS is assumed to be able to act as a measuring apparatus, with…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
The applications of the recent results obtained in the theory of generalized Lambert functions, to the mean field theory of ferromagnetism are presented. As a consequence, all the predictions of the Weiss theory of ferromagnetism can be…
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
We show that the linearity of an evolution of Quantum Mechanics follows from the definition of kinematics. The same result is obtained for an arbitrary theory with the state space that includes mixtures of different preparations. Next, we…
We present a general framework and procedure to derive uncertainty relations for observables of quantum systems in a covariant manner. All such relations are consequences of the positive semidefiniteness of the density matrix of a general…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied…
We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We present a 4-dimensional generally covariant gauge theory which leads to the Gauss constraint but lacks both the Hamiltonian and spatial diffeomorphism constraints. The canonical theory therefore resembles Yang-Mills theory without the…
In this paper, we study implications of the geometrical nature of space- time for some of the basic tenets of quantum mechanics. That is, we study two different implications of the principle of general covariance; first we quantize a…
We generalise the relativistic expression of Ohm's law by studying a multi-fluid system of charged species using the 1+3 covariant formulation of general relativistic electrodynamics. This is done by providing a fully relativistic, fully…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
Quantum simulation of quantum field theories offers a new way to investigate properties of the fundamental constituents of matter. We develop quantum simulation algorithms based on the light-front formulation of relativistic field theories.…