Related papers: A Possible Generalization of Quantum Mechanics
A Lagrangian description of the qubit based on a generalization of Schwinger's picture of Quantum Mechanics using the notion of groupoids is presented. In this formalism a Feynman-like computation of its probability amplitudes is done. The…
Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
We give a geometrical interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively ``counts'' the possible…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
Schwinger's quantization scheme is extended in order to solve the problem of the formulation of quantum mechanics on a space with a group structure. The importance of Killing vectors in a quantization scheme is showed. Usage of these…
In this paper we bring together the method of Lagrangian descriptors and the principle of least action, or more precisely, of stationary action, in both deterministic and stochastic settings. In particular, we show how the action can be…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
A complete, straightforward and natural Lagrangian description is given for the classical non-relativistic dynamics of a particle with colour or internal symmetry degrees of freedom moving in a background Yang-Mills field. This provides a…
GUP is a phenomenological model aimed for a description of a minimal length in quantum and classical systems. However, the analysis of problems in classical physics is usually approached preferring a different formalism than the one used…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange…
A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…