Related papers: Formalisme de Dirac et surprises mathematiques en …
Authoritative appraisals qualified this book as an axiomatic theory. However, being its essential content no more than an analogy, its theoretical organization cannot be an axiomatic one. In fact, in the first edition Dirac declares to…
Inertial effects in non-inertial reference frames are compared with quantum properties of tests objects. The real space-time and perfect inertial reference frame can be compared accurate to the uncertainty relation. Complexities if…
A qualitative representation of what is called 'microstates' is constructed quite independently from the mathematical formalism of fundamental Quantum Mechanics, by taking into accont exclusively the constraints imposed by (a) the cognitive…
A novel technique to determine invariant curves in nonlinear beam dynamics based on the method of formal series has been developed. It is first shown how the solution of the Hamilton equations of motion describing nonlinear betatron…
I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations…
The worldline formalism offers an alternative framework to the standard diagrammatic approach in quantum field theory, grounded in first-quantized relativistic path integrals. Over recent decades, this formalism has attracted growing…
The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in other terms. However, it seems that the Hamiltonian formalism…
The theory of Non-Relativistic Quantum Mechanics was created (or discovered) back in the 1920's mainly by Schr\"odinger and Heisenberg, but it is fair enough to say that a more modern and unified approach to the subject was introduced by…
We present a relativistic formalism inspired on the Minkowski four-vectors that also includes conservation laws such as the first law of thermodynamics. It remains close to the relativistic four-vector formalism developed for a single…
This paper argues that the traditional opposition between determinism and indeterminism in physics is representational rather than ontological. Deterministic-stochastic dualities are available in principle, and arise in a non-contrived way…
In the present article we use the quantum formalism to describe the process of choice under rational ignorance. We consider as a basic task a question or an issue where the only answers are 0 and 1. We show that under rational ignorance the…
The antibracket formalism for gauge theories, at both the classical and quantum level, is reviewed. Gauge transformations and the associated gauge structure are analyzed in detail. The basic concepts involved in the antibracket formalism…
In the present article we consider the inverse fallacy, a well known cognitive heuristic experimentally tested in cognitive science, which occurs for intuitive judgments in situations of bounded rationality. We show that the quantum…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…
We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…
We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to…