arXiv subjects

Ennio Gozzi

Publications and source records attributed to Ennio Gozzi.

9 recordsLinked to original sources

arXiv2022

Are there any problem for large values of the action like there were for small ones ?

In this paper we show that a method of quantization proposed few years ago (ann.of phys. (314),2005, 24) is equivalent to studying the system for values of the action close to zero. In this paper we also study the behaviour when the action gets very very large which could be the regime where dark energy and dark matter are invoked. Surprisingly the behaviour at this regime is not the one of classical mechanics but it resembles the one of quantum mechanics with of course different constants.

quant-ph↗

arXiv2018

From quantum to classical without Planck constant going to zero

In this paper we put forward some simple rules which can be used to pass from the quantum Moyal evolution operator to the classical Liouville one without taking the Planck constant to zero. These rules involve the averaging over some auxiliary variables.

quant-ph↗

arXiv2016

NEWTON's trajectories versus MOND's trajectories

MOND dynamics consists of a modification of the acceleration with respect to the one provided by Newtonian mechanics. In this paper we investigate whether it can be derived from a velocity-dependent deformation of the coordinates of the systems. The conclusion is that it cannot be derived this way because of the intrinsic non-local character in time of the MOND procedure. This is a feature pointed out some time ago already by Milgrom himself.

gr-qc↗

arXiv2012

Universal local symmetries in classical mechanics and physical degrees of freedom

In a recent paper we have analyzed the role that a universal set of local symmetries plays in suppressing the superposition principle in classical mechanics via a path-integral formulation of classical mechanics itself. In this paper first we generalize those symmetries, second we study the role which the gauge fixing plays and third we put forward the idea of which ones should be the physical degrees of freedom of the theory.

hep-th↗

arXiv2010

Diagrammar In Classical Scalar Field Theory

In this paper we analyze perturbatively a g phi^4 classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that several of those diagrams cancel against each other due to a universal supersymmetry present in the classical path integral mentioned above. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost "identical" formally to the quantum ones. Using the super-diagrams technique we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.

hep-th↗

arXiv2009

Classical and quantum mechanics via supermetrics in time

Koopman-von Neumann in the 30's gave an operatorial formululation of Classical Mechanics. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for classical path-integral) to distinguish it from the quantum mechanical one, which we will indicate with QPI. In the CPI two Grassmannian partners of time make their natural appearance and in this manner time becomes something like a three dimensional supermanifold. Next we introduce a metric in this supermanifold and show that a particular choice of the supermetric reproduces the CPI while a different one gives the QPI.

quant-ph↗

arXiv1997

Universal Hidden Supersymmetry in Classical Mechanics and its Local Extension

We review here a path-integral approach to classical mechanics and explore the geometrical meaning of this construction. In particular we bring to light a universal hidden BRS invariance and its geometrical relevance for the Cartan calculus on symplectic manifolds. Together with this BRS invariance we also show the presence of a universal hidden genuine non-relativistic supersymmetry. In an attempt to understand its geometry we make this susy local following the analogous construction done for the supersymmetric quantum mechanics of Witten.

hep-th↗

arXiv1997

Can We Look at The Quantisation Rules as Constraints?

In this paper we explore the idea of looking at the Dirac quantisation conditions as $\hbar$-dependent constraints on the tangent bundle to phase-space. Starting from the path-integral version of classical mechanics and using the natural Poisson brackets structure present in the cotangent bundle to the tangent bundle of phase- space, we handle the above constraints using the standard theory of Dirac for constrained systems. The hope is to obtain, as total Hamiltonian, the Moyal operator of time-evolution and as Dirac brackets the Moyal ones. Unfortunately the program fails indicating that something is missing. We put forward at the end some ideas for future work which may overcome this failure.

dg-ga↗

arXiv1997

Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics

In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets structure which allows us to re-do all the usual Cartan calculus on symplectic manifolds via these brackets. We also briefly sketch how the Schouten-Nijenhuis, the Frölicher- Nijenhuis and the Nijenhuis-Richardson brackets look in our formalism.

q-alg↗