From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics

  title={From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics},
  author={Gabriele Carcassi and Christine A. Aidala and David John Baker and Lydia Bieri},
  journal={Journal of Physics Communications},
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a dynamical system whose set of states forms a topological space and whose law of evolution is a self-homeomorphism. Assuming the system is infinitesimally reducible—specifying the state and the dynamics of the whole system is equivalent to giving the state and the… 

Geometrical and physical interpretation of the action principle

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

The fundamental connections between classical Hamiltonian mechanics, quantum mechanics and information entropy

The main difference between classical and quantum systems can be understood in terms of information entropy, which provides insights that allow to understand the analogies and differences between the two theories.

Space-time structure may be topological and not geometrical

In a previous effort we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental

Hamiltonian mechanics is conservation of information entropy

A pr 2 02 0 Hamiltonian mechanics is conservation of information entropy

In this work we show the equivalence between Hamiltonian mechanics and conservation of information entropy. We will show that distributions with coordinate independent values for information entropy

Classical mechanics and infinitesimal reducibility

We briefly show how classical mechanics can be rederived and better understood as a consequence of three assumptions: infinitesimal reducibility, deterministic and reversible evolution, and kinematic

Towards a general mathematical theory of experimental science

This article shows that the set of possible cases distinguishable by verifiable statements is equipped with a natural Kolmogorov and second countable topology and a natural $\sigma$-algebra.



Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems

We will present a consistent description of Hamiltonian dynamics on the 'symplectic extended phase space' that is analogous to that of a time-independent Hamiltonian system on the conventional

Any Hamiltonian System Is Locally Equivalent to a Free Particle

In this work we use the Hamilton-Jacobi theory to show that locally all the Hamiltonian systems with n degrees of freedom are equivalent. That is, there is a canonical transformation connecting two

The mathematical foundations of quantum mechanics

Classical mechanics was first envisaged by Newton, formed into a powerful tool by Euler, and brought to perfection by Lagrange and Laplace. It has served as the paradigm of science ever since. Even

The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?

We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.

Quantum Dissipative Systems

Fundamentals Survey of the Various Approaches Path Integral Description of Open Quantum Systems Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic

Variational Principles in Mechanics

The recognition that minimizing an integral function through variational methods (as in the last chapters) leads to the second-order differential equations of Euler-Lagrange for the minimizing

Bose-Einstein condensation

In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein

The Quantum Postulate and the Recent Development of Atomic Theory

IN connexion with the discussion of the physical interpretation of the quantum theoretical methods developed during recent years, I should like to make the following general remarks regarding the

Pseudo holomorphic curves in symplectic manifolds

Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called