Related papers: A geometric approach to a generalized virial theor…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
It is conjectured that in the geometric formulation of quantum computing, one can study quantum complexity through classical entropy of statistical ensembles established non-relativistically in the group manifold of unitary operators. The…
Collective center-of-mass variables are introduced in the Lagrangian formalism of the relativistic classical mechanics of directly interacting particles. It is shown that the transition to the Hamiltonian formalism leads to the…
We investigate the tension between symplecticity and gauge covariance in classical Hamiltonian mechanics. The pursuit of manifest covariance over manifest symplecticity results in a unique geometric formulation. Firstly, covariant yet…
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic…
Canonical coordinates for the Schr\"odinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schr\"odinger equation, considered as a classical field theory, shares with Liouville completely…
The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in…
Applied to field theory, the familiar symplectic technique leads to instantaneous Hamiltonian formalism on an infinite-dimensional phase space. A true Hamiltonian partner of first order Lagrangian theory on fibre bundles $Y\to X$ is…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
This note gives an introduction to Lagrangian field theories in the presence of boundaries. After an overview of the classical aspects, the cohomological formalisms to resolve singularities in the bulk and in the boundary theories (the BV…
This paper presents (in its Lagrangian version) a very general "historical" formalism for dynamical systems, including time-dynamics and field theories. It is based on the universal notion of history. Its condensed and universal formulation…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
The virial theorem is formulated both intrinsically and in local coordinates for a Lagrangian system of mechanical type on a Riemann manifold. An import case studied in this paper is that of an affine virial function associated to a vector…
The authors previous derivation of a variational principle from the total work functional, as a generalization of the first variation of an action functional, is extended by deriving a corresponding generalization of the Hamiltonian…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
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…
Using the recently developed groupoidal description of Schwinger's picture of Quantum Mechanics, a new approach to Dirac's fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function…
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…