相关论文: Quantum Variational Principle and quantum multifor…

Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…

Soon after the Yang-Mills work, the gauge invariance became one of the basic principles in the elementary particles theory. The gauge invariance idea is that Lagrangian has to be invariant not only with respect to the coordinates…

A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for…

We propose a general-purpose, self-adaptive approach to construct variational wavefunction ans\"atze for highly accurate quantum dynamics simulations based on McLachlan's variational principle. The key idea is to dynamically expand the…

The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…

A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between…

We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time as well as in continuous time, as a first example of a Lagrange 1-form structure in the sense of the recent paper [19]. The discrete-time…

Motivated by the notion of Lagrangian multiforms, which provide a Lagrangian formulation of integrability, and by results of the authors on the role of covariant Hamiltonian formalism for integrable field theories, we propose the notion of…

In this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing…

We put forward a finite theory of quantum scattering of fundamental particles without using auxiliary particles. It suggests that to avoid ultraviolet divergencies and model faster-than-light effects it suffices to appropriately change only…

In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…

New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…

Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path integral formalism. It is proven that correct Hamiltonian quantization of these models yields the same result as…

A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…

Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically and…

This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…

A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…

With this paper, a consistent and comprehensive treatise on the foundations of the extended Hamilton-Lagrange formalism will be presented. In this formalism, the system's dynamics is parametrized along a system evolution parameter $s$, and…

We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…