相关论文: Noether conservation laws in quantum mechanics

Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable…

Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…

A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determining Noether symmetries from the metric. The curvature of…

We apply the Noether symmetry analysis in $f\left( Q\right)$-Cosmology to determine invariant functions and conservation laws for the cosmological field equations. For the FLRW background and the four families of connections, it is found…

Noether's Theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. Typically the systems are described in the particle-based context of…

We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a…

Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated…

Internal global symmetries exist for the free non-relativistic Schr\"{o}dinger particle, whose associated Noether charges--the space integrals of the wavefunction and the wavefunction multiplied by the spatial coordinate--are exhibited.…

Spherical symmetry for f(R)-gravity is discussed by searching for Noether symmetries. The method consists in selecting conserved quantities in form of currents that reduce dynamics of f(R)-models compatible with symmetries. In this way we…

Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…

The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar…

A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the…

This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating…

We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…

Noether's theorem and the invariances of the Willmore functional are used to derive conservation laws that are satisfied by the critical points of the Willmore energy subject to generic constraints. We recover in particular previous results…

The main objective of this article is to examine some physically viable solutions through the Noether symmetry technique in $f(R, T^{2})$ theory. For this purpose, we assume a generalized anisotropic and homogenous spacetime that yields…

The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…

Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this…

We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…

It is well-known that all 2d models of gravity---including theories with nonvanishing torsion and dilaton theories---can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines…