scholarly journals COVARIANT FORMULATION OF NOETHER'S THEOREM FOR κ-MINKOWSKI TRANSLATIONS

2009 ◽  
Vol 24 (07) ◽  
pp. 1333-1358 ◽  
Author(s):  
ALESSANDRA AGOSTINI
Keyword(s):  
Plane Waves ◽  
Equation Of Motion ◽  
Space Time ◽  
Noncommutative Space ◽  
Covariant Formulation ◽  
Scalar Theory ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Free Scalar ◽  
Conserved Currents

The problem of finding a formulation of Noether's theorem in noncommutative geometry is very important in order to obtain conserved currents and charges for particles in noncommutative space–times. In this paper, we formulate Noether's theorem for translations of κ-Minkowski noncommutative space–time on the basis of the five-dimensional κ-Poincaré covariant differential calculus. We focus our analysis on the simple case of free scalar theory. We obtain five conserved Noether currents, which give rise to five energy–momentum charges. By applying our result to plane waves it follows that the energy–momentum charges satisfy a special-relativity dispersion relation with a generalized mass given by the fifth charge. In this paper, we provide also a rigorous derivation of the equation of motion from Hamilton's principle in noncommutative space–time, which is necessary for the Noether analysis.

scholarly journals The Lie group approach to solving differential equations

2020 ◽  
Vol 104 (559) ◽  
pp. 82-106
Author(s):  
Rory Allen
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Galois Theory ◽  
Quantum Field ◽  
Group Approach ◽  
Noether’S Theorem ◽  
Conservation Of Energy ◽  
Noether's Theorem ◽  
Full Power ◽  
Conserved Currents

Certain ideas recur in many areas of mathematics. One example is groups of symmetries, which appear in the Galois theory of equations and in Lie groups. Lie groups are of great value in physics, where Noether’s theorem enables us to derive a conservation law for every case in which a function known as the Lagrangian is invariant under a one-parameter Lie group. The importance of this approach can be seen from the fact that the laws of the conservation of energy, linear momentum and angular momentum are all outcomes of Noether’s theorem, though they can of course be derived by simpler methods. The full power of Noether’s approach is shown in its applications to quantum field theory, where it can be used to find conserved currents and charges.

Introduction

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Conservation Laws ◽  
Lagrangian Mechanics ◽  
General Introduction ◽  
Noether’S Theorem ◽  
Noether's Theorem

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is included.

scholarly journals Stochastic fractal and Noether's theorem

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Rakibur Rahman ◽  
Fahima Nowrin ◽  
M. Shahnoor Rahman ◽  
Jonathan A. D. Wattis ◽  
Md. Kamrul Hassan
Keyword(s):  
Noether’S Theorem ◽  
Noether's Theorem

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

scholarly journals BLACK HOLE EVAPORATION BASED UPON A q-DEFORMATION DESCRIPTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6039-6049 ◽  
Author(s):  
XIN ZHANG
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Radiation Spectrum ◽  
Correlation Effect ◽  
Space Time ◽  
Noncommutative Space ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation ◽  
Starting Point ◽  
New Distribution

A toy model based upon the q-deformation description for studying the radiation spectrum of black hole is proposed. The starting point is to make an attempt to consider the space–time noncommutativity in the vicinity of black hole horizon. We use a trick that all the space–time noncommutative effects are ascribed to the modification of the behavior of the radiation field of black hole and a kind of q-deformed degrees of freedom are postulated to mimic the radiation particles that live on the noncommutative space–time, meanwhile the background metric is preserved as usual. We calculate the radiation spectrum of Schwarzschild black hole in this framework. The new distribution deviates from the standard thermal spectrum evidently. The result indicates that some correlation effect will be introduced to the system if the noncommutativity is taken into account. In addition, an infrared cutoff of the spectrum is the prediction of the model.

Sign in / Sign up

Export Citation Format

Share Document