Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Shenyang Gongye Daxue xuebao

Symmetry group and conservation law

Guo Lian

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

This paper derives the relationship between the fundamental mechanical quantity in quantum mechanics and the generation element in symmetry transformation group. Further theoretical analysis indicates that there is a conversation law only when unitary transformation symmetry group exist.

Related papers

The Conservation Quantity in Quantum Mechanics

Zheng Wei-qiang

The relationship between conservation quantity and symmetry transformation in Quantum mechanics is discussed.Special cases,such as conservation of momentum,conservation of angular momentum,and conservation of energy in quantum mechanics,are discussed.

Journal of Gansu Lianhe University•Jan 1, 2006•0 citations

Symmetries of the hamiltonian operator and constants of motion

G. F. Torres del Castillo, J.E. Herrera Flores

It is shown that, in the framework of non-relativistic quantum mechanics, any conserved Hermitian operator (which may depend explicitly on the time) is the generator of a one-parameter group of unitary symmetries of the Hamiltonian and that, conversely, any one-parameter family of unitary symmetries of the Hamiltonian is generated by a conserved Hermitian operator.

arXiv:1510.04876•Revista Mexicana de Física•Jan 1, 2016•0 citations

Symmetry and Conservation Law

Tao Xiang

Corresponding to each symmetry, there is a conservation law with a characteristic conserving quantity which is invariant under that transformation. One of the aims of physical research is to search for symmetries and the corresponding observables that are invariant under certain classes of transformation. The Stone theorem ensures the existence of a Hermitian infinitesimal generator for an Abelian group of unitary transformation. The spatial translation operator is a specific example of this theorem and the momentum operator is the generator of spatial translation. This Galilean principle of relativity must be true in quantum mechanics as well. Time-reversal symmetry is a symmetry of the system under the transformation of time reversal.

CRC Press eBooks•Mar 31, 2022•0 citations

Symmetry in Quantum Mechanics

Масуд Чайчиан, Rolf Hagedorn

The structures are physical systems and/or their mathematical descriptions consisting of elements such as particles, fields, observables, operators etc and of relations between these elements: the equations of motion and the rules of quantum mechanics. Examples of symmetries are reflections, permutations of particles, time reversal. The physical system has a symmetry group means, then, that there is a group of transformations leaving the equations of motion and the rules of quantum mechanics invariant. The discrete symmetries lead to conservation laws frequently expressible in terms of quantum numbers, but sometimes requiring a more elaborate description. The observables corresponding to the super-selection quantum numbers can be measured without disturbing any other measurement; their values are always sharp. The chapter shows that the invariant subspace may be labelled by continuous quantum numbers (for instance momentum) when the direct sum becomes a direct integral.

CRC Press eBooks•Jul 14, 2023•0 citations

Intimate Connections: Symmetries and Conservation Laws in Quantum versus Classical Mechanics

Pablo Ruiz de Olano

In this article, I use a number of remarks made by Eugene Wigner to defend the claim that the nature of the connection between symmetries and conservation laws is different in quantum and in classical mechanics. In particular, I provide a list of three differences that obtain between the Hilbert space formulation of quantum mechanics and the Lagrangian formulation of classical mechanics. I also show that these differences are due to the fact that conservation laws are not the only consequence that symmetries have in quantum mechanics and to the fact that, in classical mechanics, the connection between symmetries and conservation laws does not always obtain.

Philosophy of Science•Dec 1, 2017•1 citation

Symmetries and conservation laws

Gennaro Auletta, Mauro Fortunato, Giorgio Parisi A

A symmetry is an equivalence of different physical situations, and is therefore strictly associated with the concept of invariance . One of the main aims of physics is the search in nature for symmetries and, therefore, for observables that are invariant under certain classes of transformation. In this context, it becomes particularly interesting to look for the conditions under which a certain symmetry is eventually broken. We have already discussed some symmetries of quantum mechanics: time translations (Ch. 3), space translations (Ch. 2) and rotations (Ch. 6). Another example of invariance is represented by the indistinguishability of identical particles, which we discussed in the previous chapter. Symmetries are induced by physical transformations that generate some invariant properties (see Sec. 8.1). In Sec. 8.2, the continuous transformations induced by rotations and space translations are analyzed, whereas in Sec. 8.3, space reflection and time reversal ( discrete symmetries) are discussed. As we shall see in the next chapter, time reversibility is lost in the measurement process. The rigorous mathematical framework of a theory of transformations and of their invariance is called group theory (the subject of Sec. 8.4). Quantum transformations and symmetries Active and passive transformations We have seen that time evolution may be represented either in the Schrödinger picture (state vectors evolve and observables are kept constant) or in the Heisenberg picture (states vectors remain constant and observables evolve) (see Subsec. 3.6.1 and Sec. 5.3).

Cambridge University Press eBooks•Apr 16, 2009•1 citation
Corresponding to each symmetry, there is a conservation law with a characteristic conserving quantity which is invariant under that transformation. One of the aims of physical research is to search for symmetries and the corresponding observables that are invariant under certain classes of transformation. The Stone theorem ensures the existence of a Hermitian infinitesimal generator for an Abelian group of unitary transformation. The spatial translation operator is a specific example of this theorem and the momentum operator is the generator of spatial translation. This Galilean principle of relativity must be true in quantum mechanics as well. Time-reversal symmetry is a symmetry of the system under the transformation of time reversal.
The structures are physical systems and/or their mathematical descriptions consisting of elements such as particles, fields, observables, operators etc and of relations between these elements: the equations of motion and the rules of quantum mechanics. Examples of symmetries are reflections, permutations of particles, time reversal. The physical system has a symmetry group means, then, that there is a group of transformations leaving the equations of motion and the rules of quantum mechanics invariant. The discrete symmetries lead to conservation laws frequently expressible in terms of quantum numbers, but sometimes requiring a more elaborate description. The observables corresponding to the super-selection quantum numbers can be measured without disturbing any other measurement; their values are always sharp. The chapter shows that the invariant subspace may be labelled by continuous quantum numbers (for instance momentum) when the direct sum becomes a direct integral.
In this article, I use a number of remarks made by Eugene Wigner to defend the claim that the nature of the connection between symmetries and conservation laws is different in quantum and in classical mechanics. In particular, I provide a list of three differences that obtain between the Hilbert space formulation of quantum mechanics and the Lagrangian formulation of classical mechanics. I also show that these differences are due to the fact that conservation laws are not the only consequence that symmetries have in quantum mechanics and to the fact that, in classical mechanics, the connection between symmetries and conservation laws does not always obtain.
A symmetry is an equivalence of different physical situations, and is therefore strictly associated with the concept of invariance . One of the main aims of physics is the search in nature for symmetries and, therefore, for observables that are invariant under certain classes of transformation. In this context, it becomes particularly interesting to look for the conditions under which a certain symmetry is eventually broken. We have already discussed some symmetries of quantum mechanics: time translations (Ch. 3), space translations (Ch. 2) and rotations (Ch. 6). Another example of invariance is represented by the indistinguishability of identical particles, which we discussed in the previous chapter. Symmetries are induced by physical transformations that generate some invariant properties (see Sec. 8.1). In Sec. 8.2, the continuous transformations induced by rotations and space translations are analyzed, whereas in Sec. 8.3, space reflection and time reversal ( discrete symmetries) are discussed. As we shall see in the next chapter, time reversibility is lost in the measurement process. The rigorous mathematical framework of a theory of transformations and of their invariance is called group theory (the subject of Sec. 8.4). Quantum transformations and symmetries Active and passive transformations We have seen that time evolution may be represented either in the Schrödinger picture (state vectors evolve and observables are kept constant) or in the Heisenberg picture (states vectors remain constant and observables evolve) (see Subsec. 3.6.1 and Sec. 5.3).