Topic
Lorentz group
About: Lorentz group is a research topic. Over the lifetime, 2059 publications have been published within this topic receiving 45513 citations.
Papers published on a yearly basis
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Papers
TL;DR: The superposition principle of the wave function is defined in this article, which is the fundamental principle of quantum mechanics that the system of states forms a linear manifold, in which a unitary scalar product is defined.
Abstract: It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state. It is possible, therefore, to normalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (ψ,Φ) of two normalized wave functions ψ and Φ is called the transition probability from the state ψ into Φ, or conversely. This is supposed to give the probability that an experiment performed on a system in the state Φ, to see whether or not the state is ψ, gives the result that it is ψ. If there are two or more different experiments to decide this (e.g., essentially the same experiment, performed at different times) they are all supposed to give the same result, i.e., the transition probability has an invariant physical sense.
3,248 citations
1,329 citations
TL;DR: In this article, a generalized Bondi-Metzner group (GBM group) is proposed to re-derive the Lorentz group as an "asymptotic symmetry group" which leaves invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields.
Abstract: It is pointed out that the definition of the inhomogeneous Lorentz group as a symmetry group breaks down in the presence of gravitational fields even when the dynamical effects of gravitational forces are completely negligible. An attempt is made to rederive the Lorentz group as an "asymptotic symmetry group" which leaves invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields. By analyzing recent work of Bondi and others on gravitational radiation it is shown that, with apparently reasonable boundary conditions, one obtains not the Lorentz group but a larger group. The name "generalized Bondi-Metzner group" ("GBM group") is suggested for this larger group.It is shown that the GBM group contains an Abelian normal subgroup whose factor group is isomorphic to the homogeneous orthochronous Lorentz group; that the GBM group contains precisely one Abelian four-dimensional normal subgroup, which can be identified with the group of rigid translations; that the GBM group contains an infinite number of different subgroups isomorphic to the inhomogeneous orthochronous Lorentz group; that the infinitesimal GBM group algebra permits at least one nontrivial representation, which is directly analogous to the rest-mass-zero and spin-zero representation of the Lorentz group; that in any representation of the infinitesimal GBM group algebra there is a "rest mass" operator which commutes with all the other operations; and that no similar "spin" operator appears to exist. It is argued that the GBM group is so similar to the inhomogeneous Lorentz group that the former may be compatible as a symmetry group with present microphysics.Two applications are given: Certain quantum commutation relations covariant under GBM transformations are presented; and a denumerably infinite set of integral invariants, for classical asymptotically flat gravitational fields, are derived. The four simplest integral invariants constitute the total energy momentum radiated to infinity by gravitational waves.
1,163 citations
TL;DR: In this article, the relationship of the sTlm (θ, φ) to the spherical harmonics of R 4 is also indicated, and the behavior of sYlm under the conformal group of the sphere is shown to realize a representation of the Lorentz group.
Abstract: Recent work on the Bondi‐Metzner‐Sachs group introduced a class of functions sYlm (θ, φ) defined on the sphere and a related differential operator ð. In this paper the sYlm are related to the representation matrices of the rotation group R 3 and the properties of ð are derived from its relationship to an angular‐momentum raising operator. The relationship of the sTlm (θ, φ) to the spherical harmonics of R 4 is also indicated. Finally using the relationship of the Lorentz group to the conformal group of the sphere, the behavior of the sTlm under this latter group is shown to realize a representation of the Lorentz group.
992 citations
TL;DR: In this paper, the authors show that the κ-deformed Poincare quantum algebra proposed for particle physics has the structure of a Hopf algebra bicrossproduct U(so (1, 3)) T.
971 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 10 |
| 2023 | 31 |
| 2022 | 88 |
| 2021 | 36 |
| 2020 | 48 |