The Lorentz Group and its Representations

2006 ◽  
pp. 407-566
Author(s):  
K. N. Srinivasa Rao
Keyword(s):  
Lorentz Group

scholarly journals The Topological Origin of Quantum Randomness

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 581
Author(s):  
Stefan Heusler ◽  
Paul Schlummer ◽  
Malte S. Ubben
Keyword(s):  
High School ◽  
Hilbert Space ◽  
Group Theory ◽  
Lorentz Group ◽  
Quantum Physics ◽  
Time Development ◽  
Mathematical Structures ◽  
Stochastic Nature ◽  
Quantum Randomness ◽  
And Topology

What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the ‘4π-realm’) lead to a probabilistic behaviour of observables in space-time (the ‘2π-realm’)? We propose a simple topological model for quantum randomness. Following Kauffmann, we elaborate the mathematical structures that follow from a distinction(A,B) using group theory and topology. Crucially, the 2:1-mapping from SL(2,C) to the Lorentz group SO(3,1) turns out to be responsible for the stochastic nature of observables in quantum physics, as this 2:1-mapping breaks down during interactions. Entanglement leads to a change of topology, such that a distinction between A and B becomes impossible. In this sense, entanglement is the counterpart of a distinction (A,B). While the mathematical formalism involved in our argument based on virtual Dehn twists and torus splitting is non-trivial, the resulting haptic model is so simple that we think it might be suitable for undergraduate courses and maybe even for High school classes.

scholarly journals ON THE KALUZA–KLEIN GEOMETRIZATION OF THE ELECTROWEAK MODEL WITHIN A GAUGE THEORY OF THE FIVE-DIMENSIONAL LORENTZ GROUP

2006 ◽  
Vol 15 (05) ◽  
pp. 717-736
Author(s):  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Lorentz Group ◽  
Lagrangian Density ◽  
Gauge Fields ◽  
Normalization Factor ◽  
Current Term ◽  
Electroweak Model ◽  
Kaluza Klein

The geometrization of the Electroweak Model is achieved in a five-dimensional Riemann–Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extracoordinate and of a normalization factor. U (1) weak hypercharge gauge fields are obtained from a Kaluza–Klein scheme, while the tetradic projections of the extradimensional contortion fields are interpreted as SU (2) weak isospin gauge fields. SU (2) generators are derived by the identification of the weak isospin current to the extradimensional current term in the Lagrangian density of the local Lorentz group. The geometrized U (1) and SU (2) groups will provide the proper transformation laws for bosonic and spinorial fields. Spin connections will be found to be purely Riemannian.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

Physical operators and the representations of the inhomogeneous lorentz group

1965 ◽  
Vol 37 (4) ◽  
pp. 1396-1406 ◽  
Author(s):  
D. J. Candlin
Keyword(s):  
Lorentz Group ◽  
Inhomogeneous Lorentz Group

Partial-Wave Analysis in Terms of the Homogeneous Lorentz Group

1967 ◽  
Vol 164 (5) ◽  
pp. 1981-1990 ◽  
Author(s):  
R. Delbourgo ◽  
Abdus Salam ◽  
J. Strathdee
Keyword(s):  
Partial Wave ◽  
Lorentz Group ◽  
Partial Wave Analysis ◽  
Wave Analysis ◽  
Homogeneous Lorentz Group

The relativistic semi-group, Lorentz group, and tachyons. II

1976 ◽  
Vol 19 (5) ◽  
pp. 616-619
Author(s):  
V. V. Yudin
Keyword(s):  
Lorentz Group ◽  
Semi Group

scholarly journals Two subgroups of the lorentz group and their physical significance

1968 ◽  
Vol 24 (1) ◽  
pp. 139-139
Author(s):  
L. Jánossy
Keyword(s):  
Lorentz Group ◽  
Physical Significance

scholarly journals Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group

1993 ◽  
Vol 156 (3) ◽  
pp. 607-638 ◽  
Author(s):  
S. Majid
Keyword(s):  
Lorentz Group ◽  
Matrix Structure ◽  
Sklyanin Algebra
Sign in / Sign up

Export Citation Format

Share Document