Group structure of superluminal Lorentz transformations and their representation

1989 ◽  
Vol 67 (7) ◽  
pp. 645-648
Author(s):  
H. C. Chandola ◽  
B. S. Rajput
Keyword(s):  
Lorentz Group ◽  
Group Structure ◽  
Lorentz Transformations ◽  
Poincaré Group ◽  
Poincare Group ◽  
Inertial Frames ◽  
Homogeneous Lorentz Group

Constructing the generalized superluminal Lorentz transformations for inertial frames with nonpreferred orientation, we have investigated their group theoretical and commutation properties. The extended homogeneous Lorentz group in terms of these transformations has been constructed and its generators have been derived; these have been shown to generate the ray representation of the resulting Poincaré group.

QUANTUM MECHANICS ON HYPERBOLOIDS

1994 ◽  
Vol 06 (01) ◽  
pp. 19-38
Author(s):  
LARS-ERIK LUNDBERG
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Symmetry Group ◽  
Lorentz Group ◽  
Scattering Matrix ◽  
Approximate Symmetry ◽  
Poincaré Group ◽  
Poincare Group ◽  
Homogeneous Lorentz Group

We consider a quantum theory on hyperboloids, a theory whose symmetry group is the homogeneous Lorentz group and with Schrödinger theory as its nonrelativistic analogue. The Poincaré group is a good approximate symmetry of the scattering matrix.

Relativistic symmetry

2021 ◽  
pp. 8-30
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Group Theory ◽  
Lorentz Group ◽  
Irreducible Representations ◽  
Lorentz Transformations ◽  
Not Given ◽  
Poincare Group ◽  
Relativistic Symmetry ◽  
Tensor Representations ◽  
The Subject ◽  
Spinor Representations

This chapter discusses relativistic symmetry, starting from the Lorentz transformations. Basic notions of group theory are introduced before a more detailed discussion of the Lorentz and Poincaré groups is given. Tensor representations and spinor representations of the Lorentz group are described, although full proofs of the theorems are not given. The chapter ends with the irreducible representations of the Poincaré group. This chapter provides all of the necessary notions for group theory, although it is not intended to replace a textbook on the subject.

Reduction of the Poincaré Group with Respect to the Lorentz Group

1972 ◽  
Vol 13 (10) ◽  
pp. 1585-1592 ◽  
Author(s):  
W. W. MacDowell ◽  
Ralph Roskies
Keyword(s):  
Lorentz Group ◽  
Poincaré Group ◽  
Poincare Group

Errata: Reduction of the Poincaré group with respect to the Lorentz group

1973 ◽  
Vol 14 (12) ◽  
pp. 2018-2018
Author(s):  
S. W. MacDowell ◽  
Ralph Roskies
Keyword(s):  
Lorentz Group ◽  
Poincaré Group ◽  
Poincare Group

scholarly journals Quaternion generalization of super-Poincaré group

2019 ◽  
Vol 34 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Bhupendra C. S. Chauhan ◽  
Pawan Kumar Joshi ◽  
O. P. S. Negi
Keyword(s):  
Lorentz Group ◽  
Space Time ◽  
Poincaré Group ◽  
Poincare Group ◽  
Poincaré Algebra

Super-Poincaré algebra in [Formula: see text] space–time dimensions has been studied in terms of quaternionic representation of Lorentz group. Starting the connection of quaternion Lorentz group with [Formula: see text] group, the [Formula: see text] spinors for Dirac and Weyl representations of Poincaré group are described consistently to extend the Poincaré algebra to super-Poincaré algebra for [Formula: see text] space–time.

scholarly journals Particles with 2 states and Lorentz transformations

1966 ◽  
Vol 6 (2) ◽  
pp. 221-222 ◽  
Author(s):  
John M. Blatt ◽  
C. A. Hurst
Keyword(s):  
Lorentz Group ◽  
Lorentz Transformations ◽  
Natural Connection ◽  
Discrete States ◽  
Homogeneous Lorentz Group

In this note, we draw attention to a natural connection between a group closely related to the homogeneous Lorentz group, and the most general set of measurements possible on particles with only two discrete states. We may think of these two states as “spin up” and “spin down’, represented by the vectors α = (1, 0) and β = (0, 1), respectively.

scholarly journals SPACETIME FROM SYMMETRY: THE MOYAL PLANE FROM THE POINCARÉ–HOPF ALGEBRA

2009 ◽  
Vol 24 (23) ◽  
pp. 1811-1821 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
M. MARTONE
Keyword(s):  
Hopf Algebra ◽  
Lorentz Group ◽  
Commutative Algebra ◽  
Poincaré Group ◽  
Poincare Group ◽  
Group Invariant ◽  
Spacetime Algebra ◽  
Algebra Of Functions ◽  
Moyal Plane ◽  
The Right

We show how to get a noncommutative product for functions on spacetime starting from the deformation of the coproduct of the Poincaré group using the Drinfel'd twist. Thus it is easy to see that the commutative algebra of functions on spacetime (ℝ4) can be identified as the set of functions on the Poincaré group invariant under the right action of the Lorentz group provided we use the standard coproduct for the Poincaré group. We obtain our results for the noncommutative Moyal plane by generalizing this result to the case of the twisted coproduct. This extension is not trivial and involves cohomological features. As is known, spacetime algebra fixes the coproduct on the diffeomorphism group of the manifold. We now see that the influence is reciprocal: they are strongly tied.

scholarly journals Massless finite and infinite spin representations of Poincaré group in six dimensions

2021 ◽  
pp. 136064
Author(s):  
I.L. Buchbinder ◽  
S.A. Fedoruk ◽  
A.P. Isaev ◽  
M.A. Podoinitsyn
Keyword(s):  
Poincaré Group ◽  
Poincare Group ◽  
Six Dimensions ◽  
Spin Representations
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