scholarly journals Relativity and irreversibility

2004 ◽  
Vol 2004 (1) ◽  
pp. 35-49 ◽  
Author(s):  
I. Antoniou ◽  
E. Karpov ◽  
I. Prigogine ◽  
G. Pronko
Keyword(s):  
Hilbert Space ◽  
Lorentz Transformation ◽  
Relativistic Model ◽  
Decaying States ◽  
Nonlocal Action ◽  
Nonintegrable Systems

The Lorentz transformation is extended to the decaying states in a relativistic model of interacting fields. The nonlocal action is defined beyond the Hilbert space. This shows that irreversible extensions of dynamics of Poincaré nonintegrable systems are compatible with relativity.

Rotations and Lorentz transformations

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Hilbert Space ◽  
Lorentz Transformation ◽  
Computational Approach ◽  
Lorentz Transformations ◽  
Helicity Formalism ◽  
Mathematical Properties ◽  
Finite Dimensional ◽  
Lorentz Boosts ◽  
Dirac Spinors ◽  
Finite Dimensional Hilbert Space

A computational approach to rotations and Lorentz transformation is presented. The discussion starts with the mathematical properties of the rotation and the proper orthochronous Lorentz groups. Rotation and Lorentz transformations are implemented by exponentiating generators of SU(2). This approach allows rotations of states in a finite-dimensional Hilbert space to be carried out with the same machinery used to rotate ordinary vectors and it allows Lorentz boosts of Dirac spinors to be carried out with the same machinery used to boost four-vectors. Rotations and boosts can be applied to other objects with simple transformation properties. A computational approach to the helicity formalism used in scattering and decay theory is presented, and a library devoted to the manipulation of objects in spacetime is introduced.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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