The exponential map for the unitary group SU(2,2)

@article{Barut1994TheEM,
  title={The exponential map for the unitary group SU(2,2)},
  author={Asim Orhan Barut and Jos{\'e} Ricardo R. Zeni and Alexander Laufer},
  journal={Journal of Physics A},
  year={1994},
  volume={27},
  pages={6799-6805}
}
In this article, we extend our previous results for the orthogonal group SO(2,4) to its homomorphic group SU(2,2). Here we present a closed finite formula for the exponential of a 4*4 traceless matrix, which can be viewed as the generator (Lie algebra elements) of the SL(4,C) group. We apply this result to the SU(2,2) group, the lie algebra of which can be represented by Dirac matrices, and discuss how the exponential map for SU(2,2) can be written by means of Dirac matrices. 
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References

SHOWING 1-10 OF 27 REFERENCES
The exponential map for the conformal group O(2,4)
We present a general method to obtain a closed finite formula for the exponential map from the Lie algebra to the Lie group for the defining representation of orthogonal groups. Our method is basedExpand
a Thoughtful Study of Lorentz Transformations by Clifford Algebras
We give a thoughtful presentation of proper orthocronous Lorentz transformations using the space-time (ℝ1,3) and the Pauli (ℝ3,0) algebras. We present in a closed finite form, a generic written asExpand
Parametrization of SU(n) with n−1 orthonormal vectors
A generalization to SU(n) of a well‐known relation in SU(2) is proposed. It relies on the observation that an element of SU(n) has associated with it in a natural way n−1 orthonormal vectors inExpand
A generalized local U(1) gauge invariance for both the standard and pauli couplings of QED
It is proved that both the standard minimal coupling, eψγμψAμ, and the anomalous Pauli coupling, aψσ μvψFμv, of quantumelectrodynamics are locally invariant under the one-parameter local U(1) gaugeExpand
Matrix and tensor constructions from a generic SU(n) vector
Projection operators appropriate to the general multispinor representations of SU(n) are constructed in a systematic way from the components of a single generic SU(n) vector transforming as theExpand
Unitary irreducible representations ofSU(2,2)
Using a Lie algebra method based on works byHarish-Chandra, several series of unitary, irreducible representations of the groupSU(2,2) are obtained.
Gauge field theory of gravity.
  • Dehnen, Ghaboussi
  • Physics, Medicine
  • Physical review. D, Particles and fields
  • 1986
We propose a Yang-Mills field theory of gravity based on a unitary phase gauge invariance of the Lagrangian where the gauge transformations are those of the SU(2) x U(1) symmetry of the two spinors.Expand
Theory of group representations and applications
The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book onExpand
Unified spin gauge theory of electroweak and gravitational interactions
A spin gauge theory describing fundamental fermions and their electroweak and gravitational interactions is proposed. It is modelled on an eight-dimensional curved manifold M and uses its associatedExpand
Theory of Group Representations
I Algebraic Foundations of Representation Theory.- 1. Fundamental Concepts of Group Theory.- 2. Fundamental Concepts and the Simplest Propositions of Representation Theory.- II Representations ofExpand
...
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2
3
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