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2005•Journal of Mathematical PhysicsRequires access

On unitary, irreducible representations of the proper, orthochronous Lorentz group

Joanna Kubieniec

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Abstract

The theory of unitary, irreducible representations of the proper, orthochronous Lorentz group is presented by means of the usual tensor calculus in Minkowski space–time. This makes all steps manifestly Lorentz invariant. Explicit expressions for spherically symmetric eigenfunctions of the first Casimir operator C1 of the proper, orthochronous Lorentz group are calculated and their completeness is proved.

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What this paper is about

The theory of unitary, irreducible representations of the proper, orthochronous Lorentz group is presented by means of the usual tensor calculus in Minkowski space–time. This makes all steps manifestly Lorentz invariant. Explicit expressions for spherically symmetric eigenfunctions of the first Casimir operator C1 of the proper, orthochronous Lorentz group are calculated and their completeness is proved.

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Available abstract

The theory of unitary, irreducible representations of the proper, orthochronous Lorentz group is presented by means of the usual tensor calculus in Minkowski space–time. This makes all steps manifestly Lorentz invariant. Explicit expressions for spherically symmetric eigenfunctions of the first Casimir operator C1 of the proper, orthochronous Lorentz group are calculated and their completeness is proved.

Key concepts: Lorentz group, Minkowski space, Representation theory of the Lorentz group, Lorentz transformation, Unitary state, Lorentz covariance, Mathematics, Four-vector

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