XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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First principle theory for the material constants
Marco Anelli, Dan Jonsson, Kenneth Ruud
Centre for Theoretical and Computational Chemistry, Department of
Chemistry, University of Tromsoe , 9037 Tromsoe , Norway
The interactions between matter and electromagnetic fields are commonly analyzed using the constitutive relations,
which relate the applied electric and magnetic fields (E,B) to the response fields (D,H) through the material constants.
Therefore, material constants (also known as constitutive tensors) describe the response of the matter to the external fields.
In the case of a static perturbation, material constants are observable/measurable quantities, and they can been defined using multipole theory.
In contrast, when a dynamic field is considered, multipole theory leads to origin-dependent expressions for the material constants, and thus do not correspond to
physically acceptable observable quantities. There is therefore a need for origin-independent definitions of the material constants.
Origin-independent expressions of the material constants have been derived by Raab and de Lange applying a transformed multipole theory. They have also derived expressions for the material constants based on a covariant formulation of the constitutive relations. Both these theories provide expressions of the material constants
which are covariant, origin-independent and preserve the spatial invariance of the wave equations. In the dynamic case, a unique definitions of the material constants still do not exist, and the possibility of deriving unique definitions for these quantities is still unresolved.
We will discuss our recent analysis of the problem, focusing on the pure electric and magnetic material constants, namely the electric permittivity and the inverse permeability. In particular, we will provide arguments in order to distinguish between the two possible definitions of the material constants proposed so far.
An important part of our analysis will be how to relate the material constants to well-known measurable quantities. We propose that the absorption coefficient and the scattering amplitude, as defined in QED, can be expressed in terms of the electric permittivity, consistently with the definition provided by transformed multipole theory.


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