Quantum electrodynamics of inhomogeneous anisotropic media

ADRIAN E. RUBIO LOPEZ; FERNANDO C. LOMBARDO

EUROPEAN PHYSICAL JOURNAL C - PARTICLES AND FIELDS

SPRINGER

Lugar: Berlin; Año: 2015 vol. 75 p. 75 - 93

1434-6044

In this work we calculate the closed time path generating functional for the electromagnetic (EM) field interacting with inhomogeneous anisotropic matter. For this purpose, we first find a general expression for the electro- magnetic field?s influence action from the interaction of the field with a composite environment consisting in the quan- tum polarization degrees of freedom in each point of space, at arbitrary temperatures, connected to thermal baths. Then we evaluate the generating functional for the gauge field, in the temporal gauge, by implementing the Faddeev?Popov proce- dure. Finally, through the point-splitting technique, we cal- culate closed expressions for the energy, the Poynting vector, and the Maxwell tensor in terms of the Hadamard propaga- tor. We show that all the quantities have contributions from the field?s initial conditions and also from the matter degrees of freedom. Throughout the whole work we discuss how the gauge invariance must be treated in the formalism when the EM-field is interacting with inhomogeneous anisotropic mat- ter. We study the electrodynamics in the temporal gauge, obtaining the EM-field?s equation and a residual condition. Finally we analyze the case of the EM-field in bulk material and also discuss several general implications of our results in relation with the Casimir physics in a non-equilibrium scenario.