Polarimetry is a highly sensitive method to quantify changes of the polarization state of light when passing through matter and is therefore widely applied in material science. The progress of synchrotron and X-ray free electron laser (XFEL) sources has led to significant developments of X-ray polarizers, opening perspectives for new applications of polarimetry to study source and beamline parameters as well as sample characteristics. X-ray polarimetry has shown to date a polarization purity of less than $1.4\times {10}^{-11}$, enabling the detection of very small signals from ultrafast phenomena. A prominent application is the detection of vacuum birefringence. Vacuum birefringence is predicted in quantum electrodynamics and is expected to be probed by combining an XFEL with a petawatt-class optical laser. We review how source and optical elements affect X-ray polarimeters in general and which qualities are required for the detection of vacuum birefringence.

A new generation of high power laser facilities will provide laser pulses with extremely high powers of 10 petawatt (PW) and even 100 PW, capable of reaching intensities of $10^{23}~\text{W}/\text{cm}^{2}$ in the laser focus. These ultra-high intensities are nevertheless lower than the Schwinger intensity $I_{S}=2.3\times 10^{29}~\text{W}/\text{cm}^{2}$ at which the theory of quantum electrodynamics (QED) predicts that a large part of the energy of the laser photons will be transformed to hard Gamma-ray photons and even to matter, via electron–positron pair production. To enable the investigation of this physics at the intensities achievable with the next generation of high power laser facilities, an approach involving the interaction of two colliding PW laser pulses is being adopted. Theoretical simulations predict strong QED effects with colliding laser pulses of ${\geqslant}10~\text{PW}$ focused to intensities ${\geqslant}10^{22}~\text{W}/\text{cm}^{2}$.

Algebras associated with quantum electrodynamics and other gauge theories share some mathematical features with T-duality. Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be regarded as a braided Clifford algebra over a braided commutative boson algebra, sharing much of the structure of ordinary Clifford algebras.