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Sergey Bragin

Publications and source records attributed to Sergey Bragin.

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Commutative algebraic monoid structures on affine spaces

We study commutative associative polynomial operations $\mathbb{A}^n\times\mathbb{A}^n\to\mathbb{A}^n$ with unit on the affine space $\mathbb{A}^n$ over an algebraically closed field of characteristic zero. A classification of such operations is obtained up to dimension 3. Several series of operations are constructed in arbitrary dimension. Also we explore a connection between commutative algebraic monoids on affine spaces and additive actions on toric varieties.

math.AG

High-Energy Vacuum Birefringence and Dichroism in an Ultrastrong Laser Field

A long-standing prediction of quantum electrodynamics, yet to be experimentally observed, is the interaction between real photons in vacuum. As a consequence of this interaction, the vacuum is expected to become birefringent and dichroic if a strong laser field polarizes its virtual particle--antiparticle dipoles. Here, we derive how a generally polarized probe photon beam is influenced by both vacuum birefringence and dichroism in a strong linearly polarized plane-wave laser field. Furthermore, we consider an experimental scheme to measure these effects in the nonperturbative high-energy regime, where the Euler-Heisenberg approximation breaks down. By employing circularly polarized high-energy probe photons, as opposed to the conventionally considered linearly polarized ones, the feasibility of quantitatively confirming the prediction of nonlinear QED for vacuum birefringence at the $5σ$ confidence level on the time scale of a few days is demonstrated for upcoming 10 PW laser systems. Finally, dichroism and anomalous dispersion in vacuum are shown to be accessible at these facilities.

hep-ph