Dr. Marco Schreck
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Theoretical arguments strongly suggest that not only matter consists of impartible constituents, but that at the very smallest length scales spacetime itself is characterized by a structure. The origin of such a spacetime granularity is that any quantum system constrained to a region with its size lying in the magnitude of the Planck length may have energy fluctuations associated with the Planck energy. Therefore energy density highly fluctuates at this scale, which then has impact on the geometry of spacetime due to Einstein's field equations. If such a small-scale structure of spacetime (spacetime foam) exists indeed, it is reasonable to assume that for length scales being much larger than the Planck length, the vacuum effectively behaves like a medium.This leads us back to the notion of an ether, which is however neither ponderable nor considered as a carrier for electromagnetic waves. Instead it is a fundamental property of spacetime due to quantum fluctuations at the Planck scale. A nontrivial refraction index of the vacuum makes the physical laws for a particle energy-dependent and this is a clear indication for a violation of Lorentz invariance.

An effective framework describing Lorentz violation at energies much smaller than the Planck scale is the Standard-Model Extension (SME). It uses field theory language to incorporate Lorentz violation into the Standard Model of elementary particle physics and General Relativity, i.e., the action of the SM and the Einstein-Hilbert action form the basis. Both are modified by adding further terms, which only involve Standard-Model fields and the Riemannian notion of curvature (plus torsion).

The additional contributions to the action are constructed such that they do not have any free Lorentz indices. This makes them invariant under coordinate changes induced by Lorentz transformations of the underlying spacetime coordinates (observer Lorentz invariance).

Each additional term can be decomposed into a part containing the ordinary Standard-Model fields and the curvature tensor plus a background field giving rise to preferred spacetime directions. The latter is interpreted as a low-energy manifestation of physics at the Planck scale such as a small-scale structure of spacetime. A physical Lorentz transformation acts on a particle propagating through the background field, but it leaves the background field invariant. This changes the laws of nature of the particle in analogy to the different behavior of an electron propagating along differing paths inside the electric field of a capacitor (particle Lorentz violation).

Classical Lagrangians and Finsler geometry

For several years research has been performed on how to map the field description of the Standard-Model Extension (SME) to a classical-particle analog. This is carried out to have a base for incorporating Lorentz violation into gravity. General Relativity and extensions of it are classical theories. Therefore, it is reasonable to obtain from the SME how classical, relativistic pointlike particles are affected by Lorentz violation. This puts us into a position to couple such a particle to a curved spacetime and to consider its modified behavior.

In the recent article I obtain the first classical Lagrangians for various sectors of the nonminimal SME. Recall that the nonminimal SME incorporates all CPT- and Lorentz-violating contributions based on higher-dimensional field operators.

In another paper  I collect all classical Lagrangians obtained for the minimal SME. Each of these Lagrangians is promoted to a quantum-mechanical Hamilton operator. The latter are shown to correctly match the low-energy limit of the SME Hamiltonian, i.e., quantization can be performed consistently. Furthermore, it is proven that at first order in Lorentz violation and at second order in the momentum, all minimal Lagrangians are linked to the Hamilton functions by a simple transformation.

Lorentz-violating electromagnetic waves in gravitational fields

Describing Lorentz-violating particles in the presence of gravity is a challenge. In one of my latest projects I consider photons underlying a particular  type of Lorentz violation that propagate in a background gravity field.  As long as quantum processes do not play a role it suffices to restrict  ourselves to classical considerations. The classical equivalent of a photon is an electromagnetic wave described by the eikonal equation. Thereby the Lorentz-violating vacuum behaves like a medium with nontrivial refractive index. In my most recent article photons being subject to isotropic Lorentz violation are investigated propagating nearby a massive body such as the Sun or a big planet. This leads to a modification of the deflection angle according to General Relativity. Experimental sensitivities on Lorentz violation can be obtained from the parameters of currently running and future space missions.

Analytical studies of bunch compression in a linear accelerator

I am still working on a project that I started (in collaboration with P. Wesolowski) more than two years ago at the ANKA storage ring facility of the Karlsruhe Institute of Technology (KIT). It resides in the field of accelerator physics and it is based on the linear electron accelerator FLUTE that is currently being built at the KIT. One of the goals of the accelerator is two generate particle bunches with lengths ranging from few femtoseconds to several hundreds of femtoseconds. Bunch compression is carried out in a chicane of four dipole magnets. The bunch is then subject to space charge forces and to the back reaction of emitted coherent synchrotron radiation where such effects were treaded numerically with simulation tools. In our article we cross check some of these numerical results with semi-analytical methods.


Marco Schreck, Sep. 2015, proudly created with Microsoft Expression Web 4

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