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Faculty of Physics, Lomonosov Moscow State University

Advanced Quantum Field Theory: Modern Applications in HEP, Astro & Cond-Mat
Instructor: assist. prof., Dr. Oleg Kharlanov

Term 1 Examination Syllabus (Spring 2015)
1. London dispersion forces between hydrogen atoms: second-quantized formulation, electric dipole polarizability, calculation of the force. 2. Second quantization of a real massless scalar field in a compact domain. Vacuum energy as a formal series over 1-particle states and via point-splitting. Point-split stress tensor and the Green's function. Casimir tension via the `energy' T00 and the `pressure' Tnn . 3. Casimir effect for a massless scalar field between two plates with the Dirichlet boundary conditions: one-particle states between the plates, explicit energy regularization and renormalization using the smooth cutoff. 4. Electromagnetic Casimir effect between two conducting plates: second quantization, vacuum energy as a series over one-photon energies, one-particle states in the Coulomb gauge. Zeta function of 2 defined on 1-photon wavefunctions between the plates and the Casimir energy. 5. Casimir tension of a massless scalar field between two plates with the Dirichlet boundary conditions using the Green's function technique (the `pressure' Tnn version). The normal-normal component of the stress tensor via the Fourier image of the Green's function, the Wick rotation. 6. Casimir tension for a massless scalar field between a resting and a uniformly moving plate. The Green's function in terms of the reflection operators. Casimir energy renormalization. 7. The Dynamical Casimir Effect for a massless scalar field and an arbitrarily moving `mirror' in D 1 1 . Functional equation on the conformal map `stopping' the mirror. Second-quantized field operator. The point-split stress tensor and regularization of its v.e.v.'s. Mirror energy loss per 1 second due to the Casimir effect. 8. Quantization of the D 1 1 4 theory around a classical solution in the weak-coupling approximation. Vacuum energy (a formal series) and the second-quantized field operator of the excitations. Kink mass renormalization via normal ordering. 9. Photon splitting in a strong external magnetic field. Kinematic considerations. Tensor structure of the matrix elements, hexagon diagram and the Heisenberg­Euler effective Lagrangian. Matrix element for photon splitting and the splitting length (in brief). 10. Neutrino oscillations in dense media. Density matrix description, forward scattering on the neutral dense e/p/n background medium and the effect of neutrino self-action on the oscillations. The effective Hamiltonian for collective neutrino oscillations. 11. Dynamical Lorentz violation in the Axion-Wess­Zumino model. Photons in a constant axion gradient background, 1-loop effective potential for axions (a photon loop). UV completion of the theory and the renormalized potential. Dynamical symmetry violation, critical coupling.