# Majdouline BORJI

**Phd student**

**Research group : **Mathematical physics

**Thesis: **"Renormalization of quantum field theories that break translation invariance."**Advisor: **Christoph Kopper

**Research interests**

*flow equations, renormalization group, quantum field theory, half-space, lattice, film geometry, Casimir effect*

Quantum field theories that break translation invariance appear in many physical context. The translation invariance can be broken by the regularization scheme used such as the lattice regularization [1], by the geometry of the space-time (a Riemanian manifold for example) [2], or by the presence of a boundary. When the loss of this symmetry is induced by the properties of the space-time, the renormalization of the QFT is affected. The less symmetric the theory is, the more counter-terms are needed to make it finite. The aim of this thesis is to study first the perturbative renormalization of the massive scalar field theory with a quartic interaction regularized by a lattice, using the method of the flow equations and prove that the Euclidean symmetries are restored in the continuum limit. We would like also to investigate the perturbative renormalizability of boundary field theories. The massive scalar field theory in a half-space [3] is the simplest model of such theories. We compute first all the possible propagators that correspond to all possible boundary conditions and prove the renormalizability of this theory for the Robin boundary condition.

[1] M. Borji, Ch. Kopper, Perturbative renormalization of the lattice regularized phi 44 with flow equations, Journal of Mathematical Physics. 2020;31(11):112304.

[2] Ch. Kopper, V. F. Müller, Renormalization proof for massive phi44 theory on Riemannian manifolds, Communications in Mathemathical Physics 2007; 275(2): 331-372.

[3] H.W. Diehl, in: Phase Transitions and Critical Phenomena, Vol. 10. Eds. C. Domb and J.L. Lebowitz (Academic Press, London, 1986) p. 75

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