Lattice Field Theory (Lecture I)

Who: Jarno Rantaharju (CP3-Origins)
When: Thursday, February 18, 2016 at 14:30
Where: The CP³ meeting room

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Jarno will give a mini course on Lattice Field Theory.
The mini course will consist of 5 lectures of 2 hours each. All the lectures will be in the CP³ meeting room at 14:30 and will be recorded.

The topics of the lectures are:

1) Path integrals and the lattice
We introduce the path integral quantization, the conceptual framework
of regularized quantum field theory and the
connection to statistical physics. The scalar field theory provides a
useful illustration.



2) Fermions
We discuss the lattice regularization of fermion fields. We introduce
the fermion doubling problem and the two most
used fermion discretizations: Wilson fermions and staggered fermions.
We discuss the symmetry properties of
different discretizations.

3) Gauge fields
We complete the our model by adding a lattice regularized gauge field.
We discuss weak and strong coupling
expansions and introduce observables related to the gauge field.

4) The continuum limit and renormalization
We discuss continuum limits, critical lines and the renormalization of
a lattice model with Wilson fermions.
Approaching the continuum in lattice simulations is expensive, and the
cost can be alleviated by improving the
model at fixed lattice spacing.

5) Applications in BSM
Lattice simulations are a useful tool for studying the
non-perturbative structure of gauge field theories. We
introduce observables for studying chiral symmetry breaking and the
beta function in these models. We discuss
challenges specific to beyond Standard Model physics.