Learning objectives
The course aims at providing the students with both concepts and technical tools which are made use of in the study of Lattice Gauge Theories. Emphasis will be both on foundations and on current trends. Special care will be taken of stressing what are the main issues which can be addressed in a non-perturbative approach to quantum field theories.<br />
Students will be provided the opportunity to grasp which numerical tools are needed in this framework and what are best practices for a careful usage of them.<br />
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The interdisciplinary nature of many technical tools used in lattice gauge theories will also be stressed.
Prerequisites
Students are supposed to be familiar with the basic tools in Quantum Field Theories.
Course unit content
Tentative syllabus:<br />
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- Lattice as a regulator for the functional integral; the case of Quantum Mechanics.<br />
- Lattice approach to renormalization; connections to Renormalization Group.<br />
- Lattice formulation of a bosonic theory.<br />
- Lattice formulation of a fermionic theory; doubling problem and solutions to it.<br />
- Wilson formulation of Lattice Gauge Theories: compact QED; lattice SU(3) and the <br />
issues of an auto-interacting theory; lattice QCD.<br />
- Wilson loop, Polyakov loop, interquark potentials, string tension.<br />
- Strong coupling expansion.<br />
- Lattice Perturbation Theory.<br />
- Symanzik's improvement programs for gluonic and fermionic sectors of lattice QCD with <br />
their perturbative and nonperturbative implementations.<br />
- Chirality in lattice QCD.<br />
- Finite temperature and finite density gauge theories: the phase diagram of QCD.<br />
* Introduction to Monte Carlo methods. Numerical results and their interpretation. Examples:<br />
string tension; glueball and hadron spectrum; quark masses; matrix elements <br />
computations; numerical studies of deconfinement and chiral transitions.<br />
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Last item (marked with *) will be introduced in itinere, as the course makes progress, in order to grasp how numerical results can be obtained with respect to the variuos topics.
Full programme
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Bibliography
Main reference books:<br />
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- H. Rothe, Lattice Gauge Theories, An Introduction, World Scientific 1992<br />
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- I. Montvay and G. Münster, Quantum Fields on a Lattice, Cambridge1994
Teaching methods
There will be both oral lessons and labs. In particular, numerical results will be introduced in itinere, as the course makes progress, in order to grasp how they can be obtained with respect to the variuos topics. 2 CFU are to be taken into account as lab credits.<br />
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Examination will be oral, starting from a report the student will be asked to present on a topic chosen fron recent literature.
Assessment methods and criteria
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Other information
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