# Algebraic Geometry and Landau Gauge Fixing on the Lattice

#### Algebraic Geometry and Landau Gauge Fixing on the Lattice

- Event time: 2:00pm
- Event date: 4th November 2009
- Speaker: Dhagash Mehta (National University of Ireland Maynooth, Ireland )
- Location: Lecture Theatre B, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

On the lattice, the standard way to fix Landau gauge is to minimizing the so-called lattice Landau gauge (LLG)-fixing functional numerically. Minimizing a multivariate function efficiently is one of the fundamental problems in many branches of theoretical physics. The conventional numerical minimization methods such as Simulated Annealing and Over-relaxation are known to fail in obtaining the global minimum. We observe that the extremizing equations for the LLG-fixing functional and, in general, for multivariate functions arising in many physical phenomena have 'polynomial-like' non-linearity. After explaining how one can transform the extremizing equations for the LLG, for the compact U(1) case as an example, to a system of multivariate polynomial equations, we propose a few methods to solve these equations and obtain all the extrema of the LLG-fixing functional. I will demonstrate our preliminary results from both these methods. If time permits, I will also present the results for the modified lattice Landau gauge which was proposed recently, in order to establish the BRST symmetry on the lattice.

### About Particle Physics Theory seminars

The Particle Physics Theory seminar is a weekly series of talks reflecting the diverse interests of the group. Topics include analytic and numerical calculations based on the Standard Model of elementary particle physics, theories exploring new physics, as well as more formal developments in gauge theories and gravity..