Exploring the Unstable Modes Dynamics by the Lattice Schrodinger Functional.pdf

1 ¨ Exploring the Unstable Modes Dynamics by the Lattice Schrodinger Functional Paolo Ceaa,b and Leonardo Cosmaib aDipartimento di Fisica - Universit`a di Bari, via Amendola 173, 70126 Bari, Italy bINFN - Sezione di Bari, via Amendola 173, 70126 Bari, Italy We analyze the problem of the Nielsen-Olesen unstable modes in the SU (2) lattice gauge theory by means of a recently intro- duced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic 6 field. We find that for lattice sizes above a certain critical length the density of effective action shows a behaviour compatible 9 with the presence of the unstable modes. 9 1 l 1. The Lattice Effective Action In Eq. (6) T is the extension in Euclidean time, u ext ext ext J Z [U ] = Z [U , U ] and Z (0) is is the lattice 0 The Euclidean Schr¨odinger functional in Yang- Schr¨odinger functional without external background Mills theories without matter fields is: ext field (U = 1). 1 Z A(f ) , A(i) = A(f ) |exp(−HT )P|A(i) (1) Our effective action is by definition gauge invariant 1 and can be used for a non-perturbative investigation of v where P projects onto the physical states and H is the the properties of the quantum vacuum. In