scholarly journals UNSTABLE MODES AND CONFINEMENT IN THE LATTICE SCHRÖDINGER FUNCTIONAL APPROACH

1998 ◽  
Vol 13 (11) ◽  
pp. 861-871 ◽  
Author(s):  
PAOLO CEA ◽  
LEONARDO COSMAI
Keyword(s):  
Gauge Theory ◽  
Numerical Simulations ◽  
Effective Action ◽  
Lattice Gauge Theory ◽  
Critical Length ◽  
Functional Approach ◽  
Gauge Invariant ◽  
Lattice Gauge ◽  
Chromomagnetic Field

We analyze the problem of the Nielsen–Olesen unstable modes in the SU(2) lattice gauge theory by means of a recently introduced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic field. We find that for lattice sizes above a certain critical length, the density of effective action shows a behavior compatible with the presence of the unstable modes. We put out a possible relation between the dynamics of the unstable modes and the confinement.

scholarly journals DETERMINATION OF EFFECTIVE ACTIONS FOR SU(3) LATTICE GAUGE THEORY

1995 ◽  
Vol 10 (06) ◽  
pp. 503-513 ◽  
Author(s):  
T. TAKAISHI
Keyword(s):  
Gauge Theory ◽  
Effective Action ◽  
Lattice Gauge Theory ◽  
Good Precision ◽  
Coupling Constant ◽  
Lattice Gauge ◽  
Dimensional Coupling

The demon method is applied to determine the effective action on blocked SU(3) gauge configurations. First the method is tested on SU(3) gauge configurations with known couplings. It turns out that the method works well to determine couplings with good precision in rather short microcanonical updates. Next the method is implemented for a set of blocked SU(3) gauge configurations and we successfully determine an effective action in seven-dimensional coupling constant space.

scholarly journals Preserving gauge invariance in neural networks

2022 ◽  
Vol 258 ◽  
pp. 09004
Author(s):  
Matteo Favoni ◽  
Andreas Ipp ◽  
David I. Müller ◽  
Daniel Schuh
Keyword(s):  
Neural Networks ◽  
Gauge Theory ◽  
Gauge Invariance ◽  
Lattice Gauge Theory ◽  
Process Data ◽  
Regression Problem ◽  
Gauge Invariant ◽  
Lattice Gauge ◽  
Linear Regression Problem ◽  
Equivariant Functions

In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the architecture and show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice. We compare the performance of L-CNNs and non-equivariant networks using a non-linear regression problem and demonstrate how gauge invariance is broken for non-equivariant models.

TOPOLOGY AND SU(2) LATTICE GAUGE THEORY WITH DYNAMICAL WILSON FERMIONS

1992 ◽  
Vol 03 (01) ◽  
pp. 53-59
Author(s):  
B. JOZEFINI ◽  
V. LINKE ◽  
M. MÜLLER-PREUSSKER ◽  
A. NAKAMURA
Keyword(s):  
Gauge Theory ◽  
Effective Action ◽  
Topological Charge ◽  
Lattice Gauge Theory ◽  
Exact Algorithm ◽  
Parameter Expansion ◽  
Vacuum Structure ◽  
Lattice Gauge ◽  
Wilson Fermions

In this talk we present results of a recent investigation of the topological vacuum structure in SU(2) lattice gauge theory with Wilson fermions. An effective action given by the hopping parameter expansion up to the 6-th order is used. To check the reliability of this approximation we compare it with the outcomes of an exact algorithm. The topological charge is measured according to a geometric prescription.

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