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.

scholarly journals Testing the mechanism of lepton compositeness

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Vincenzo Afferrante ◽  
Axel Maas ◽  
René Sondenheimer ◽  
Pascal Törek
Keyword(s):  
Gauge Theory ◽  
Standard Model ◽  
Gauge Invariance ◽  
Bound States ◽  
Lattice Gauge Theory ◽  
Higgs Field ◽  
Left Handed ◽  
Lattice Gauge ◽  
The Standard Model ◽  
Weyl Fermions

Strict gauge invariance requires that physical left-handed leptons are actually bound states of the elementary left-handed lepton doublet and the Higgs field within the standard model. That they nonetheless behave almost like pure elementary particles is explained by the Fr"ohlich-Morchio-Strocchi mechanism. Using lattice gauge theory, we test and confirm this mechanism for fermions. Though, due to the current inaccessibility of non-Abelian gauged Weyl fermions on the lattice, a model which contains vectorial leptons but which obeys all other relevant symmetries has been simulated.

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 Biological Lattice Gauge Theory as Modeling of Quantum Neural Networks

2018 ◽  
Vol 10 (1) ◽  
pp. 23
Author(s):  
Yi-Fang Chang
Keyword(s):  
Field Theory ◽  
Neural Networks ◽  
Gauge Theory ◽  
Lattice Theory ◽  
Lattice Gauge Theory ◽  
Helical Structure ◽  
Gauge Field Theory ◽  
Quantum Field ◽  
Double Helical Structure ◽  
Lattice Gauge

Based on quantum biology and biological gauge field theory, we propose the biological lattice gauge theory as modeling of quantum neural networks. This method applies completely the same lattice theory in quantum field, but, whose two anomaly problems may just describe the double helical structure of DNA and violated chiral symmetry in biology. Further, we discuss the model of Neural Networks (NN) and the quantum neutral networks, which are related with biological loop quantum theory. Finally, we research some possible developments on described methods of networks by the extensive graph theory and their new mathematical forms.

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