scholarly journals On Existence of Non-Renormalizable Field Theory: Pure SU(2) Lattice Gauge Theory in Five Dimensions

1992 ◽  
Vol 88 (2) ◽  
pp. 341-350 ◽  
Author(s):  
H. Kawai ◽  
M. Nio ◽  
Y. Okamoto
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Five Dimensions ◽  
Lattice Gauge

scholarly journals Lattice gauge field theory and prismatic sets

2011 ◽  
Vol 108 (1) ◽  
pp. 26 ◽  
Author(s):  
B. Akyar ◽  
J. L. Dupont
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Lie Group ◽  
Lattice Gauge Theory ◽  
Parallel Transport ◽  
Gauge Field Theory ◽  
Classifying Space ◽  
Simplicial Sets ◽  
Lattice Gauge ◽  
Simplicial Set

We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set $S$ and the prismatic star of $S$. Both have the same homotopy type as $S$ and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group $G$ and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying space of $G$. In turn this defines a $G$-bundle over the prismatic star.

VARIATIONAL-CUMULANT EXPANSION TREATMENT OF SU(2) MIXED MODEL IN LATTICE GAUGE THEORY

1986 ◽  
Vol 01 (03) ◽  
pp. 215-220 ◽  
Author(s):  
XI-TE ZHENG ◽  
ZU-GUO TAN ◽  
JIE WANG
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Mixed Model ◽  
Lattice Gauge Theory ◽  
Cumulant Expansion ◽  
Five Dimensions ◽  
Treatment Comparison ◽  
Lattice Gauge ◽  
Variational Treatment ◽  
Better Than

The phase diagrams of the SU(2) mixed model are calculated in four and five dimensions by using the variational method with the cumulant expansion as its corrections. The results are much better than that of the original variational treatment. Comparison with the Monte Carlo results and other approximate analytic results are given.

scholarly journals ASPECTS OF ANOMALIES IN FIELD THEORY

2001 ◽  
Vol 16 (03) ◽  
pp. 331-345 ◽  
Author(s):  
KAZUO FUJIKAWA
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Path Integral Formulation ◽  
Lattice Gauge ◽  
Soft Pion ◽  
Quantum Anomaly ◽  
Quantum Anomalies ◽  
True Quantum

We discuss some formal aspects of quantum anomalies with an emphasis on the regularization of field theory. We briefly review how ambiguities in perturbation theory have been resolved by various regularization schemes. To single out the true quantum anomaly among ambiguities, the combined ideas of PCAC, soft pion limit and renormalizability were essential. As for the formal treatment of quantum anomalies, we mainly discuss the path integral formulation both in continuum and lattice theories. In particular, we discuss in some detail the recent development in the treatment of chiral anomalies in lattice gauge theory.

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.

scholarly journals Looking behind the Standard Model with lattice gauge theory

2018 ◽  
Vol 175 ◽  
pp. 01017 ◽  
Author(s):  
Benjamin Svetitsky
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Standard Model ◽  
Recent Work ◽  
Lattice Gauge Theory ◽  
Strongly Coupled ◽  
Lattice Methods ◽  
Lattice Gauge ◽  
The Standard Model ◽  
Coupled Field

Models for what may lie behind the Standard Model often require nonperturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to address fundamental dynamical questions. I survey recent work in this area.

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