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 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.

scholarly journals EXACT-PROPAGATOR INSTANTANEOUS BETHE–SALPETER EQUATION FOR QUARK–ANTIQUARK BOUND STATES

2006 ◽  
Vol 21 (21) ◽  
pp. 1657-1673 ◽  
Author(s):  
ZHI-FENG LI ◽  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Bound States ◽  
Lattice Gauge Theory ◽  
Bound State ◽  
State Equation ◽  
Wave Functions ◽  
Quantum Field ◽  
Lattice Gauge ◽  
Instantaneous Approximation

Recently an instantaneous approximation to the Bethe–Salpeter formalism for the analysis of bound states in quantum field theory has been proposed which retains, in contrast to the Salpeter equation, as far as possible the exact propagators of the bound-state constituents, extracted nonperturbatively from Dyson–Schwinger equations or lattice gauge theory. The implications of this improvement for the solutions of this bound-state equation, i.e. the spectrum of the mass eigenvalues of its bound states and the corresponding wave functions, when considering the quark propagators arising in quantum chromodynamics are explored.

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 Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Mendel Nguyen ◽  
Yuya Tanizaki ◽  
Mithat Ünsal
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Lattice Theory ◽  
Lattice Gauge Theory ◽  
Global Symmetry ◽  
Leading Order ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Lattice Gauge ◽  
Abelian Lattice

Abstract We study a 3d lattice gauge theory with gauge group U(1)N−1 ⋊ SN, which is obtained by gauging the SN global symmetry of a pure U(1)N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤN, we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.

scholarly journals QCD Thermodynamics on the Lattice

2013 ◽  
Vol 2013 ◽  
pp. 1-26 ◽  
Author(s):  
Sayantan Sharma
Keyword(s):  
Gauge Theory ◽  
Lattice Theory ◽  
Lattice Gauge Theory ◽  
Heavy Ion ◽  
Heavy Ion Experiments ◽  
Lattice Gauge ◽  
Remarkable Progress ◽  
Made In

A remarkable progress has been made in the understanding of the hot and dense QCD matter using lattice gauge theory. The issues which are very well understood as well as those which require both conceptual and algorithmic advances are highlighted. The recent lattice results on QCD thermodynamics which are important in the context of the heavy ion experiments are reviewed. Instances of greater synergy between the lattice theory and the experiments in the recent years are discussed where lattice results could be directly used as benchmarks for experiments, and results from the experiments would be a crucial input for lattice computations.

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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