Computational Quantum Field Theory. Part II: Lattice Gauge Theory

1994 ◽  
Vol 8 (2) ◽  
pp. 170
Author(s):  
Jean Potvin ◽  
Harvey Gould ◽  
Jan Tobochnik
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Quantum Field ◽  
Lattice Gauge ◽  
Computational Quantum

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 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 GAUGE THEORY OF GRAVITY REQUIRES MASSIVE TORSION FIELD

1999 ◽  
Vol 14 (16) ◽  
pp. 2531-2535
Author(s):  
RAINER W. KÜHNE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Theory ◽  
Gauge Boson ◽  
Rest Mass ◽  
Quantum Field ◽  
Spin Field ◽  
Torsion Field ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

One of the greatest unsolved issues of the physics of this century is to find a quantum field theory of gravity. According to a vast amount of literature, unification of quantum field theory and gravitation requires a gauge theory of gravity which includes torsion and an associated spin field. Various models including either massive or massless torsion fields have been suggested. We present arguments for a massive torsion field, where the probable rest mass of the corresponding spin three gauge boson is the Planck mass.

The application of Regge calculus to quantum gravity and quantum field theory in a curved background

1982 ◽  
Vol 383 (1785) ◽  
pp. 359-377 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Gravity ◽  
Quantum Field ◽  
Regge Calculus ◽  
Curved Space ◽  
Monte Carlo Techniques ◽  
Lattice Gauge ◽  
Discrete Laplacians ◽  
Lattice Gauge Theories

The application of Regge calculus to quantum gravity and quantum field theory in a curved background is discussed. A discrete form of exterior differential calculus is developed, and this is used to obtain Laplacians for P -forms on the Regge manifold. To assess the accuracy of these approximations, the eigenvalues of the discrete Laplacians were calculated for the regular tesselations of S 2 and S 3 . The results indicate that the methods obtained in this paper may be used in curved space–times with an accuracy comparing with that obtained in lattice gauge theories on a flat background. It also becomes evident that Regge calculus provides particularly suitable lattices for Monte-Carlo techniques.

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 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.

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