Related papers: Lattice Regularization and Symmetries
We study the structure and perform some explicit calculations for the power ultraviolet divergences and their renormalization in the Chiral Pertubation Theory with lattice regularization in 1 and 2 loops.
The physics of strong interactions is invariant under the exchange of left-handed and right-handed quarks, at least in the massless limit. This invariance is reflected in the chiral symmetry of quantum chromodynamics. Surprisingly, it has…
The model with the fermions coupled in the non - minimal way to the gauge theory of Lorentz group is considered. The lattice regularization is suggested. It is argued that this model may exist in the phase with broken chiral symmetry and…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
We propose a formulation of lattice fermions with one-sided differences that is hermitian, chirally symmetric (barring a bare mass term) and completely free of doubling. To obtain the axial anomaly in perturbation theory it was necessary to…
For two decades it was believed that chiral symmetries cannot be realized in lattice field theory but this has changed now. Highlights of these new developments will be presented with emphasis on the mathematical structure of the so called…
Starting from the continuum Dirac operator, I construct a renormalisation group blocking which transforms the continuum action into a lattice action, and I specifically consider the Wilson and overlap formalisms. For Wilson fermions the…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations…
This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity…
We compare the results of renormalization-group and lattice studies for the properties of the electroweak phase transition. This comparison reveals the mechanisms that underlie the phenomenology of the phase transition.
While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a…
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix…
Different aspects concerning the rigorous definition of the traces and determinants of the operators involved in a procedure ---proposed by Neuberger and others--- for avoiding fermion doublers on the lattice, are considered. A result of…
We present a general formulation of chiral gauge theories, which admits Dirac operators with more general spectra, reveals considerably more possibilities for the structure of the chiral projections, and nevertheless allows appropriate…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
When a quantum field theory has a symmetry, global or local like in gauge theories, in the tree or classical approximation formal manipulations lead to believe that the symmetry can also be implemented in the full quantum theory, provided…
An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.
Recently we have discussed realization of an exact chiral symmetry in theories with self-interacting fermions on the lattice, based upon an auxiliary field method. In this paper we describe construction of the lattice chiral symmetry and…