Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
76
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories (fermion doubling). We investigate the possibility of projecting out these states at the various levels in the construction, but we find that the results of these attempts are either physically unacceptable or geometrically unappealing.
rate research
Read More
I review results from recent investigations of anomalies in fermion--Yang Mills systems in which basic notions from noncommutative geometry (NCG) where found to naturally appear. The general theme is that derivations of anomalies from quantum field theory lead to objects which have a natural interpretation as generalization of de Rham forms to NCG, and that this allows a geometric interpretation of anomaly derivations which is useful e.g. for making these calculations efficient. This paper is intended as selfcontained introduction to this line of ideas, including a review of some basic facts about anomalies. I first explain the notions from NCG needed and then discuss several different anomaly calculations: Schwinger terms in 1+1 and 3+1 dimensional current algebras, Chern--Simons terms from effective fermion actions in arbitrary odd dimensions. I also discuss the descent equations which summarize much of the geometric structure of anomalies, and I describe that these have a natural generalization to NCG which summarize the corresponding structures on the level of quantum field theory. Contribution to Proceedings of workshop `New Ideas in the Theory of Fundamental Interactions, Szczyrk, Poland 1995; to appear in Acta Physica Polonica B.
The Connes and Lott reformulation of the strong and electroweak model represents a promising application of noncommutative geometry. In this scheme the Higgs field naturally appears in the theory as a particular `gauge boson, connected to the discrete internal space, and its quartic potential, fixed by the model, is not vanishing only when more than one fermion generation is present. Moreover, the exact hypercharge assignments and relations among the masses of particles have been obtained. This paper analyzes the possibility of extensions of this model to larger unified gauge groups. Noncommutative geometry imposes very stringent constraints on the possible theories, and remarkably, the analysis seems to suggest that no larger gauge groups are compatible with the noncommutative structure, unless one enlarges the fermionic degrees of freedom, namely the number of particles.
We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons and there is no fermion permutation sign to worry about. We argue that as $U$ becomes finite fermions are liberated but are naturally confined to regions which we refer to as {em fermion bags}. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the silver blaze problem also emerges. Using the three dimensional massless lattice Thirring model as an example we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find $ u=0.87(2)$ and $eta=0.62(2)$.
We discuss ideal delocalization of fermions in a bulk SU(2) x SU(2) x U(1) Higgsless model with a flat or warped extra dimension. So as to make an extra dimensional interpretation possible, both the weak and hypercharge properties of the fermions are delocalized, with the U(1)_Y current of left-handed fermions being correlated with the SU(2)_W current. We find that (to subleading order) ideal fermion delocalization yields vanishing precision electroweak corrections in this continuum model, as found in corresponding theory space models based on deconstruction. In addition to explicit calculations, we present an intuitive argument for our results based on Georgis spring analogy. We also discuss the conditions under which the essential features of an SU(2) x SU(2) x U(1) bulk gauge theory can be captured by a simpler SU(2) x SU(2) model.
We calculate conformal anomalies in noncommutative gauge theories by using the path integral method (Fujikawas method). Along with the axial anomalies and chiral gauge anomalies, conformal anomalies take the form of the straightforward Moyal deformation in the corresponding conformal anomalies in ordinary gauge theories. However, the Moyal star product leads to the difference in the coefficient of the conformal anomalies between noncommutative gauge theories and ordinary gauge theories. The $beta$ (Callan-Symanzik) functions which are evaluated from the coefficient of the conformal anomalies coincide with the result of perturbative analysis.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
