Search results for "Lattice Gauge theory"
showing 10 items of 49 documents
Monte Carlo study of cluster-diameter distribution: An observable to estimate correlation lengths
1997
We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function $G_{diam}(x)$, which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter $x$, $G_{diam} \propto \exp(-x/\xi)$, where $\xi$ is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with $q=10$, 15, and $20$ on large square lattices of si…
Multi-boson block factorization of fermions
2017
The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g-2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the g…
A partial elucidation of the gauge principle
2008
The elucidation of the gauge principle "is the most pressing problem in current philosophy of physics" said Michael Redhead in 2003. This paper argues for two points that contribute to this elucidation in the context of Yang–Mills theories. (1) Yang–Mills theories, including quantum electrodynamics, form a class. They should be interpreted together. To focus on electrodynamics is potentially misleading. (2) The essential role of gauge and BRST symmetries is to provide a local field theory that can be quantized and would be equivalent to the quantization of the non-local reduced theory. If this is correct, the gauge symmetry is significant, not so much because it implies ontological conseque…
A new lattice action for studying topological charge
1996
We propose a new lattice action for non-abelian gauge theories, which will reduce short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. If the latter is fine enough, the action of all configurations with non-zero topological charge will satisfy the continuum bound. As a simpler example we consider the $O(3)$ $\sigma$-model in two dimensions, where a numerical analysis of discretized continuum instantons indicates that a finer lattice with half the lattice spacing of the original is enough to satisfy the continuum bound.
Three-dimensional singletons
1990
The three-dimensional analog of singleton gauge theory turns out to be related to the topological gauge theory of Schwartz and Witten. It is a fully-fledged gauge theory, though it involves only a single scalar field. Real, physical degrees of freedom propagate in 3-space, but they are ‘confined’ in the sense that they cannot be detected locally. The physical Hamiltonian density is not zero, but it is concentrated on the boundary at spatial infinity. This boundary surface, a torus, supports a two-dimensional conformal field theory.
The pinch technique at two loops
1999
It is shown that the fundamental properties of gauge-independence, gauge-invariance, unitarity, and analyticity of the $S$-matrix lead to the unambiguous generalization of the pinch technique algorithm to two loops.
Quantum simulation of gauge potentials with cold atoms in optical lattices: a tunable platform for relativistic fermions and axions
2014
We offer here a brief introduction to the idea of quantum simulations with cold atomic gases, with focus on the recent efforts towards artificial gauge potentials and fields. This is mainly intended as a sort of “pedestrian guide” for people not yet working in the field, but curious to get a first contact with it; longer and deeper reviews are addressed for deeper details. As a special case, we focus here on reviewing some own previous contributions about a flexible toolbox based on bichromatic optical lattices and Raman assisted tunnelling. Such a scheme would allow good control on the mass and kinetic terms of a lattice Hamiltonian in different effective dimensions. If realized with fermi…
Hamiltonian lattice QCD at finite density: equation of state in the strong coupling limit
2001
The equation of state of Hamiltonian lattice QCD at finite density is examined in the strong coupling limit by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the many body system. This solution exactly diagonalizes the Hamiltonian to second order in field operators for all densities and is used to evaluate the vacuum energy density from which we obtain the equation of state. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. Our result is in qualitative agreement with continuum models and should be verifiabl…
Abelian charges in a nonabelian Yang-Mills theory from the stratification of the space of gauge potentials
1992
Abstract The Abelian charges in a non-Abelian Yang-Mills-Dirac theory arising from the reduction of the structure group are studied. They are defined by the concept of the stabilizer gauge transformations. Their properties are investigated. The relationship between the whole class of stabilizers and the stratification of the space of gauge potentials is given. The effect of the spontaneous symmetry breaking mechanism on these charges is discussed.
The Higgs Mechanism and Spontaneous Symmetry Breaking
2002
As is well known all gauge bosons of a pure Yang-Mills theory are necessarily massless. This is so because any ad-hoc mass term such as $$ m_i^2 A_\mu ^{(i)} A^{(i)\mu } or \sum\limits_{ik} {M_{ik} } A_\mu ^{(i)} A^{(k)\mu } $$ is incompatible with local gauge invariance. It is saidthat W. Pauli hadd evelopednonab elian gauge theory for himself (or knew about it from the work of H. Weyl and O. Klein) before the work of C.N. Yang and R. Mills (1954) but dismissedit because he hadrealizedthat the gauge particles wouldall be massless. As there was only one massless spin-1 particle known at the time (the photon) nonabelian gauge theory was to be rejectedon physical grounds. The few facts that w…