相关论文: Topological Obstruction in Block-spin Transformati…
In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a…
A transformation is devised to convert any lattice Dirac fermion operator into a Ginsparg-Wilson Dirac fermion operator. For the standard Wilson-Dirac lattice fermion operator, the transformed new operator is local, free of O(a) lattice…
A Ginsparg-Wilson Relation (GWR) is obtained in the presence of chiral symmetry breaking terms. It leads to the PCAC relation as well as an anomaly relation on the lattice. For general fermions, the deviation from the exact GWR is getting…
In the continuum, a topological obstruction to the vanishing of the non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac…
We pursue Ginsparg and Wilsons' block spin approach in the derivation of the Ginsparg-Wilson relation and study the correspondence of the eigenmodes of the Dirac operators in the continuum and lattice theories. After introducing a suitable…
The inclusion of the unstable features of a spin-1 particle, without breaking the electromagnetic gauge invariance, can be properly accomplished by including higher order contributions as done in the so-called fermion loop scheme (for the W…
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…
The Baxter 8-vertex model is equivalent to a particular lattice formulation of a self-interacting, massive Dirac fermion theory. In the time-continuum limit, the lattice Hamiltonian (XYZ spin chain) can be explicitly transformed to a…
A novel quantum representation of lattice spin operators (LSOs) is achieved by mapping quantum spins onto their classical analogues for spin size $S=1/2$ and $S=1$. The "braket" representations of LSOs are attained thanks to a profound…
The Ginsparg-Wilson relation is extended to interacting field theories with general linear symmetries. Our relation encodes the remnant of the original symmetry in terms of the blocked fields and guides the construction of invariant lattice…
A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial…
The Ginsparg-Wilson relation, if written in a suitable form, can be used as a condition for lattice Dirac operators of massless fermions also in odd dimensions. The fermion action with such a Dirac operator is invariant under a generalized…
We construct a lattice Dirac operator of overlap type that describes the propagation of a Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it is believed…
A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =…
Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein condensates with hyperfine spin F=1 are investigated theoretically based on the Ginzburg-Pitaevskii equations near $T_{c}$. The Abrikosov lattice with clear core regions…
The overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, realizes exact chiral symmetry on the lattice without any unphysical doubler modes. To perform the path integrals, one should, however, note that the overlap fermion…
Our aim is to compute the lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon on the lattice. The theoretical basis of the calculation is the operator product expansion. To construct operators…
Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form…
Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set $\{\U(2), \textrm{CNOT}\}$, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1,…
The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be…