Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.

We define topological orthoalgebras (TOAs), and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space (in its norm or strong operator topology) is an example of a lattice-ordered TOA that is not a topological lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show tha...

In this paper we begin on a new lattice formulation of the non-linear change of variables called the Cho–Faddeev–Niemi decomposition in SU(2) Yang-Mills theory. This is a compact lattice formulation improving the non-compact lattice formulation proposed in our previous paper. Based on this formulation, we propose a new gauge-invariant definition of the magnetic monopole current which guarantees...

A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, all anomalous non-abelian theories are includ...

We analyze the chiral Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. For non-compact and Wilson formulation of the gauge field action it is proven that the effective lattice model is Osterwalder-Schrader positive, which is a sufficient condition for the reconstruction of a physical Hilbert ...

Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4+5+6+5+4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 2(23)+2(12) different sequence...

We analyze the Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. The possible class of interpolations for the gauge fields, compatible with gauge invariance is discussed. The effective action for the lattice gauge field is computed for the Wilson formulation as well as for non-compact lattice ...

In this paper, we shall introduce generalized fuzzy compactness in L-spaces where L is a complete de Morgan algebra. This definition does not rely on the structure of basis lattice L and no distributivity is required. The intersection of a generalized fuzzy compact L-set and a generalized closed Lset is a generalized fuzzy compact L-set. The generalized irresolute image of a generalized fuzzy c...

In this paper, the concept of intuitionistic fuzzy soft sets is applied to residuated lattices. The notion of intuitionistic fuzzy soft filters of a residuated lattice is introduced and some related properties are investigated. Then the representations of generated intuitionistic fuzzy soft filters are established. We prove that the lattice of all intuitionistic fuzzy soft filters of a residuat...