Does noncommutative geometry encompass lattice gauge theory?
نویسندگان
چکیده
منابع مشابه
Lattice Gauge Fields and Noncommutative Geometry
Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the supporting manifold (compactified spacetime or spatial slice) interpreting it as a finite topological approximation in the sense of Sorkin. This finite space...
متن کاملApplication of Noncommutative Differential Geometry on Lattice to Anomaly Analysis in Abelian Lattice Gauge Theory
The chiral anomaly in lattice abelian gauge theory is investigated by applying the geometric and topological method in noncommutative differential geometry(NCDG). A new kind of double complex and descent equation are proposed on infinite hypercubic lattice in arbitrary even dimensional Euclidean space, in the framework of NCDG. Using the general solutions to proposed descent equation, we derive...
متن کاملGauge Networks in Noncommutative Geometry
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known s...
متن کاملNoncommutative Geometry and Spacetime Gauge Symmetries of String Theory
We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex operator algebra and show that its algebraic properties bear a striking resemblence to some structures appearing in M Theory, such as the noncommutative torus. We...
متن کاملNoncommutative Geometry and Gauge Theory on Discrete Groups
We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action functionals for unitary gauge theories. A detailed analysis of two simple models based on Z2 and Z3 follows. Finally we study the method of combining the discrete an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physics Letters B
سال: 1998
ISSN: 0370-2693
DOI: 10.1016/s0370-2693(98)00734-5