Gauge theory and gravity in the loop formulation [chapter]

Renate Loll
Canonical Gravity: From Classical to Quantum  
still require a more complete understanding. outlook contains a list of mathematical and physical inputs for the loop formulation which the discussion, Section 7 describes some features of quantized loop theories, and the final regularized loop approach and enabled us to do certain calculations explicitly. To round off Section 6, I introduce some ideas from lattice gauge theory which have proved useful in a the loop approach, and describes the content of the underlying reconstruction theorems.
more » ... truction theorems. ln the equivalence between the connection and the loop formulation which lies at the heart of constraints. It is shown how a group structure arises on the space of loops. Section 5 discusses tities satisfied by the holonomies and their traces, the latter also known as the Mandelstam holonomies, and briefly review past applications in physics. Section 4 is devoted to the iden deal with specific aspects of the loop formulation. In Section 3, I define paths, loops and theory and gravity as theories on connection space, to set the stage for Sections 3-5 which The-following Section 2 summarizes the classical and quantum description of both gauge
doi:10.1007/3-540-58339-4_21 fatcat:pk5dxqa5bjdd3lgc54ziuuv7gu