SU(2) QCD in the Path Representation: General Formalism and Mandelstam Indentities
Rodolfo Gambini, Leonardo Setaro
TL;DR
This paper develops a path-dependent Hamiltonian formalism for SU(2) gauge theory with fermions in 3+1 dimensions, introducing new Mandelstam identities linking open and closed path operators.
Contribution
It presents a novel path representation formalism for SU(2) gauge theories with fermions, including new Mandelstam identities relating open and closed paths.
Findings
New path representation formalism for SU(2) gauge theories
Two types of Mandelstam identities involving open and closed paths
Framework for gauge-invariant operators in a path-based Hilbert space
Abstract
We introduce a path-dependent hamiltonian representation (the path representation) for SU(2) with fermions in 3 + 1 dimensions. The gauge-invariant operators and hamiltonian are realized in a Hilbert space of open path and loop functionals. We obtain two new types of Mandelstam identities one that connects open path operators with loop operators and other involving the end points of the paths.
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