On the stratified classical configuration space of lattice QCD

A Gauge Model for Quantum Mechanics on a Stratified Space

“…In [10,11,18], T * K has been trivialized by right translation and the sign conventions necessarily differ. The (classical unreduced) Hamiltonian H : T * K → R of our model is given by…”

“…This leads to a finite-dimensional Hamiltonian system with symmetries. For first results on the stratified structure of both the reduced configuration space and the reduced phase space of systems of this type, see [10,11,18,29,30]. Within canonical quantization for the unreduced system, the algebra of observables and its representations have been extensively investigated, see [40][41][42] for quantum electrodynamics and [36,38,39] for quantum chromodynamics.…”

Singular Poisson–Kähler geometry of certain adjoint quotients

“…shows that, in the coordinates (a 1 , a 2 , a 3 , a 4 ), the variety D (2,2) in A a 2 ) → (a 1 , a 2 , a 3 , a 4 ) identifies D (2,2) with a copy of 2-dimensional complex affine space A 2 . Inspection of the coefficients a 1 and a 2 of the polynomial…”

“…The purpose of the present paper is to complement the results in [16]: For the special case where K = SU(n) (n ≥ 2) we shall elucidate the complex algebraic stratified Kähler structure in terms of complex discriminant varieties and variants thereof. We will also interpret the resulting stratified Kähler geometry on the adjoint quotient for the special case where K = SU (2) in terms of the reduced phase space of a spherical pendulum constrained to move with angular momentum zero. In physics, a space of the kind (T * K) 0 is the building block for certain lattice gauge theories.…”

“…shows that, in terms of the coordinates a 1 and a 2 , the variety D 4 ⊆ D (2,2) is the curve given by the equation (4.24) 3a 2 1 − 8a 2 = 0. We intend to work out elsewhere how equations for varieties of the kind D ν which are not ordinary discriminant varieties (i.e.…”