2002/03/13 by J. Wosiek · 3 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Code (set theory) #Computer science #Convergence (economics) #Gauge (firearms) #Gauge group #Gauge theory #Hilbert space #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quantum statistical mechanics #Supersymmetric quantum mechanics #Theoretical physics #Yang–Mills existence and mass gap #hep-th
paper · pdf · doi:10.1016/s0550-3213(02)00810-6
published as Nucl.Phys.B644:85-112,2002 · 39 pages, 9 Postscript figures
arxiv created 2002/03/13 · openalex publication_date 2002/11/01 · arxiv updated 2011/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of a given system is then automatically obtained. The technique is applied to Wess-Zumino quantum mechanics and D=2 and D=4 supersymmetric Yang-Mills quantum mechanics with SU(2) gauge group. Convergence with increasing cut-off was observed in many cases, well within the reach of present machines. Many old results were confirmed and some new ones, especially for the D=4 system, are derived. Extension to D=10 is possible but computationally demanding for higher gauge groups.