Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations

Abstract

In this paper we consider three-dimensional quantum q-oscillator field theory without spectral parameters. We construct an essentially big set of eigenstates of evolution with unity eigenvalue of discrete time evolution operator. All these eigenstates belong to a subspace of total Hilbert space where an action of evolution operator can be identified with quantized discrete BKP equations (synonym Miwa equations). The key ingredients of our construction are specific eigenstates of a single three-dimensional R-matrix. These eigenstates are boundary states for hidden three-dimensional structures of U_q(B_n^1) and U_q(D_n^1)$.

13 pages

References in corpus (6)

• Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups
• Discrete differential geometry. Consistency as integrability
• Quantum geometry of 3-dimensional lattices
• Super-tetrahedra and super-algebras
• Quantization of three-wave equations
• Classical integrable field theories in discrete 2+1 dimensional space-time