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Dynamics of discrete-space structure

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Abstract

We introduce a model for self-generating discrete-space structure based on the “local” quantum mechanics of graphs. In this approach, the dimension of space becomes a scale-dependent quantity (ρ dimension); it can, at least in principle, be calculated from the theory. We show that the straightforward use of the creation and annihilation operator approach (with standard commutation relations) leads to contradiction when applied to graphs. We define a reformulated Fock-space method based on a topological description. The properties of the theory are discussed in the framework of a simple solvable model.

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Dadić, I., Pisk, K. Dynamics of discrete-space structure. Int J Theor Phys 18, 345–358 (1979). https://doi.org/10.1007/BF00670430

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Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Commutation Relation
  • Operator Approach