Abstract
We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S(x 0,r) where x 0 and r are positive integers representing time and maximal total energy, respectively. The operator S(x 0,r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy (x 0,r). In order to maintain total unit probability, the transition probabilities need to be reconditioned at each (x 0,r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter.
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References
Bisco, A., D’Ariano, G., Perinotti, P.: Special relativity in a discrete quantum universe. arXiv:quant-ph.1503.01017v3 (2016)
Crouse, D.: On the nature of discrete space-time. arXiv:quant-ph.1608.08506v1 (2016)
Crouse, D.: The lattice world, quantum foam and the universe as a metamaterial. Appl. Phys. A 122(4), 1–7 (2016)
Dowker, F.: The birth of spacetime atoms as the passage of time. Ann. New York Acad. Sci. 1326.1, 18–25 (2014)
Feynman, R.: Simulating physics with computers. Intern. J. Theor. Phys. 21, 467–488 (1982)
Gudder, S.: Discrete spacetime and quantum field theory (to appear)
Gudder, S.: Discrete scalar quantum field theory. arXiv:physics.gen-ph.1610.07877v1 (2016)
Hagar, A.: Discrete or Continuous?: The Quest for Fundamental Length in Modern Physics. Cambridge University Press (2014)
Heisenberg, W.: The Physical Principles of Quantum Mechanics. University of Chicago Press, Chicago (1930)
McKenze, A.: Proposal for an experiment to demonstrate the block universe. arXiv:physics.pop-ph.1603.008959
Peskin, M., Schroeder, D.: An Introduction to Quantum Field Theory. Addison-Wesely, Reading Mass (1995)
Russell, B.: The Analysis of Matter. Dover, New York (1954)
‘t Hooft, G.: Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics. Found. Phys. 44, 406–425 (2014)
Veltman, M.: Diagrammatica. Cambridge University Press, Cambridge (1994)
Zahedi, R: On discrete physics: a perfect deterministic structure for reality – and a direct logical derivation of the fundamental laws of nature. arXiv:physics.gen-ph.1501.01373v12 (2016)
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Gudder, S. Reconditioning in Discrete Quantum Field Theory. Int J Theor Phys 56, 3838–3851 (2017). https://doi.org/10.1007/s10773-017-3350-6
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DOI: https://doi.org/10.1007/s10773-017-3350-6