The Heisenberg Matrix Formulation of Quantum Field Theory

  1. Dr. Dietrich Papenfuß2,
  2. Professor Dr. Dieter Lüst3 and
  3. Professor Dr. Wolfgang P. Schleich4
  1. Stanley J. Brodsky

Published Online: 29 NOV 2007

DOI: 10.1002/9783527610853.ch10

100 Years Werner Heisenberg: Works and Impact

100 Years Werner Heisenberg: Works and Impact

How to Cite

Brodsky, S. J. (2002) The Heisenberg Matrix Formulation of Quantum Field Theory, in 100 Years Werner Heisenberg: Works and Impact (eds D. Papenfuß, D. Lüst and W. P. Schleich), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527610853.ch10

Editor Information

  1. 2

    Alexander von Humboldt-Stiftung, Bonn, Germany

  2. 3

    Humboldt Universität, Institut für Physik, Germany

  3. 4

    Universität Ulm, Abteilung f. Quantenphysik, Albert-Einstein-Allee 11, 89069 Ulm, Germany

Author Information

  1. Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309, USA

  1. Work supported by Department of Energy contract DE–AC03–76SF00515.

Publication History

  1. Published Online: 29 NOV 2007
  2. Published Print: 27 AUG 2002

ISBN Information

Print ISBN: 9783527403929

Online ISBN: 9783527610853

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Keywords:

  • elementary particles theory;
  • Heisenberg matrix formulation of quantum field theory;
  • relativistic systems by evolving in light-front time;
  • periodic boundary conditions;
  • light-front quantization;
  • event generator for high energy physics reactions;
  • light-front partition function;
  • boost properties;
  • shadowing of nuclear structure functions;
  • nuclear light-front wavefunctions

Summary

Heisenberg's matrix formulation of quantum mechanics can be generalized to relativistic systems by evolving in light-front time τ = t + z/c. The spectrum and wavefunctions of bound states, such as hadrons in quantum chromodynamics, can be obtained from matrix diagonalization of the light-front Hamiltonian on a finite dimensional light-front Fock basis defined using periodic boundary conditions in x and x. This method, discretized light-cone quantization (DLCQ), preserves the frame-independence of the front form even at finite resolution and particle number. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-front partition function, summed over exponentially-weighted light-front energies, has simple boost properties, which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-front wavefunctions.