Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-03-11
J.Phys.A30:3145-3163,1997
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, LateX, To be published in J.Phys.A: Math.Gen: contact email address: jag@maths.nott.ac.uk
Scientific paper
10.1088/0305-4470/30/9/023
We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate the methodology. Stationary solutions to the discrete time Schrodinger wave equation are found to be identical to standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein Gordon system, deriving the equations of motion and conserved quantities such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical particle-like solutions. We extend the formalism to the charged scalar field coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantisation of discrete time mechanics and discrete time Quantum Electrodynamics.
Jaroszkiewicz George
Norton Keith
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