Lie symmetries on timescales in field theory
Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, 060042, Bucharest, Romania
Accepted: 4 August 2022
Published online: 13 August 2022
Through this paper, the success of dynamic equations on timescale is extended to field theory, in which only the time parameter belongs to the timescale. The method of Lie symmetries is not yet sufficiently developed on a timescale, especially in field theory, and therefore we need to present specific demonstrations of these symmetries. We begin by defining the Lie group generalized infinitesimal transformations on timescales and their jth extension, and we immediately discuss their implication in the invariance of Dirac and Klein–Gordon dynamic equations on timescale. Then, we discuss the Lie symmetries for the Lagrangian and Hamiltonian. For this, we first demonstrate the second Euler–Lagrange equation on timescale. The corresponding conserved quantities for field theories on timescales are derived by using the Lie symmetries. Throughout the paper, we consider some examples in which we apply our theory.
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