This article is cited in 2 papers

Nonstandard Lagrangians for a real scalar field and a fermion field from the nonuniqueness principle

S. Supanyo^ab, M. Tanasittikosol^ab, S. Yoo-Kong<sup>c

a</sup> Theoretical and Computational Physics Group, Department of Physics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok, Thailand
^b Theoretical and Computational Science Centre, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok, Thailand
^c Institute for Fundamental Study, Naresuan University, Phitsanulok, Thailand

Abstract: We construct a nonstandard Lagrangian, called the multiplicative form, for a homogeneous scalar field and a fermion field via the inverse calculus of variations with the equations of motion that still satisfy the respective Klein–Gordon and Dirac equations. By employing the nonuniqueness of the Lagrangian, we show that the Lagrangians can be written as linear combinations of the standard and nonstandard Lagrangians. The stability of the ghost field, an unnatural smallness of the cosmological constant, and the chiral condensate are discussed by using these new Lagrangians.

Keywords: nonuniqueness, nonstandard Lagrangian, quantum field theory, Klein–Gordon equation, Dirac equation.

Received: 06.02.2024
Revised: 01.04.2024

DOI: 10.4213/tmf10694

 English version: Theoretical and Mathematical Physics, 2024, 221:1, 1695–1710

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