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A novel nonlocal spin-1/2 theory: classical and quantum aspects

J. R. Nascimento, Gonzalo J. Olmo, A. Yu. Petrov, P. J. Porfírio, Ramires N. da Silva

TL;DR

This paper introduces a nonlocal spin-1/2 theory with a form factor that is an entire function of the Dirac operator, $f(\\slashed{\\partial})$, aiming to preserve unitarity while incorporating nonlocality. It derives the classical dispersion and shows deviations from the standard relation as the nonlocal scale $\\Lambda$ becomes relevant, with locality recovered in the $\\Lambda\\to\\infty$ limit. It analyzes quantum corrections by computing the fermionic one-loop effective action with a Yukawa coupling, finding UV-dominated nonlocal effects suppressed in the IR, and demonstrates gauge invariance under minimal coupling to a $U(1)$ field. It also derives a nonlocal Pauli equation in the nonrelativistic limit, revealing a nonlocal correction to the $g$-factor, and discusses potential extensions to curved spacetime and phenomenological implications.

Abstract

We propose a novel nonlocal spin-1/2 theory in which the form factor depends on the Dirac operator rather than on the d'Alembert operator. In this scenario, we explore some classical and quantum aspects of this new theory. At the classical level, we investigate the dispersion relation of free spin-1/2 particles and find that it increasingly deviates from the standard case as the nonlocal effects become relevant. At the quantum level, we compute the fermionic one-loop effective action for the nonlocal spin-1/2 theory with Yukawa coupling and show that the contributions of nonlocal effects are significant in the UV limit, while in the IR they are suppressed by a UV cutoff scale, which has been chosen to coincide with the nonlocality scale $Λ$. We minimally couple a $U(1)$ gauge field to the nonlocal spin-1/2 field theory and explicitly demonstrate that this theory is gauge invariant. Finally, we obtain a nonlocal version of the Pauli equation and the impact of the nonlocality in the $g$-factor of massive particles.

A novel nonlocal spin-1/2 theory: classical and quantum aspects

TL;DR

This paper introduces a nonlocal spin-1/2 theory with a form factor that is an entire function of the Dirac operator, , aiming to preserve unitarity while incorporating nonlocality. It derives the classical dispersion and shows deviations from the standard relation as the nonlocal scale becomes relevant, with locality recovered in the limit. It analyzes quantum corrections by computing the fermionic one-loop effective action with a Yukawa coupling, finding UV-dominated nonlocal effects suppressed in the IR, and demonstrates gauge invariance under minimal coupling to a field. It also derives a nonlocal Pauli equation in the nonrelativistic limit, revealing a nonlocal correction to the -factor, and discusses potential extensions to curved spacetime and phenomenological implications.

Abstract

We propose a novel nonlocal spin-1/2 theory in which the form factor depends on the Dirac operator rather than on the d'Alembert operator. In this scenario, we explore some classical and quantum aspects of this new theory. At the classical level, we investigate the dispersion relation of free spin-1/2 particles and find that it increasingly deviates from the standard case as the nonlocal effects become relevant. At the quantum level, we compute the fermionic one-loop effective action for the nonlocal spin-1/2 theory with Yukawa coupling and show that the contributions of nonlocal effects are significant in the UV limit, while in the IR they are suppressed by a UV cutoff scale, which has been chosen to coincide with the nonlocality scale . We minimally couple a gauge field to the nonlocal spin-1/2 field theory and explicitly demonstrate that this theory is gauge invariant. Finally, we obtain a nonlocal version of the Pauli equation and the impact of the nonlocality in the -factor of massive particles.
Paper Structure (10 sections, 98 equations, 1 figure)

This paper contains 10 sections, 98 equations, 1 figure.

Table of Contents

  1. INTRODUCTION
  2. General setup
  3. Free nonlocal spin-$1/2$ theory
  4. Dispersion relation
  5. One-loop nonlocal fermionic effective action with Yukawa coupling
  6. Fermionic effective action
  7. On Wick rotation versus Euclidean formulation in nonlocal theories
  8. Comments on coupling of nonlocal spinor within the electromagnetic field
  9. Nonrelativistic limit and nonlocal Pauli equation
  10. Summary and Conclusions

Figures (1)

  • Figure 1: This figure shows different plots of \ref{['Lam']} for different mass values: $m=1$ (blue line), $m=2$ (yellow line) and $m=3$ (green line).