TY - JOUR

T1 - Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

T2 - A Life in Mathematical Physics: Conference in Honour of Tekin Dereli (DERELI-FS-2021) 26/11/2021 - 28/11/2021 Istanbul

AU - Tucker, R.W.

AU - Walton, T.J.

PY - 2022/2/10

Y1 - 2022/2/10

N2 - We review a technique for solving a class of classical linear partial diferential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar Laplacian and a complexifed Hertz potential. The complexifcation prescription ensures the existence of regular physical solutions with chirality and propagating, non-singular, pulse-like characteristics that are bounded in all three spatial dimensions. The technique is applied to the source-free Maxwell, Bopp-Lande-Podolsky and linearised Einstein feld systems, and particular solutions are used for constructing classical models describing single-cycle laser pulses and a mechanism is discussed for initiating astrophysical jets. Our article concludes with a brief introduction to spacetime Cliford algebra ideals that we use to represent spinor felds. We employ these to demonstrate how the same technique used for tensor felds enables one to construct new propagating, chiral, non-singular, pulse-like spinor solutions to the massless Dirac equation in Minkowski spacetime.

AB - We review a technique for solving a class of classical linear partial diferential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar Laplacian and a complexifed Hertz potential. The complexifcation prescription ensures the existence of regular physical solutions with chirality and propagating, non-singular, pulse-like characteristics that are bounded in all three spatial dimensions. The technique is applied to the source-free Maxwell, Bopp-Lande-Podolsky and linearised Einstein feld systems, and particular solutions are used for constructing classical models describing single-cycle laser pulses and a mechanism is discussed for initiating astrophysical jets. Our article concludes with a brief introduction to spacetime Cliford algebra ideals that we use to represent spinor felds. We employ these to demonstrate how the same technique used for tensor felds enables one to construct new propagating, chiral, non-singular, pulse-like spinor solutions to the massless Dirac equation in Minkowski spacetime.

KW - Tensors

KW - Complex solution

KW - Hertz's potentials

KW - Laplacians

KW - Minkowski space-time

KW - Pulse-like

KW - Spacetime

KW - Spatial dimension

KW - Spinors

KW - System solution

KW - Tensor fields

KW - Linear equations

U2 - 10.1088/1742-6596/2191/1/012020

DO - 10.1088/1742-6596/2191/1/012020

M3 - Conference article

VL - 2191

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

M1 - 012020

Y2 - 26 November 2021 through 28 November 2021

ER -