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Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

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Published on: July 19, 2019

Green dyadic for the Proca fields.

Paul Dragulin¹, P T Leung

¹Department of Physics, Portland State University, P. O. Box 751, Portland, Oregon 97207-0751, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

This summary is machine-generated.

This study derives dyadic Green functions for Proca fields, revealing identical singular terms in massless and massive electrodynamics. These findings accurately describe oscillating dipoles, simplifying to known static field expressions.

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Area of Science:

Theoretical physics
Electromagnetism
Quantum field theory

Background:

The Proca field describes massive spin-1 particles, extending Maxwell's equations to massive photons.
Dyadic Green functions are essential for solving inhomogeneous field equations in electromagnetism.
Previous work has focused on static or simplified field scenarios.

Purpose of the Study:

To derive dyadic Green functions for Proca fields in free space, incorporating singular terms.
To analyze the behavior of these functions in both massive and massless limits.
To apply the derived functions to a specific physical system, an oscillating dipole.

Main Methods:

Derivation of dyadic Green functions for Proca fields.
Analysis of singular terms in the derived functions.
Limiting case analysis by setting photon mass to zero.
Application to calculate dynamical fields for an oscillating dipole.

Main Results:

The dyadic Green functions for Proca fields, including singular terms, have been successfully derived.
The singular terms are found to be identical for both massive (Proca) and massless (Maxwell) electrodynamics.
The derived functions correctly reproduce known static field expressions for massive electrodynamics when applied to an oscillating dipole.

Conclusions:

The inclusion of singular terms in dyadic Green functions is consistent across massive and massless electrodynamics.
The derived Green functions provide a unified framework for describing electromagnetic fields in different mass regimes.
This work offers a rigorous method for calculating dynamical fields in electrodynamics with massive photons.