The Electromagnetic Gauge Field Interpolation between the Instant Form and the Front Form of the Hamiltonian Dynamics

Abstract

We present the electromagnetic gauge field interpolation between the instant form and the front form of the relativistic Hamiltonian dynamics and extend our interpolation of the scattering amplitude presented in the simple scalar field theory to the case of the electromagnetic gauge field theory with the scalar fermion fields known as the sQED theory. We find that the Coulomb gauge in the instant form dynamics (IFD) and the light-front gauge in the front form dynamics, or the light-front dynamics (LFD), are naturally linked by the unified general physical gauge that interpolates between these two forms of dynamics and derive the spin-1 polarization vector for the photon that can be generally applicable for any interpolation angle. Corresponding photon propagator for an arbitrary interpolation angle is found and examined in terms of the gauge field polarization and the interpolating time ordering. Using these results, we calculate the lowest-order scattering processes for an arbitrary interpolation angle in sQED. We provide an example of breaking the reflection symmetry under the longitudinal boost, $P^z\leftrightarrow -P^z$, for the time-ordered scattering amplitude in any interpolating dynamics except the LFD and clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame (IMF) and the LFD. The particular correlation found in our previous analysis of the scattering amplitude in the simple scalar field theory, coined as the J-shaped correlation, between the total momentum of the system and the interpolation angle persists in the present analysis of the sQED scattering amplitude. We discuss the singular behavior of this correlation in conjunction with the zero-mode issue in the LFD.

arXiv comment22 pages, 5 figures

References in corpus (14)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Unified description of light- and strange-baryon spectra
• Covariant nucleon electromagnetic form factors from the Goldstone-boson-exchange quark model
• Light-Front-Quantized QCD in Light-Cone Gauge: The Doubly Transverse Gauge Propagator
• Pauli--Villars as a Nonperturbative Ultraviolet Regulator in Discretized Light-Cone Quantization
• Electromagnetic nucleon form factors in instant and point form
• The light-cone gauge and the calculation of the two-loop splitting functions
• Interpolating Scattering Amplitudes between Instant Form and Front Form of Relativistic Dynamics
• Poincare Invariant Algebra From Instant to Light-Front Quantization
• Light-Front View of The Axial Anomaly
• Light-front gauge propagator reexamined
• Two-Loop Quark Self-Energy in a New Formalism (II): Renormalization of the Quark Propagator in the Light-Cone Gauge
• Surveillance on the light-front gauge fixing Lagrangians
• Quantum gauge boson propagators in the light front

Cited by in corpus (10)

• Pauli-Villars Regularization Elucidated in Bopp-Podolsky's Generalized Electrodynamics
• Interpolating Helicity Spinors Between the Instant Form and the Light-front Form
• Revisiting the equivalence of light-front and covariant QED in the light-cone gauge
• Interpolating Quantum Electrodynamics between Instant and Front Forms
• Tadpoles and vacuum bubbles in light-front quantization
• Equivalence of One Loop Diagrams in Covariant and Light Front QED Revisited
• Equivalence of Light-Front and Covariant Quantum Electrodynamics at One Loop Level and the form of the Gauge Boson Propagator
• Quantum orientation entanglement analysis of the interpolating helicity states between the instant form dynamics and the light-front dynamics
• Interpolating 't Hooft model between instant and front forms
• Interpolating conformal algebra in $(1+1)$ dimensions between the instant form and the light-front form of relativistic dynamics