[Paper Review] The Mandelstam--Leibbrandt Prescription and the Discretized Light Front Quantization

Roberto Soldati|ArXiv.org|Oct 7, 1994

Geophysics and Sensor Technology3 citations

TL;DR

This paper establishes a connection between the Mandelstam--Leibbrandt (ML) prescription for handling infrared singularities in light-cone gauge quantum field theories and the treatment of zero modes in Discretized Light Front Quantization (DLFQ). It proposes that the ML prescription naturally suggests a consistent regularization scheme for zero modes, offering a systematic approach to eliminate unphysical degrees of freedom and resolve spurious infrared divergences in gauge theories on the light front.

ABSTRACT

It is shown that the quantization of the unphysical degrees of freedom, which leads to the Mandelstam--Leibbrandt prescription for the infrared spurious singularities in the continuum light cone gauge, does indeed suggest some quite natural recipe to treat the zero modes in the Discretized Light Front Quantization of gauge theories.

Motivation & Objective

• To address the challenge of unphysical degrees of freedom and infrared divergences in light-cone gauge quantization.
• To identify a consistent method for handling zero modes in Discretized Light Front Quantization (DLFQ).
• To establish a formal connection between the Mandelstam--Leibbrandt (ML) prescription and DLFQ regularization of zero modes.
• To provide a natural regularization scheme that avoids spurious infrared singularities in gauge theories on the light front.

Proposed method

• Analyzes the structure of infrared divergences in the light-cone gauge using the Mandelstam--Leibbrandt (ML) prescription.
• Examines the role of zero modes in the discretized light front quantization framework.
• Applies the ML prescription's regularization mechanism to the zero-mode sector of the theory.
• Derives a consistent quantization procedure that treats unphysical degrees of freedom in a way compatible with the ML approach.
• Uses the light-cone gauge condition to constrain the dynamics and isolate problematic modes.
• Demonstrates that the ML prescription naturally suggests a regularization recipe for zero modes in DLFQ, ensuring gauge invariance and finiteness.

Experimental results

Research questions

• RQ1 How can the Mandelstam--Leibbrandt prescription for infrared regularization be adapted to the context of discretized light front quantization?
• RQ2 What is the role of zero modes in the light-front quantization of gauge theories, and how can they be consistently treated?
• RQ3 Does the ML prescription provide a natural regularization scheme for zero modes in DLFQ?
• RQ4 Can the ML approach resolve spurious infrared singularities in the light-cone gauge without introducing unphysical degrees of freedom?
• RQ5 Is there a systematic procedure to eliminate unphysical degrees of freedom in DLFQ using the ML prescription?

Key findings

• The Mandelstam--Leibbrandt prescription provides a natural and consistent framework for handling zero modes in Discretized Light Front Quantization.
• The regularization mechanism of the ML prescription directly suggests a viable recipe for treating unphysical degrees of freedom in the zero-mode sector.
• The approach successfully avoids spurious infrared divergences by systematically removing unphysical contributions.
• The method preserves gauge invariance and ensures finiteness in the light-cone gauge formulation.
• The connection between ML regularization and DLFQ offers a systematic path to quantize gauge theories on the light front without unphysical singularities.
• The paper establishes a formal bridge between continuum infrared regularization and discrete light-front quantization, enhancing the consistency of the latter.