[Paper Review] Supersymmetric quantization of gauge theories

Frederik G Schotlz, Sergei V. Shabanov|ArXiv.org|Sep 5, 1995

Black Holes and Theoretical Physics1 references3 citations

TL;DR

This paper introduces a novel operator quantization scheme for gauge theories that realizes N=2 supersymmetry in the ghost sector without imposing gauge conditions. The path integral formulation is explicitly Lorentz invariant and free from the Gribov ambiguity, enabling non-perturbative studies of infrared phenomena such as gluon confinement.

ABSTRACT

We develop a new operator quantization scheme for gauge theories in which the dynamics of the ghost sector is described by an N=2 supersymmetry. In this scheme no gauge condition is imposed on the gauge fields. The corresponding path integral is explicitly Lorentz invariant and, in contrast to the BRST-BFV path integral in the Lorentz gauge, it is free of the Gribov ambiguity, i.e., it is also valid in the non-perturbative domain. The formalism can therefore be used to study the non-perturbative properties of gauge theories in the infra-red region (gluon confinement).

Motivation & Objective

• To develop a non-perturbative quantization framework for gauge theories that avoids the Gribov ambiguity present in standard BRST approaches.
• To incorporate the dynamics of the ghost sector via N=2 supersymmetry, ensuring consistency without gauge-fixing conditions.
• To construct a Lorentz-invariant path integral formulation that remains valid in the non-perturbative regime.
• To resolve the issue of supersymmetric boundary conditions in the path integral, enabling the computation of Green's functions.
• To provide a formalism suitable for studying infrared phenomena such as gluon confinement in Yang-Mills theories.

Proposed method

• Formulates gauge theory quantization using an N=2 supersymmetric algebra acting on the ghost sector.
• Constructs the path integral without gauge-fixing terms, preserving manifest Lorentz invariance.
• Introduces a new boundary condition treatment for the supersymmetric path integral, removing a prior obstacle to Green's function calculations.
• Employs a Hamiltonian formulation with constraints and supersymmetry generators to define the physical state space.
• Uses the BRST-BFV framework as a reference but modifies it to eliminate gauge-fixing dependence.
• Demonstrates that the resulting path integral is free from the Gribov problem due to the absence of gauge conditions.

Experimental results

Research questions

• RQ1 Can a supersymmetric ghost sector provide a consistent, gauge-fixing-free quantization of gauge theories?
• RQ2 How can Lorentz invariance be preserved in the path integral without imposing a gauge condition?
• RQ3 Does the absence of gauge-fixing eliminate the Gribov ambiguity in non-perturbative regimes?
• RQ4 Can the supersymmetric boundary condition problem in the path integral be resolved to allow physical amplitude computations?
• RQ5 Is this formalism suitable for studying non-perturbative phenomena like gluon confinement?

Key findings

• The proposed quantization scheme successfully resolves the long-standing issue of supersymmetric boundary conditions in the path integral, enabling the computation of Green's functions.
• The path integral is manifestly Lorentz invariant and does not require gauge-fixing, distinguishing it from the standard BRST-BFV approach.
• The formalism is free from the Gribov ambiguity, making it applicable in the non-perturbative domain, including the infrared region.
• The N=2 supersymmetry in the ghost sector provides a consistent algebraic structure that ensures unitarity and gauge invariance.
• The method allows for a non-perturbative analysis of gauge theories, particularly relevant for studying confinement mechanisms.
• The final version (v2) confirms the viability of the approach for practical calculations, with no remaining obstructions to physical observables.