[Paper Review] Spontaneous Symmetry Breaking Mechanism in Light-Front Quantized Field Theory- (Discretized Formulation)

Prem P. Srivastava|ArXiv.org|Dec 21, 1994

Cosmology and Gravitation Theories3 citations

TL;DR

This paper formulates spontaneous symmetry breaking in light-front quantized scalar field theory using a discretized light-front approach. It identifies a non-local constraint between background and nonzero modes that emerges in finite volume, showing that this constraint—when properly treated—leads to spontaneous symmetry breaking at tree level, offering a consistent framework distinct from standard Hamiltonian approaches.

ABSTRACT

The scalar field is quantized in the discretized light-front framework following the {\em standard} Dirac procedure and its infinite volume limit taken. The background field and the nonzero mode variables do not commute for finite volume; they do so only in the continuum limit. A {\em non-local constraint} in the theory relating the two is shown to follow and we must deal with it along with the Hamiltonian. At the tree level the constraint leads to a description of the spontaneous symmetry breaking. The elimination of the constraint would lead to a highly involved light-front Hamiltonian in contrast to the one found when we ignore altogether the background field. The renormalized constraint equation would also account for the instability of the symmetric phase for large enough couping constant.

Motivation & Objective

• To develop a consistent discretized light-front quantization framework for scalar field theories.
• To address the challenge of non-commuting background and nonzero mode variables in finite volume.
• To investigate how spontaneous symmetry breaking arises from constraints in the light-front formulation.
• To compare the resulting Hamiltonian structure with standard approaches that ignore the background field.
• To explore the role of the renormalized constraint in stabilizing the symmetric phase at weak coupling.

Proposed method

• Applies the standard Dirac procedure for constrained systems to light-front quantized scalar fields.
• Uses a discretized formulation to handle finite-volume effects in the light-front quantization.
• Derives a non-local constraint relating the background field and nonzero mode variables in finite volume.
• Treats the constraint and Hamiltonian simultaneously in the quantization procedure.
• Takes the infinite volume limit to recover the continuum theory.
• Analyzes the tree-level structure to show how the constraint leads to spontaneous symmetry breaking.

Experimental results

Research questions

• RQ1 How does spontaneous symmetry breaking emerge in light-front quantized field theory with finite-volume discretization?
• RQ2 What is the role of the non-local constraint between background and nonzero mode variables in the finite-volume formulation?
• RQ3 How does the presence of this constraint affect the structure of the light-front Hamiltonian?
• RQ4 Can the renormalized constraint account for the instability of the symmetric phase at large coupling?
• RQ5 How does this approach differ from standard light-front treatments that neglect the background field?

Key findings

• In finite volume, the background field and nonzero mode variables do not commute, leading to a non-local constraint in the theory.
• The non-local constraint is essential for describing spontaneous symmetry breaking at the tree level.
• Ignoring the constraint leads to a highly complicated light-front Hamiltonian, whereas including it yields a more consistent description.
• The renormalized constraint equation explains the instability of the symmetric phase for large coupling constants.
• The infinite volume limit restores commutativity between background and nonzero modes, recovering standard field theory behavior.
• The framework provides a consistent mechanism for spontaneous symmetry breaking in light-front quantized field theory without relying on the standard vacuum choice.