Spontaneous symmetry breaking at infinite momentum without P+ zero modes

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Mathematical Physics

Background:

• Nonrelativistic quantum field theory (QFT) interpretations often rely on infinite momentum frame quantization.
• The inclusion of a zero mode (p(+) = 0) in this framework can disrupt the nonrelativistic interpretation.
• Spontaneous symmetry breaking (SSB) typically necessitates the presence of such a zero mode.

Purpose of the Study:

• To investigate the necessity of a zero mode in spontaneous symmetry breaking (SSB) within quantum field theory.
• To determine if accurate physical descriptions of SSB can be achieved without a zero mode.
• To test the robustness of SSB models in the absence of a conventionally required field mode.

Main Methods:

• Quantization in an infinite momentum frame was employed.
• A scalar quantum field theory model in 1+1 space-time dimensions was analyzed.
• The study focused on scenarios involving spontaneous symmetry breaking (SSB).
• The presence and impact of a zero mode (p(+) = 0) were specifically examined and then omitted.

Main Results:

• The inclusion of a zero mode was found to spoil the nonrelativistic interpretation of QFT.
• It was demonstrated that spontaneous symmetry breaking (SSB) in scalar QFT in 1+1 dimensions can be accurately described without a zero mode.
• The physics of SSB remains consistent and valid even when the zero mode is excluded.

Conclusions:

• The zero mode is not essential for describing spontaneous symmetry breaking (SSB) in this specific quantum field theory context.
• This finding offers a potentially simplified approach to nonrelativistic QFT interpretations.
• The study validates alternative frameworks for understanding SSB in quantum field theory.