Document Type : Regular article

Authors

• Chen-Te Ma ^{1, 2, 3, 4, 5, 6}
• Yiwen Pan ⁷
• Hui Zhang ^{8, 3, 9}

¹ Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, US;

² Asia Pacific Center for Theoretical Physics, Asia Pacific Center for Theoretical Physics, Pohang University of Science and Technology, Pohang 37673, Gyeongsangbuk-do, South Korea;

³ Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, Guangdong, China;

⁴ School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, Guangdong, China;

⁵ Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Southern Nuclear Science Computing Center, South China Normal University, Guangzhou 510006, Guangdong, China;

⁶ The Laboratory for Quantum Gravity and Strings, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7700, South Africa.

⁷ School of Physics, Sun Yat-Sen University, Guangzhou 510275, Guangdong, China

⁸ Key Laboratory of Atomic and Subatomic Structure and Quantum Control, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, Guangdong, China;

⁹ Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Southern Nuclear Science Computing Center, South China Normal University, Guangzhou 510006, Guangdong, China.

Abstract

Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $\phi^4$ theory is relatively simple compared to other more complex theories, making it a good starting point for investigating the origin of non-trivial vacua. The adaptive perturbation method is a technique used to handle strongly coupled systems. The study of strongly correlated systems is useful in testing holography. It has been successful in strongly coupled QM and is being generalized to scalar field theory to analyze the system in the strong-coupling regime. The unperturbed Hamiltonian does not commute with the usual number operator. However, the quantized scalar field admits a plane-wave expansion when acting on the vacuum. While quantizing the scalar field theory, the field can be expanded into plane-wave modes, making the calculations more tractable. However, the Lorentz symmetry, which describes how physical laws remain the same under certain spacetime transformations, might not be manifest in this approach. The proposed elegant resummation of Feynman diagrams aims to restore the Lorentz symmetry in the calculations. The results obtained using this method are compared with numerical solutions for specific values of the coupling constant $\lambda = 1, 2, 4, 8, 16$. Finally, we find evidence for quantum triviality, where self-consistency of the theory in the UV requires $\lambda = 0$. This result implies that the $\phi^4$ theory alone does not experience SSB, and the $\langle \phi\rangle = 0$ phase is protected under the RG-flow by a boundary of Gaussian fixed-points.

Keywords

• Spontaneous Symmetry Breaking
• Perturbation Method
• Resummation
• Renormalization Group Flow
• Quantum Triviality

Main Subjects

• Physics