Pseudo-hermitian QFT Enables Relativistic Scattering with Conserved Probability Via a Defined Inner Product

The fundamental principle of unitarity, which ensures the conservation of probability in physical theories, faces challenges when applied to non-Hermitian systems. Ruifeng Leng of Fudan University, alongside Cheng-Yang Lee and Siyi Zhou from Chongqing University, and their colleagues, now demonstrate how to extend the concept of pseudo-Hermitian mechanics to the realm of relativistic quantum field theory. This work establishes a consistent framework for describing scattering processes, even when the underlying Hamiltonian is not Hermitian, by introducing distinct mathematical structures for initial and final states. Crucially, the team reveals that global probability conservation remains intact through a carefully defined connection between these states, and that established principles like Lorentz invariance and the CPT theorem still hold, opening up new avenues for exploring physics beyond the standard Hermitian framework.

Although non-Hermitian Hamiltonians typically relate to open or dissipative systems, pseudo-Hermitian quantum mechanics demonstrates that real spectra and unitary evolution can still emerge through a suitably defined inner product. Motivated by this insight, the researchers extend the pseudo-Hermitian framework to relativistic quantum field theory and construct a consistent formulation of scattering processes. A novel structural feature of this theory is the presence of distinct metric operators for the in and out sectors, connected through a nontrivial metric projector that guarantees global probability conservation under pseudo-unitary time evolution.

Pseudo-Hermitian Field Theory and Unitarity Challenges

This research provides a comprehensive exploration of pseudo-Hermitian quantum field theory, investigating its foundations, challenges to unitarity, and potential physical interpretations. The study meticulously outlines the mathematical framework required to work with these operators, emphasizing the importance of a positive-definite metric for probabilistic interpretations. Researchers also address the challenges to unitarity inherent in pseudo-Hermitian theories, exploring the role of PT-symmetry as a potential mechanism for its preservation. The work extends to applications within quantum field theory, including the construction of pseudo-Hermitian field theories and detailed analysis of their properties.

The study draws connections between pseudo-Hermitian quantum field theory and other areas of physics, such as string theory, cosmology, and condensed matter physics, highlighting its potential relevance to a wide range of physical phenomena. Specific models and examples of pseudo-Hermitian field theories are presented, illustrating the concepts and techniques discussed. This research represents a valuable and insightful contribution to the field, providing a comprehensive overview of the subject, highlighting its mathematical foundations, physical implications, and potential applications.

Pseudo-Hermitian Quantum Field Theory Unitarity Demonstrated

Scientists have developed a rigorous framework for interacting pseudo-Hermitian quantum field theories, extending beyond the traditional requirement of Hermiticity in quantum mechanics. This work addresses fundamental questions regarding unitarity and its conservation within systems governed by pseudo-Hermitian Hamiltonians. The research demonstrates that despite non-Hermitian characteristics, these systems can still exhibit real spectra and unitary evolution through a suitably defined inner product, opening new avenues for exploring quantum theory. The team established a mathematical structure utilizing a Hermitian linear automorphism and defined a pseudo-Hermitian conjugation operator, allowing them to formulate a consistent relativistic scattering theory.

A key innovation is the introduction of a “metric projector” which connects the in and out states of particles, ensuring a well-defined relationship between the asymptotic past and future. Measurements confirm that the resulting S-matrix admits a perturbative expansion and remains Lorentz invariant and unitary, mirroring the behavior of conventional Hermitian systems. Further analysis reveals that each symmetry within this framework corresponds to two pseudo-unitary operators associated with the in and out metrics. The team rigorously demonstrated that the fundamental CPT theorem also holds within this pseudo-Hermitian framework. This work establishes a solid foundation for exploring the physical implications of pseudo-Hermitian quantum field theories, potentially broadening the scope of quantum theory and offering new insights into the nature of unitarity and information conservation.

Non-Hermitian Scattering and Probability Conservation

This work establishes a rigorous framework for scattering theory within pseudo-Hermitian quantum field theory, extending beyond the traditional requirement of Hermiticity in quantum mechanics. Researchers have successfully demonstrated that even with non-Hermitian Hamiltonians, a consistent description of particle interactions is possible, provided the system possesses a real energy spectrum. The key achievement lies in defining distinct inner products for initial and final states, connected by a metric projector that ensures global probability conservation and unitary time evolution. The resulting scattering matrix maintains crucial properties like Lorentz invariance and admits a standard perturbative expansion, mirroring the well-established results of conventional Hermitian quantum field theory. Furthermore, the fundamental CPT theorem, a cornerstone of relativistic quantum mechanics, is also shown to hold within this new framework. This work opens new avenues for exploring the foundations of quantum theory and potentially extending its scope beyond the limitations of Hermiticity.