Lorentzian bordisms in algebraic quantum field theory

Area of Science:

• Theoretical physics
• Quantum field theory
• Algebraic quantum field theory

Background:

• Algebraic quantum field theory (AQFT) provides a rigorous framework for quantum field theories.
• Understanding the structure and properties of AQFTs is crucial for theoretical physics.
• The role of spacetime structure, particularly Lorentzian manifolds, in AQFT is an active area of research.

Purpose of the Study:

• To demonstrate that every AQFT possesses an underlying functorial field theory.
• To define this functorial field theory on a globally hyperbolic Lorentzian bordism pseudo-category.
• To explore the implications of this functorial structure for understanding time evolution and spatial locality in AQFT.

Main Methods:

• Development of a functorial field theory framework.
• Utilizing globally hyperbolic Lorentzian bordisms as the category for the functor.
• Comparison of algebraic and functorial descriptions for a free scalar quantum field.

Main Results:

• Every AQFT can be associated with a functorial field theory.
• This functorial theory is naturally defined on a pseudo-category of globally hyperbolic Lorentzian bordisms.
• The functorial field theory encodes the time evolution of the AQFT, distinct from its spatial structure.

Conclusions:

• Globally hyperbolic Lorentzian bordisms are fundamental to the structure of AQFT.
• The functorial perspective offers a new way to understand time evolution in quantum field theory.
• This work provides a detailed comparison of algebraic and functorial descriptions for a concrete example (free scalar field).