nLab time slice axiom

Idea

In quantum field theory the time slice axiom is an additional axiom often considered on top of the basic Haag-Kastler axioms: it encodes the property that the time evolution of the classical field theory underlying a QFT is governed by well-defined initial value problems.

Definition

A local net of observables $A : Op(X) \to C^\ast Alg$ satisfies the time slice axiom if whenever a causal inclusion of Lorentzian spaces $O_1 \hookrightarrow O_2$ is such that $O_1$ contains a Cauchy surface of $O_2$ then $A(O_1 \hookrightarrow O_2)$ is an isomorphism.

Related concepts

• split property

References

General

See references at AQFT.

Discussion for homotopical AQFT:

• Marco Benini, Victor Carmona, Alexander Schenkel, Strictification theorems for the homotopy time-slice axiom [arxiv:2208.04344]

Time tube theorem

• Hans-Jürgen Borchers, Über die Vollständigkeit lorentzinvarianter Felder in einer zeitartigen Röhre, Il Nuovo Cimento (1955-1965) 19 (1961) 787–793 [doi:10.1007/BF02733373]

• Huzihiro Araki, A generalization of Borchers’ theorem, Helvetica Physica Acta 36 (1963) 132-139

Generalization to AQFT on curved but real analytic spacetimes:

• Alexander Strohmaier, On the Local Structure of the Klein–Gordon Field on Curved Spacetimes, Letters in Mathematical Physics 54 (2000) 249–261 [doi:10.1023/A:1010927625112, arXiv:math-ph/0008043]

• Alexander Strohmaier, Edward Witten, Analytic states in quantum field theory on curved spacetimes [arXiv:2302.02709]

• Alexander Strohmaier, Edward Witten, The Timelike Tube Theorem in Curved Spacetime [arXiv:2303.16380]