Arrow of Causality and Quantum Gravity

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Quantum Gravity

Background:

• Causality in quantum field theory relies on field commutators for spacelike separations.
• Standard definitions do not inherently establish a direction for causal effects.
• Quantization conventions implicitly define the arrow of causality (past vs. future).

Purpose of the Study:

• To explore the connection between quantization conventions and the arrow of causality.
• To investigate the implications of mixed quantization conventions within a single theory.
• To examine the role of stable states in defining causality in such theories.

Main Methods:

• Analysis of field commutators and quantization conventions.
• Theoretical examination of microcausality violation.
• Identification of theories exhibiting mixed causality conditions.

Main Results:

• Mixing quantization conventions leads to a violation of microcausality.
• In theories with mixed conventions, stable states determine the arrow of causality.
• This mixed causality condition is relevant to quantum gravity theories like quadratic gravity and asymptotic safety.

Conclusions:

• The choice of quantization conventions is crucial for defining the arrow of causality.
• Theories with mixed conventions present unique challenges to understanding causality.
• Implications for quantum gravity theories require further investigation.