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What Spatial Geometries do (2+1)-Dimensional Quantum Field Theory Vacua Prefer?
Sebastian Fischetti1, Lucas Wallis1, Toby Wiseman1
1Theoretical Physics Group, Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom.
Relativistic quantum field theories in (2+1) dimensions favor crumpled spaces due to negative vacuum free energy. This quantum effect is significant for graphene, even at room temperature, influencing material configurations.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Condensed Matter Physics
Background:
- Investigating vacuum free energy in relativistic (2+1)-dimensional quantum field theories (QFTs).
- Analyzing the influence of temperature and spatial geometry on vacuum energy.
- Considering free scalar and Dirac fields on perturbed flat space.
Purpose of the Study:
- To determine the vacuum free energy as a function of temperature and spatial geometry.
- To understand the energetic preference of QFTs for specific spatial configurations.
- To assess the relevance of vacuum energy effects in materials like graphene.
Main Methods:
- Calculated vacuum free energy for free scalar and Dirac fields.
- Examined arbitrary perturbations of flat space in (2+1) dimensions.
- Analyzed the leading-order contribution to the free energy difference from flat space.
Main Results:
- The free energy difference from flat space is finite and negative.
- Relativistic (2+1)-dimensional QFTs energetically favor crumpled spaces.
- This effect holds true for both quantum (zero temperature) and thermal (high temperature) contributions.
Conclusions:
- Free (2+1)-dimensional QFTs consistently favor crumpled spatial geometries.
- The vacuum energy effect is non-negligible for relativistic Dirac fields in materials like graphene.
- This quantum effect must be considered for accurate analysis of graphene's equilibrium configuration.
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