Odd statistics in odd dimensions for odd couplings

Abstract

We consider the response of a uniformly accelerated monopole detector that is coupled non-linearly to the nth power of a quantum scalar field in (D+1)-dimensional flat spacetime. We show that, when (D+1) is even, the response of the detector in the Minkowski vacuum is characterized by a Bose-Einstein factor for all n. Whereas, when (D+1) is odd, we find that a Fermi-Dirac factor appears in the detector response when n is odd, but a Bose-Einstein factor arises when n is even. We emphasize the point that, since, along the accelerated trajectory, the Wightman function and, as a result, the (2n)-point function satisfy the Kubo-Martin-Schwinger condition (as required for a scalar field) in all dimensions, the appearance of a Fermi-Dirac factor (instead of the expected Bose-Einstein distribution) for odd (D+1) and n reflects a peculiar feature of the detector rather than imply a fundamental change in field theory.

9 pages, 2 figures, LaTeX, Invited talk at the ``First IUCAA Meeting on the Interface of Gravitational and Quantum Realms'', Pune, India, December 2001. To appear in Modern Physics Letters A

References in corpus (6)

• Accelerated Detectors and Temperature in (Anti) de Sitter Spaces
• Mapping Hawking into Unruh Thermal Properties
• Equivalence of Hawking and Unruh Temperatures and Entropies Through Flat Space Embeddings
• Comment on "Accelerated Detectors and Temperature in (Anti) de Sitter Spaces"
• Fluctuation-dissipation theorem and the Unruh effect of scalar and Dirac fields
• On the response of detectors in classical electromagnetic backgrounds

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• Decoherence and thermalization of Unruh-DeWitt detector in arbitrary dimensions
• Fermionic condensate and the mean energy-momentum tensor in the Fulling-Rindler vacuum
• Interpolating between the Bose-Einstein and the Fermi-Dirac distributions in odd dimensions
• Unruh Effect and Takagi's Statistics Inversion in Strained Graphene
• Accelerated paths and Unruh effect I: scalars and fermions in Anti De Sitter spacetime
• Accelerated paths and Unruh effect II: finite time detector response in (Anti) de Sitter spacetime and Huygen's Principle