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Journal of Mathematical Physics / Volume 49 / Issue 5 / RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY, BRANE THEORY (INCLUDING STRINGS)

J. Math. Phys. 49, 052301 (2008); http://dx.doi.org/10.1063/1.2907660 (10 pages)

Reflection positivity and monotonicity

Arthur Jaffe and Gordon Ritter

Harvard University, 17 Oxford St., Cambridge, Massachusetts 02138, USA

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(Received 3 March 2008; accepted 14 March 2008; published online 1 May 2008)

We prove general reflection positivity results on Riemannian manifolds for both scalar fields and Dirac fields, and comment on applications to quantum field theory. As another application, we prove the inequality CD ⩽ CN between Dirichlet and Neumann covariance operators on a manifold with a reflection.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. REFLECTIONS AND THE LAPLACE OPERATOR
  3. COMPARISON OF DIRICHLET AND NEUMANN COVARIANCE
  4. THE DIRAC OPERATOR
    1. Clifford bundles
    2. Reflection positivity
    3. Flat spacetimes
  5. FURTHER DIRECTIONS

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KEYWORDS and PACS

Keywords

black holes, Dirac equation, mathematical operators, quantum field theory, space-time configurations

PACS

  • 04.62.+v

    Quantum fields in curved spacetime

  • 11.10.-z

    Field theory

  • 02.40.-k

    Geometry, differential geometry, and topology

  • 04.70.Dy

    Quantum aspects of black holes, evaporation, thermodynamics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2907660

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    Symanzik, K., “Euclidean quantum field theory. I. Equations for a scalar model,” J. Math. Phys. 7, 510 (1966)JMAPAQ000007000003000510000001.


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