We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality between Dirichlet and Neumann covariance operators on a manifold with a reflection.
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4 results for “reflection-positive”
Mathematical construction of Chern-Simons partition function using reflection positivity.
problem Constructing a mathematical framework for Chern-Simons functional integrals.
method Reflection positive functional on Banach space of connections, unitary operators, weak limit.
result Nonperturbative construction of partition function without renormalization.
Transgression of D-branesmath-ph
Develops a new perspective on D-branes using loop spaces.
problem No specific problem stated; focuses on developing a new perspective.
method Loop space perspective on D-branes involving bundles of simple Frobenius algebras and bimodules.
result Classical and new perspectives on D-branes are equivalent.
Classifies dissecting involutions on symmetric spaces.
problem Identifying dissecting involutions on symmetric spaces.
method Analyzing properties of involutions and fixed point sets.
result Characterizes dissecting involutions on specific symmetric spaces.