TL;DR
This paper studies the mathematical properties of bosonic quadratic Hamiltonians, focusing on conditions for their self-adjointness and explicit formulas for their infimum, motivated by applications in Local Quantum Field Theory.
Contribution
It provides new criteria for defining bosonic quadratic Hamiltonians as self-adjoint operators, including cases requiring infinite renormalization, and derives explicit formulas for their infimum.
Findings
Conditions for self-adjointness of bosonic quadratic Hamiltonians
Explicit formulas for the infimum of these Hamiltonians
Application to examples in Local Quantum Field Theory
Abstract
We discuss self-adjoint operators given formally by expressions quadratic in bosonic creation and annihilation operators. We give conditions when they can be defined as self-adjoint operators, possibly after an infinite renormalization. We also discuss explicit formulas for their infimum. Our main motivation comes from Local Quantum Field Theory, which furnishes interesting examples of bosonic quadratic Hamiltonians that require an infinite renormalization.
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