Combining spatio-temporal and particle-number degrees of freedom
Filippus S. Roux
TL;DR
This paper develops orthogonal quadrature bases that integrate spatio-temporal and particle-number degrees of freedom, demonstrating their completeness and potential for advanced quantum state analysis.
Contribution
It introduces a novel framework of quadrature bases combining spatio-temporal and particle-number degrees of freedom, with proofs of orthogonality and completeness.
Findings
Quadrature bases are orthogonal in both degrees of freedom.
The bases are complete, enabling comprehensive quantum state representation.
The approach utilizes momentum-dependent quadrature operators and functional integration.
Abstract
Quadrature bases that incorporate spatio-temporal degrees of freedom are derived as eigenstates of momentum dependent quadrature operators. The resulting bases are shown to be orthogonal for both the particle-number and spatio-temporal degrees of freedom. Using functional integration, we also demonstrate the completeness of these quadrature bases.
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