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Projection operator formalism for quantum constraints

J. Scott Little

Jan 1, 20070 citations

Projection Operators and the Mori-Zwanzig Formalism

George D. J. Phillies

Graduate texts in contemporary physicsJan 1, 20003 citations

O the Projection Operator Formalism and Some of its Applications.

David T. Ng

Jan 1, 19750 citations

Approach to projection operator formalism for second-order response

G�nter Sauermann, K.-P. Karmann

Physica A Statistical Mechanics and its ApplicationsOct 1, 19833 citations

Quantum Corrections in Constrained Systems

N. Okamoto, Masayoshi Nakamura

Using the projection operator method, the quantization of a dynamical system constrained to a submanifold MN−1 embedded in the Euclidean space RN is investigated. The resultant Hamiltonian contains the quantum correction terms which are missed in the usual approach with Dirac's formalism. Such correction terms are investigated from a geometrical point of view in the case that the system is constrained to a 2-dimensional orientatable compact curved spaces M2 embedded in R3. It is shown that the curvatures of these submanifolds are closely related to the quantum correction terms.Using the projection operator method, the quantization of a dynamical system constrained to a submanifold MN−1 embedded in the Euclidean space RN is investigated. The resultant Hamiltonian contains the quantum correction terms which are missed in the usual approach with Dirac's formalism. Such correction terms are investigated from a geometrical point of view in the case that the system is constrained to a 2-dimensional orientatable compact curved spaces M2 embedded in R3. It is shown that the curvatures of these submanifolds are closely related to the quantum correction terms.

Progress of Theoretical PhysicsJul 1, 19964 citations

“A Constraint-Based Update Formalism for Measurement Across Physical Domains”

Hugh Bradford Cornick The 6th

This project formalizes a general update operator for “measurement” that is constrained only by three conditions already established in physics: (1) no signaling (2) monotone proper scoring / Bayesian consistency (3) Landauer-feasible energetic cost Nothing here assumes any metaphysical category. The question being tested is very narrow: Can one single update operator be parameterized to fit empirical data across distinct physical regimes — thermodynamic bit operations, quantum state update, and neural entropy reduction? If yes → a unified class of measurement models exists. If no → the approach is falsified. This project does not assert any grand unification and does not claim consciousness causation. It only investigates whether a single constrained update formalism can cross-calibrate across known measurement domains in physics.This project formalizes a general update operator for “measurement” that is constrained only by three conditions already established in physics: (1) no signaling (2) monotone proper scoring / Bayesian consistency (3) Landauer-feasible energetic cost Nothing here assumes any metaphysical category. The question being tested is very narrow: Can one single update operator be parameterized to fit empirical data across distinct physical regimes — thermodynamic bit operations, quantum state update, and neural entropy reduction? If yes → a unified class of measurement models exists. If no → the approach is falsified. This project does not assert any grand unification and does not claim consciousness causation. It only investigates whether a single constrained update formalism can cross-calibrate across known measurement domains in physics.

Nov 8, 20250 citations

Projection operator formalism on constrained systems

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