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THE OPERATOR FORMALISM IN QUANTUM PERTURBATION THEORY

Bryce Seligman DeWitt

Sep 1, 19556 citations

Stochastic physical origin of the quantum operator algebra and phase space interpretation of the Hilbert space formalism: The relativistic spin zero case

Christopher Dewdney, Peter Holland, Anastasios Kyprianidis +2 more

Physics Letters AJan 1, 198622 citations

A BOSON-FERMION DESCIPTION OF THE NUCLEAR MANY-BODY PROBLEM

Z. Yang

A new formalism of the nuclear many-body problem is established in which one ean work with various physical state vector spaces consisting of both Fermions and Bosons, all being equivalent to the original one consisting only of Fermions. With the help of the usual commutation relations and anticommutation relations between the annihilation and creation operators of Boson and Fermion, a generalized state vector space is established, which contains all the physical spaces each being equivalent to the original physical space in terms of pure Fermion operators. Transformation between the state vectors in various equivalent physical spaces are constructed. Basic operators in the original state space are transformed into effective operators in the new physical spaces.A new formalism of the nuclear many-body problem is established in which one ean work with various physical state vector spaces consisting of both Fermions and Bosons, all being equivalent to the original one consisting only of Fermions. With the help of the usual commutation relations and anticommutation relations between the annihilation and creation operators of Boson and Fermion, a generalized state vector space is established, which contains all the physical spaces each being equivalent to the original physical space in terms of pure Fermion operators. Transformation between the state vectors in various equivalent physical spaces are constructed. Basic operators in the original state space are transformed into effective operators in the new physical spaces.

Chinese Physics CJan 1, 19780 citations

Operator approach to quantum mechanics

Graduate studies in mathematicsJan 1, 20260 citations

Origin of the Correspondence Rules of Quantum Theory

Philip Goyal

To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the correspondence rules of quantum theory. The physical origin of these rules is obscure, and their physical interpretation and their degree of generality is presently unclear. In this paper, we show that all of the commonly-used correspondence rules can be systematically derived from a new physical principle, the Average-Value Correspondence Principle. This principle shows that the correspondence rules result from the systematic translation of relations between measurement results known to hold in a classical model of a system, providing these rules with a clear physical interpretation, and clearly demarcating their domain of applicability.To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the correspondence rules of quantum theory. The physical origin of these rules is obscure, and their physical interpretation and their degree of generality is presently unclear. In this paper, we show that all of the commonly-used correspondence rules can be systematically derived from a new physical principle, the Average-Value Correspondence Principle. This principle shows that the correspondence rules result from the systematic translation of relations between measurement results known to hold in a classical model of a system, providing these rules with a clear physical interpretation, and clearly demarcating their domain of applicability.

arXiv:0910.2444Oct 13, 20091 citation

Canonical Operator Formalism of Quantum Mechanics

World Scientific lecture notes in physicsSep 1, 19851 citation

On the physical origin of the quantum operator formalism

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