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On a New Form of Quantum Mechanics

Natalia N. Gorobey, Alexander S. Lukyanenko

We propose a new form of nonrelativistic quantum mechanics which is based on a quantum version of the action principle.

arXiv:0807.3508Jul 22, 20080 citations

Quantum Action Principle in Relativistic Mechanics

Natalia N. Gorobey, Alexander S. Lukyanenko

A quantum version of the action principle is considered in the case of a free relativistic particle. The classical limit of the quantum action is obtained.

arXiv:0812.1336Dec 7, 20081 citation

Two-Time Quantum Mechanics

Natalia N. Gorobey, Alexander S. Lukyanenko, Inna Lukyanenko

A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.

arXiv:1003.2830Mar 14, 20100 citations

Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives

Natalia N. Gorobey, Alexander S. Lukyanenko, Goltsev, A. V.

A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory, in which the state of motion of the system is described by the wave functional on its trajectories in the configuration space, and the functional itself is an eigenvector of the action operator. The Pais-Uhlenbeck oscillator is considered as the simplest model. For this case, the correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit, when the Pais-Uhlenbeck oscillator is reduced to the "ordinary" harmonic oscillator.A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory, in which the state of motion of the system is described by the wave functional on its trajectories in the configuration space, and the functional itself is an eigenvector of the action operator. The Pais-Uhlenbeck oscillator is considered as the simplest model. For this case, the correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit, when the Pais-Uhlenbeck oscillator is reduced to the "ordinary" harmonic oscillator.

arXiv:2404.09608Apr 15, 20240 citations

Feynman's Thesis — A New Approach to Quantum Theory

Laurie Mark Brown

# Least Action in Classical Mechanics: # The Concept of Functional # The Principle of Least Action # Conservation of Energy. Constants of the Motion # Particles Interacting Through an Intermediate Oscillator # Least Action in Quantum Mechanics: # The Lagrangian in Quantum Mechanics # The Calculation of Matrix Elements in the Language of a Lagrangian # The Equations of Motion in Lagrangian Form # Translation to the Ordinary Notation of Quantum Mechanics # The Generalization to Any Action Function # Conservation of Energy. Constants of the Motion # The Role of the Wave Function # Transition Probabilities # Expectation Values for Observables # Application to the Forced Harmonic Oscillator # Particles Interacting Through an Intermediate Oscillator # Space-Time Approach to Non-Relativistic Quantum Mechanics # The Lagrangian in Quantum Mechanics# Least Action in Classical Mechanics: # The Concept of Functional # The Principle of Least Action # Conservation of Energy. Constants of the Motion # Particles Interacting Through an Intermediate Oscillator # Least Action in Quantum Mechanics: # The Lagrangian in Quantum Mechanics # The Calculation of Matrix Elements in the Language of a Lagrangian # The Equations of Motion in Lagrangian Form # Translation to the Ordinary Notation of Quantum Mechanics # The Generalization to Any Action Function # Conservation of Energy. Constants of the Motion # The Role of the Wave Function # Transition Probabilities # Expectation Values for Observables # Application to the Forced Harmonic Oscillator # Particles Interacting Through an Intermediate Oscillator # Space-Time Approach to Non-Relativistic Quantum Mechanics # The Lagrangian in Quantum Mechanics

WORLD SCIENTIFIC eBooksAug 1, 2005108 citations

On a Quantum Action Principle

Natalya Gorobey, Alexander S. Lukyanenko

A quantum version of the action principle is formulated in terms of real parameters of a wave functional. The classical limit of the quantum action of a harmonic oscillator is obtained.

arXiv:0810.2255Oct 13, 20080 citations

On a New Form of Quantum Mechanics (II)

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On a New Form of Quantum Mechanics (II)

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