Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

Proper-Time Formulation of Barrier Penetration in Quantum Mechanics

M. Ichiyanagi

Published Oct 1, 1983• 1 citation
Publisher

Abstract

We develop a formal theory which rests upon Nambu's description of the quantum state and especially on the use of the proper time. We show that the introduction of the proper time in quantum mechanics in understandable from the viewpoint that eligible trajectries in the well-known variational treatment of classical mechanics can be parametrized by an auxiliary variable. A new theory developed here permits a formulation of barrier penetrations in terms of the so-called Euclidean Lagrangian.

DOI
10.1143/ptp.70.1098

Related papers

Effective descriptions of localization in a proper-time parametrized framework

E. R. F. Taillebois, Ardiley Torres Avelar

Although the quantization of relativistic systems in a proper-time framework gives new insights concerning the understanding of the so-called localization problem, classical observers cannot be treated as quantum comoving frames and real measurement are typically conceived using an external parameter related to a classical frame. Here, the connection between the proper-time formalism and usual descriptions parametrized by classical observers is obtained by defining a restriction operation that mixes contributions of different values of proper-time. Such a restriction procedure allows us to retrieve the concepts of Newton-Wigner position and Kijowski time of detection in an effective fashion, opening the possibility to interpret the related causalities issues as an apparent phenomena resulting from the time uncertainty that is inherent to every physically acceptable single-particle quantum state.

arXiv:2107.11596•Jul 24, 2021•0 citations

Proper time derivatives in quantum mechanics

Juan Pablo Aparicio, Fabián H. Gaioli, Edgardo T. Garcia Alvarez

Several quantum proper time derivatives are obtained from the Beck one in the usual framework of relativistic quantum mechanics (spin-1/2 case). The ``scalar Hamiltonians'' of these derivatives should be thought of as the conjugate variables of the proper time. Then, the Hamiltonians would play the role of mass operators, suggesting the formulation of an adequate extended indefinite mass framework. We propose and briefly develop the framework corresponding to the Feynman parametrization of the Dirac equation. In such a case we derive the other parametrizations known in the literature, linking the extension of the different proposals of quantum proper time derivatives again.

arXiv:hep-th/9807212•Physical Review A•Jan 1, 1995•17 citations

Spacetime states and covariant quantum theory

Michael Reisenberger, Carlo Rovelli C

In its usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended configuration space. Such covariant formulations are natural for relativistic gravitational systems, where general covariance conflicts with the notion of a preferred physical-time variable. The standard presentation of quantum mechanics, in turn, again gives time a very special role, raising well known difficulties for quantum gravity. Is there a covariant form of (canonical) quantum mechanics? We observe that the preferred role of time in quantum theory is the consequence of an idealization: that measurements are instantaneous. Canonical quantum theory can be given a covariant form by dropping this idealization. States prepared by noninstantaneous measurements are described by ``spacetime smeared states.'' The theory can be formulated in terms of these states, without making any reference to a special time variable. The quantum dynamics is expressed in terms of the propagator, an object covariantly defined on the extended configuration space.

arXiv:gr-qc/0111016•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jun 7, 2002•75 citations

Proper Time for Spin 1/2 Particles

Shoju Kudaka, Shuichi Matsumoto

We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that the proper time itself be given by the integral of the expectation value of the operator. The tempo operator has some terms involving the Pauli spin matrices, and the evolution of the proper time is influenced by the spin state via these terms. The relation between the tempo operator and the metric tensor is elucidated.

arXiv:quant-ph/0508046•Aug 5, 2005•0 citations

Proper Time for Spin 1/21/21/2 Particles

Shoju Kudaka, Shuichi Matsumoto

We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the “tempo operator”, and that the proper time itself be given by the integral of the expectation value of the operator. The tempo operator has some terms involving the Pauli spin matrices, and the evolution of the proper time is influenced by the spin state via these terms. The relation between the tempo operator and the metric tensor is elucidated. 1

•Dec 30, 2006•0 citations

Enhanced tunneling through nonstationary barriers

Juan Pedro Palomares-Báez, Boris I. Ivlev, José Luis Rodríguez‐López

Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schr\"odinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented.

Physical Review A•Nov 7, 2007•12 citations
We develop a formal theory which rests upon Nambu's description of the quantum state and especially on the use of the proper time. We show that the introduction of the proper time in quantum mechanics in understandable from the viewpoint that eligible trajectries in the well-known variational treatment of classical mechanics can be parametrized by an auxiliary variable. A new theory developed here permits a formulation of barrier penetrations in terms of the so-called Euclidean Lagrangian.
Although the quantization of relativistic systems in a proper-time framework gives new insights concerning the understanding of the so-called localization problem, classical observers cannot be treated as quantum comoving frames and real measurement are typically conceived using an external parameter related to a classical frame. Here, the connection between the proper-time formalism and usual descriptions parametrized by classical observers is obtained by defining a restriction operation that mixes contributions of different values of proper-time. Such a restriction procedure allows us to retrieve the concepts of Newton-Wigner position and Kijowski time of detection in an effective fashion, opening the possibility to interpret the related causalities issues as an apparent phenomena resulting from the time uncertainty that is inherent to every physically acceptable single-particle quantum state.
Several quantum proper time derivatives are obtained from the Beck one in the usual framework of relativistic quantum mechanics (spin-1/2 case). The ``scalar Hamiltonians'' of these derivatives should be thought of as the conjugate variables of the proper time. Then, the Hamiltonians would play the role of mass operators, suggesting the formulation of an adequate extended indefinite mass framework. We propose and briefly develop the framework corresponding to the Feynman parametrization of the Dirac equation. In such a case we derive the other parametrizations known in the literature, linking the extension of the different proposals of quantum proper time derivatives again.
In its usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended configuration space. Such covariant formulations are natural for relativistic gravitational systems, where general covariance conflicts with the notion of a preferred physical-time variable. The standard presentation of quantum mechanics, in turn, again gives time a very special role, raising well known difficulties for quantum gravity. Is there a covariant form of (canonical) quantum mechanics? We observe that the preferred role of time in quantum theory is the consequence of an idealization: that measurements are instantaneous. Canonical quantum theory can be given a covariant form by dropping this idealization. States prepared by noninstantaneous measurements are described by ``spacetime smeared states.'' The theory can be formulated in terms of these states, without making any reference to a special time variable. The quantum dynamics is expressed in terms of the propagator, an object covariantly defined on the extended configuration space.
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that the proper time itself be given by the integral of the expectation value of the operator. The tempo operator has some terms involving the Pauli spin matrices, and the evolution of the proper time is influenced by the spin state via these terms. The relation between the tempo operator and the metric tensor is elucidated.
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the “tempo operator”, and that the proper time itself be given by the integral of the expectation value of the operator. The tempo operator has some terms involving the Pauli spin matrices, and the evolution of the proper time is influenced by the spin state via these terms. The relation between the tempo operator and the metric tensor is elucidated. 1
Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schr\"odinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented.