International Conference on the Quantum Theory of Systems Having Many Degrees of Freedom

1965 ◽  
Vol 18 (1) ◽  
pp. 96-98 ◽  
Author(s):  
P. S. Isaev
Keyword(s):  
Quantum Theory ◽  
Degrees Of Freedom ◽  
International Conference

scholarly journals Semi-classical approximations based on Bohmian mechanics

2020 ◽  
Vol 35 (14) ◽  
pp. 2050070 ◽  
Author(s):  
Ward Struyve
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Expectation Values ◽  
Usual Approach ◽  
Classical Approximation

Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only described by the wave function, but also with additional variables such as particle positions or fields. By letting the classical equations of motion depend on these variables, rather than the quantum expectation values, a semi-classical approximation is obtained that is closer to the exact quantum results than the usual approach. We discuss the Bohmian semi-classical approximation in various contexts, such as nonrelativistic quantum mechanics, quantum electrodynamics and quantum gravity. The main motivation comes from quantum gravity. The quest for a quantum theory for gravity is still going on. Therefore a semi-classical approach where gravity is treated classically may be an approximation that already captures some quantum gravitational aspects. The Bohmian semi-classical theories will be derived from the full Bohmian theories. In the case there are gauge symmetries, like in quantum electrodynamics or quantum gravity, special care is required. In order to derive a consistent semi-classical theory it will be necessary to isolate gauge-independent dependent degrees of freedom from gauge degrees of freedom and consider the approximation where some of the former are considered classical.

scholarly journals The quantum theory of the emission and absorption of radiation

1927 ◽  
Vol 114 (767) ◽  
pp. 243-265 ◽  
Keyword(s):  
Quantum Theory ◽  
Radiation Field ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Hamiltonian Function ◽  
Correct Treatment ◽  
Principle Of Relativity ◽  
Satisfactory Theory ◽  
General Method

The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory of dynamics. One can treat mathematically the problem of any dynamical system composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function, and one can interpret the mathematics physically by a quite definite general method. On the other hand, hardly anything has been done up to the present on quantum electrodynamics. The questions of the correct treatment of a system in which the forces are propagated with the velocity of light instead of instantaneously, of the production of an electromagnetic field by a moving electron, and of the reaction of this field on the electron have not yet been touched. In addition, there is a serious difficulty in making the theory satisfy all the requirements of the restricted principle of relativity, since a Hamiltonian function can no longer be used. This relativity question is, of course, connected with the previous ones, and it will be impossible to answer any one question completely without at the same time answering them all. However, it appears to be possible to build up a fairly satisfactory theory of the emission of radiation and of the reaction of the radiation field on the emitting system on the basis of a kinematics and dynamics which are not strictly relativistic. This is the main object of the present paper. The theory is noil-relativistic only on account of the time being counted throughout as a c-number, instead of being treated symmetrically with the space co-ordinates. The relativity variation of mass with velocity is taken into account without difficulty. The underlying ideas of the theory are very simple. Consider an atom interacting with a field of radiation, which we may suppose for definiteness to be confined in an enclosure so as to have only a discrete set of degrees of freedom. Resolving the radiation into its Fourier components, we can consider the energy and phase of each of the components to be dynamical variables describing the radiation field. Thus if E r is the energy of a component labelled r and θ r is the corresponding phase (defined as the time since the wave was in a standard phase), we can suppose each E r and θ r to form a pair of canonically conjugate variables. In the absence of any interaction between the field and the atom, the whole system of field plus atom will be describable by the Hamiltonian H ═ Σ r E r + H o equal to the total energy, H o being the Hamiltonian for the atom alone, since the variables E r , θ r obviously satisfy their canonical equations of motion E r ═ — ∂H/∂θ r ═ 0, θ r ═ ∂H/∂E r ═ 1.

scholarly journals The interaction of electric charges

1930 ◽  
Vol 126 (803) ◽  
pp. 696-728 ◽  
Keyword(s):  
Quantum Theory ◽  
Gauge Transformation ◽  
Degrees Of Freedom ◽  
Frame Of Reference ◽  
Degree Of Freedom ◽  
Classical Dynamics ◽  
Proper Distance ◽  
Special Degree ◽  
Odd Degree ◽  
Absolute Quantity

1. The present investigation is a sequel to two earlier papers in these 'Proceedings.' In II a theory of the electron was proposed which led to a prediction of the value of the constant 2π e 2 / hc . The theory involved an appeal to the analogies of classical dynamics, which frequently prove useful though precarious; it has been my purpose to substitute a more satisfactory geometrical basis. In a problem of this kind, concerned with the whole question of the significance of the methods of quantum theory, it is unlikely that finality can have been reached even at the second attempt; but I think that the progress is now sufficient to justify publication. According to II the value of hc /2π e 2 was 136. I remarked that, as it represented the number of degrees of freedom of a system, small mistakes were unlikely; nevertheless I appear to have made such a mistake, and the new prediction is 137 (16). The 136 symmetrical degrees of freedom are a generalisation of rotations and translations in space; but it is characteristic of a pair of electrons that they possess one special degree of freedom unlike the others which has no analogue in the theory of a single electron, viz., an alteration of the proper distance between them; and whereas the 136 rotations are relative to the frame of reference employed, the odd degree of freedom represents alteration of an absolute quantity (the interval). The mistake in the earlier theory was not so much in overlooking this degree of freedom (for it there appeared as the rotation which "interchanges the identity of the two electrons") as in not recognising its distinctness from the others. No one of the 136 relativity transformations can play the part of this non-relativity or gauge transformation.

INTERPRETATION AND PREDICTABILITY OF QUANTUM MECHANICS AND QUANTUM COSMOLOGY

1988 ◽  
Vol 03 (07) ◽  
pp. 645-651 ◽  
Author(s):  
SUMIO WADA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Meaning ◽  
Quantum Cosmology ◽  
Degrees Of Freedom ◽  
Interpretation Of Quantum Mechanics ◽  
Probabilistic Interpretation ◽  
The Universe ◽  
Classical Picture

A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.

scholarly journals Robotic hand design with linear actuators based on Toronto development

Athenea ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 22-28
Author(s):  
Oscar Vargas ◽  
Omar Flor ◽  
Carlos Toapanta
Keyword(s):  
Degrees Of Freedom ◽  
Biomedical Signal Processing ◽  
Mode Switching ◽  
Prosthetic Hand ◽  
Robotic Hand ◽  
Leap Motion ◽  
International Conference ◽  
Upper Limb Prostheses ◽  
Linear Actuators ◽  
And Control

In this work, the design of a robotic hand with 7 degrees of freedom is presented that allows greater flexibility, achieving the usual actions performed by a normal hand. The work consists of a prototype designed with linear actuators and myoelectric sensor, following the mechanism of the University of Toronto for the management of functional phalanges. The design, construction description, components and recommendations for the elaboration of a flexible and useful robotic hand for amputee patients with a residual limb for the socket are presented. Keywords: Robotic hand, Degree of freedom, Toronto´s Mechanism, lineal actuator. References [1]W. Diane, J. Braza and M. Yacub, Essentials of Physical Medicine and Rehabilitation, 4th ed. Philadelphia: Walter R. Frontera and Julie K. Silver and Thomas D. Rizzo, 2020, pp. 651 - 657. [2]A. Heerschop, C. Van Der Sluis, E. Otten, & R.M. Bongers, Looking beyond proportional control: The relevance of mode switching in learning to operate multi-articulating myoelectric upper-limb prostheses, . Biomedical Signal Processing and Control, 2020, doi:10.1016/j.bspc.2019.101647. [3]L. Heisnam, B. Suthar, 20 DOF robotic hand for tele-operation: — Design, simulation, control and accuracy test with leap motion. 2016 International Conference on Robotics and Automation for Humanitarian Applications (RAHA), 2016, doi:10.1109/raha.2016.7931886. [4]Y. Mishima, R. Ozawa, Design of a robotic finger using series gear chain mechanisms. 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2014, doi:10.1109/iros.2014.6942961. [5]N. Dechev, W. Cleghorn, S. Naumann, Multi-segmented finger design of an experimental prosthetic hand,Proceedings of the Sixth National Applied Mechanisms & Robotics Conference, december 1999. [6]O. Flor, “Building a mobile robot,” Education for the future. Accessed on: December 29, 2019. [Online] Available: https://omarflor2014.wixsite.com/misitio. [7]Vargas, O., Flor,O., Suarez, F., Design of a robotic prototype of the hand and right forearm for prostheses, Universidad, Ciencia y Tecnología, 2019. [8]O. Vargas, O. Flor, F. Suarez, C. Chimbo, Construction and functional tests of a robotic prototype for human prostheses, Revista espirales, 2020. [9]P. PonPriya, E. Priya, Design and control of prosthetic hand using myoelectric signal. International Conference on Computing and Communications Technologies (ICCCT), 2017, doi:10.1109/iccct2.2017.7972314. [10]N. Bajaj, A. Spiers, A. Dollar, State of the Art in Artificial Wrists: A Review of Prosthetic and Robotic Wrist Design. IEEE Transactions on Robotics, 2019, doi:10.1109/tro.2018.2865890.

The basis of statistical quantum mechanics

1929 ◽  
Vol 25 (1) ◽  
pp. 62-66 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Dynamical System ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Degrees Of Freedom ◽  
Present Note ◽  
Classical Mechanics ◽  
The Other ◽  
Statistical Nature ◽  
Actual System ◽  
Quantum Treatment

In classical mechanics the state of a dynamical system at any particular time can be described by the values of a set of coordinates and their conjugate momenta, thus, if the system has n degrees of freedom, by 2n numbers. In quantum mechanics, on the other hand, we have to describe a state of the system by a wave function involving a set of coordinates, thus by a function of n variables. The quantum description is, therefore, much more complicated than the classical one. Let us consider, however, an ensemble of systems in Gibbs' sense, i.e. not a large number of actual systems which could, perhaps, interact with one another, but a large number of hypothetical systems which are introduced to describe one actual system of which our knowledge is only of a statistical nature. The basis of the quantum treatment of such an ensemble has been given by Neumann. The description obtained by Neumann of an ensemble on the quantum theory is no more complicated than the corresponding classical description. Thus the quantum theory, which appears to such a disadvantage on the score of complication when applied to individual systems, recovers its own when applied to an ensemble. It is the object of the present note to examine this question more closely and to show how complete the analogy is between the quantum and classical treatments of an ensemble.

scholarly journals A minimalist pilot-wave model for quantum electrodynamics

2007 ◽  
Vol 463 (2088) ◽  
pp. 3115-3129 ◽  
Author(s):  
W Struyve ◽  
H Westman
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Wave Model ◽  
Relativistic Quantum Theory ◽  
Pilot Wave ◽  
Free Electromagnetic Field

We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic and not to the fermionic degrees of freedom of the quantum state. We show that this is sufficient to reproduce the quantum predictions. The beables will be field beables corresponding to the electromagnetic field and will be introduced in a way similar to that of Bohm's model for the free electromagnetic field. Our approach is analogous to the situation in non-relativistic quantum theory, where Bell treated spin not as a beable but only as a property of the wave function. After presenting this model, we also discuss a simple way for introducing additional beables that represent the fermionic degrees of freedom.

Lagrangian quantum theory (II). Several degrees of freedom

1973 ◽  
Vol 59 (2) ◽  
pp. 348-364 ◽  
Author(s):  
F.J. Bloore ◽  
L. Routh
Keyword(s):  
Quantum Theory ◽  
Degrees Of Freedom

scholarly journals Complex Covariance

10.14311/1809 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Frieder Kleefeld
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
Special Relativity ◽  
Degrees Of Freedom ◽  
Classical Mechanics ◽  
Space Time ◽  
Complex Phase ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Complex Valued

According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity was developed by Einstein merely for real-valued space-time and four-momentum, we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, but also to the non-Hermitian Klein-Gordon and Dirac equations, which are to lay the foundations of a non-Hermitian quantum theory.

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