scholarly journals Quantum mechanics of a point particle in -dimensional gravity

1998 ◽  
Vol 15 (10) ◽  
pp. 2981-3030 ◽  
Author(s):  
Hans-Jürgen Matschull ◽  
Max Welling
Keyword(s):  
Quantum Mechanics ◽  
Point Particle ◽  
Dimensional Gravity

scholarly journals SOLIPSISTIC HIDDEN VARIABLES

2012 ◽  
Vol 10 (08) ◽  
pp. 1241016 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Hidden Variables ◽  
Quantitative Model ◽  
Point Particle ◽  
Particle Trajectories ◽  
Bohmian Interpretation

We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV's), dubbed solipsistic HV's, that interpolates between the orthodox no-HV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic point-particle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV's, nonlocality in solipsistic HV's can be substantially reduced down to microscopic distances inside the observer. Even if such HV's may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention.

scholarly journals Feynman’s propagator in Schwinger’s picture of Quantum Mechanics

2021 ◽  
pp. 2150187
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo ◽  
L. Schiavone ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Riemannian Manifold ◽  
Point Particle ◽  
Lagrangian Function ◽  
Natural Family ◽  
Quantum Propagator ◽  
Original Derivation ◽  
Classical Lagrangian

A novel derivation of Feynman’s sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac–Feynman–Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function [Formula: see text] on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian [Formula: see text] allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman’s original derivation of the propagator for a point particle described by a classical Lagrangian L.

ON QUANTUM MECHANICS ON COMPACT SPACE

1992 ◽  
Vol 07 (27) ◽  
pp. 2477-2482 ◽  
Author(s):  
Y. OHNUKI ◽  
S. KITAKADO
Keyword(s):  
Quantum Mechanics ◽  
Compact Space ◽  
Relativistic Quantum ◽  
Point Particle ◽  
Relativistic Quantum Mechanics ◽  
Dimensional Sphere

Non-relativistic quantum mechanics is formulated on the surface of a four-dimensional sphere (S3). It is shown that a point particle on S3 can automatically carry spin.

scholarly journals Against Point Charges

2015 ◽  
Vol 7 (6) ◽  
pp. 138
Author(s):  
David L. Selke
Keyword(s):  
Quantum Mechanics ◽  
Current Theory ◽  
Point Particle ◽  
Point Of Departure

<p class="1Body">A new theory proposed by Dr. Randell Mills reproduces and surpasses the predictions of quantum mechanics and is incompatible with the current theory. A key point of departure is whether the electron is a point particle or if it extends into some shape. It is possible to choose between the two theories based on whether point or extended charges are consistent with known laws and observations.</p>

scholarly journals In Search of a New Quantum Theory: From an Electron with a Volume to the Mechanism of Light Generation

2021 ◽  
Vol 3 (2) ◽  
pp. 29-33
Author(s):  
Andrei Nechayev
Keyword(s):  
Quantum Mechanics ◽  
Fundamental Equation ◽  
Volume Density ◽  
Theoretical Concept ◽  
Point Particle ◽  
Leading Role ◽  
Material Substance ◽  
Light Generation ◽  
Relativistic Concept ◽  
Hamilton Jacobi Equation

A new theoretical concept of quantum mechanics is proposed. The leading role is assigned to the electron as a non-point particle with a volume density of charge and mass. Based on the Hamilton-Jacobi equation, a nonlinear differential equation describing the dynamics of the charged substance of an electron is proposed. This new fundamental equation is transformed into the Schrödinger equation, with the density of the material substance of the electron being proportional to the square of the wave function. Since an electron in the form of a "cloud" of matter can change its configuration in space, we can give a classical interpretation to the process of generating a photon with a frequency and energy corresponding to the principles of quantum mechanics. Interference, diffraction, and the non-relativistic concept of electron spin is discussed.

BRAID STATISTICS FOR THE SOURCES OF THE NONABELIAN CHERN-SIMONS TERM

1990 ◽  
Vol 05 (12) ◽  
pp. 2423-2470 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
M. BOURDEAU ◽  
S. JO
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Point Particle ◽  
Yang Mills ◽  
Direct Sum ◽  
Identical Point ◽  
Effective Lagrangian ◽  
All Solutions ◽  
Chern Simons

A Lagrangian consisting of an Abelian Chern-Simons term and N identical point particle sources is known to lead to fractional statistics for the sources. In this paper, we investigate the non-Abelian generalization of this system with special emphasis on source statistics. All solutions for the Yang-Mills potential in the presence of identical or nonidentical sources are found. For two or more sources, they fall in many gauge inequivalent classes whereas in the Abelian problem, there is only one such class. An effective Lagrangian for N sources is found for each of these solutions. The quantum mechanics and statistics of the sources are sensitive to the potential leading to the effective Lagrangian. There is for instance, a class of solutions for identical sources which are not invariant under exchange of sources. For these solutions, the identity of the sources obliges us to consider such a potential and all its exchange transforms at the same time, and to introduce a Hilbert space of states which is the direct sum of the Hilbert spaces associated with each of these potentials. There are also exchange invariant potentials for identical sources. For SU(3) and N = 3, all exchange invariant potentials are shown to lead to statistics defined by S3 representations. The nature of statistics for SU (M) for higher M as also the creation of intrinsic spin by self interaction are briefly considered.

scholarly journals TRANSITION AMPLITUDE IN (2+1)-DIMENSIONAL CHERN-SIMONS GRAVITY ON A TORUS

1994 ◽  
Vol 09 (27) ◽  
pp. 4727-4745 ◽  
Author(s):  
KIYOSHI EZAWA
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Transition Amplitude ◽  
Wave Functions ◽  
Probability Amplitude ◽  
Modular Invariance ◽  
Maass Forms ◽  
Dimensional Gravity ◽  
Classical Orbit ◽  
Chern Simons

In the framework of the Chern-Simons gravity proposed by Witten, a transition amplitude of a torus universe in (2+1)-dimensional quantum gravity is computed. This amplitude has the desired properties as a probability amplitude of the quantum mechanics of a torus universe, namely, it has a peak on the “classical orbit” and it satisfies the Schrödinger equation of the (2+1)-dimensional gravity. The discussion is given that the classical orbit dominance of the amplitude is not altered by taking the modular invariance into account and that this amplitude can serve as a covariant transition amplitude in a particular sense. A set of the modular-covariant wave functions is also constructed and they are shown to be equivalent to the weight-½ Maass forms.

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