TOPOLOGICAL QUANTUM MECHANICS IN 2+1 DIMENSIONS

1990 ◽  
Vol 05 (08) ◽  
pp. 1575-1595 ◽  
Author(s):  
B.-S. SKAGERSTAM ◽  
A. STERN
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Flat Space ◽  
Noncommutative Space ◽  
Quantum Mechanical ◽  
De Sitter ◽  
Spinning Particles ◽  
Topological Quantum ◽  
Quantum Mechanical Description ◽  
Adjoint Orbits

We show that the classical and quantum covariant dynamics of spinning particles in flat space in 2+1 dimensions are derived from a pure Wess-Zumino term written on the space of adjoint orbits of the ISO(2, 1) group. Similarly, the dynamics of spinning particles in 2+1 de Sitter [anti-de Sitter] space are derived from a Wess-Zumino term on the space of adjoint orbits of SO(3, 1) [SO(2, 2)]. It is shown that a quantum mechanical description of spin is possible in 2+1 dimensions without introducing explicit spin degrees of freedom, but at the expense of having a noncommutative space-time geometry.

scholarly journals THE SCATTERING MATRIX APPROACH FOR THE QUANTUM BLACK HOLE: AN OVERVIEW

1996 ◽  
Vol 11 (26) ◽  
pp. 4623-4688 ◽  
Author(s):  
G. 'T HOOFT
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Flat Space ◽  
Scattering Matrix ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Quantum Black Hole ◽  
Quantum Mechanical Description ◽  
Starting Point ◽  
Alternative Approaches

If one assumes the validity of conventional quantum field theory in the vicinity of the horizon of a black hole, one does not find a quantum-mechanical description of the entire black hole that even remotely resembles that of conventional forms of matter; in contrast with matter made out of ordinary particles one finds that, even if embedded in a finite volume, a black hole would be predicted to have a strictly continuous spectrum. Dissatisfied with such a result, which indeed hinges on assumptions concerning the horizon that may well be wrong, various investigators have now tried to formulate alternative approaches to the problem of “quantizing” the black hole. We here review the approach based on the assumption of quantum-mechanical purity and unitarity as a starting point, as has been advocated by the present author for some time, concentrating on the physics of the states that should live on a black hole horizon. The approach is shown to be powerful in producing not only promising models for the quantum black hole, but also new insights concerning the dynamics of physical degrees of freedom in ordinary flat space–time.

scholarly journals Did bohr succeed in defending the completeness of quantum mechanics?

2020 ◽  
Vol 24 (1) ◽  
pp. 51-63
Author(s):  
Kunihisa Morita
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Recent Trend ◽  
Physical Reality ◽  
Current Paper ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Completeness Of Quantum Mechanics

This study posits that Bohr failed to defend the completeness of the quantum mechanical description of physical reality against Einstein–Podolsky–Rosen’s (EPR) paper. Although there are many papers in the literature that focus on Bohr’s argument in his reply to the EPR paper, the purpose of the current paper is not to clarify Bohr’s argument. Instead, I contend that regardless of which interpretation of Bohr’s argument is correct, his defense of the quantum mechanical description of physical reality remained incomplete. For example, a recent trend in studies of Bohr’s work is to suggest he considered the wave-function description to be epistemic. However, such an interpretation cannot be used to defend the completeness of the quantum mechanical description.

scholarly journals PROLIFERATION OF OBSERVABLES AND MEASUREMENT IN QUANTUM-CLASSICAL HYBRIDS

2012 ◽  
Vol 10 (08) ◽  
pp. 1241012 ◽  
Author(s):  
HANS-THOMAS ELZE
Keyword(s):  
Quantum Mechanics ◽  
Free Will ◽  
Degrees Of Freedom ◽  
Cartesian Product ◽  
Entangled States ◽  
Quantum Mechanical ◽  
Analytical Mechanics ◽  
Hybrid Dynamics

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). Hybrids consist in coupled classical (CL) and quantum mechanical (QM) objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM–CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and nonsignaling. Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.

scholarly journals GRAVITY AND YANG–MILLS THEORY

2010 ◽  
Vol 19 (14) ◽  
pp. 2379-2384 ◽  
Author(s):  
SUDARSHAN ANANTH
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Mechanical ◽  
Yang Mills ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Theory Of Gravity

Three of the four forces of Nature are described by quantum Yang–Mills theories with remarkable precision. The fourth force, gravity, is described classically by the Einstein–Hilbert theory. There appears to be an inherent incompatibility between quantum mechanics and the Einstein–Hilbert theory which prevents us from developing a consistent quantum theory of gravity. The Einstein–Hilbert theory is therefore believed to differ greatly from Yang–Mills theory (which does have a sensible quantum mechanical description). It is therefore very surprising that these two theories actually share close perturbative ties. This essay focuses on these ties between Yang–Mills theory and the Einstein–Hilbert theory. We discuss the origin of these ties and their implications for a quantum theory of gravity.

scholarly journals Holographic naturalness and topological phase transitions

2021 ◽  
pp. 2150030
Author(s):  
Andrea Addazi
Keyword(s):  
Phase Transitions ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
Gravity Anomalies ◽  
Vacuum State ◽  
Space Time ◽  
Topological Phase ◽  
De Sitter ◽  
Topological Quantum ◽  
Topological Phase Transitions

We show that our Universe lives in a topological and non-perturbative vacuum state full of a large amount of hidden quantum hairs, the hairons. We will discuss and elaborate on theoretical evidences that the quantum hairs are related to the gravitational topological winding number in vacuo. Thus, hairons are originated from topological degrees of freedom, holographically stored in the de Sitter area. The hierarchy of the Planck scale over the Cosmological Constant (CC) is understood as an effect of a Topological Memory intrinsically stored in the space-time geometry. Any UV quantum destabilizations of the CC are re-interpreted as Topological Phase Transitions, related to the disappearance of a large ensamble of topological hairs. This process is entropically suppressed, as a tunneling probability from the [Formula: see text]- to the 0-states. Therefore, the tiny CC in our Universe is a manifestation of the rich topological structure of the space-time. In this portrait, a tiny neutrino mass can be generated by quantum gravity anomalies and accommodated into a large [Formula: see text]-vacuum state. We will re-interpret the CC stabilization from the point of view of Topological Quantum Computing. An exponential degeneracy of topological hairs non-locally protects the space-time memory from quantum fluctuations as in Topological Quantum Computers.

scholarly journals On the Relativistic Quantum Mechanics of a Particle in Space with Minimal Length

2012 ◽  
Vol 57 (9) ◽  
pp. 942
Author(s):  
Ch.M. Scherbakov
Keyword(s):  
Quantum Mechanics ◽  
Commutation Relation ◽  
Relativistic Quantum ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Group Symmetry ◽  
Relativistic Quantum Mechanics ◽  
Noncommutative Space ◽  
Quantum Mechanical

A noncommutative space and the deformed Heisenberg algebra [X,P] = iħ{1 – βP2}1/2 are investigated. The quantum mechanical structures underlying this commutation relation are studied. The rotational group symmetry is discussed in detail.

scholarly journals GRAVITOMAGNETIC MOMENTS AND DYNAMICS OF DIRAC (SPIN ½) FERMIONS IN FLAT SPACE–TIME MAXWELLIAN GRAVITY

2004 ◽  
Vol 19 (25) ◽  
pp. 4207-4229 ◽  
Author(s):  
HARIHAR BEHERA ◽  
P. C. NAIK
Keyword(s):  
Quantum Mechanics ◽  
Equivalence Principle ◽  
Relativistic Quantum ◽  
Flat Space ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Gravitational Effects ◽  
Spin Particle ◽  
Dirac Spin

The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative gravity (in flat space–time) named here as "Maxwellian gravity." The standard Dirac's approach to the intrinsic spin in the fields of Maxwellian gravity yields the gravitomagnetic moment of a Dirac (spin ½) particle exactly equal to its intrinsic spin. Violation of the Equivalence Principle (both at classical and quantum-mechanical level) in the relativistic domain has also been reported in this work.

CAN QUANTUM-MECHANICAL DESCRIPTION OF PHYSICAL REALITY BE CONSIDERED INCOMPLETE?

2006 ◽  
Vol 04 (01) ◽  
pp. 45-54 ◽  
Author(s):  
GILLES BRASSARD ◽  
ANDRÉ ALLAN MÉTHOT
Keyword(s):  
Quantum Mechanics ◽  
Critical Analysis ◽  
Albert Einstein ◽  
Physical Reality ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Influential Paper ◽  
Completeness Of Quantum Mechanics ◽  
Epr Argument

In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.

scholarly journals CPT VIOLATION IN STRING-MODIFIED QUANTUM MECHANICS AND THE NEUTRAL-KAON SYSTEM

1996 ◽  
Vol 11 (08) ◽  
pp. 1489-1507 ◽  
Author(s):  
JOHN ELLIS ◽  
N.E. MAVROMATOS ◽  
D.V. NANOPOULOS
Keyword(s):  
Quantum Mechanics ◽  
Neutral Kaon ◽  
Low Energy ◽  
Target Space ◽  
Quantum Mechanical ◽  
Cpt Violation ◽  
World Sheet ◽  
String Phenomenology ◽  
Quantum Mechanical Description ◽  
Energy Theory

We argue that CPT is in general violated in a non-quantum-mechanical way in the effective low-energy theory derived from noncritical string theory, in which pure states evolve into mixed states in general. It is known that such a dynamical framework violates the strong form of CPT invariance. We relate CPT violation in the effective low-energy theory in our formalism to apparent world-sheet charge nonconservation induced by stringy monopoles corresponding to target-space black-hole configurations. We prove that energy is conserved on the average in this CPT-violating modification of quantum mechanics. The magnitude of the effective spontaneous violation of CPT may not be far from the present experimental sensitivity in the neutral-kaon system. We demonstrate that previously proposed phenomenological modifications to the quantum-mechanical description of the neutral-kaon system violate CPT, although in a different way from that assumed in analyses within conventional quantum mechanics. We sketch the way to constrain the novel CPT-violating parameters using available data on KL→2π, KS→ 3π0 and semileptonic KL,S decay asymmetries. Could non-quantum-field-theoretical and non-quantum-mechanical CPT violation usher in the long-awaited era of string phenomenology?

Conclusion

2003 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Classical Method ◽  
Point Of View ◽  
Quantum Limit ◽  
Quantum Mechanical ◽  
Computational Point ◽  
Exact Calculations ◽  
Dynamics Problems ◽  
Classical Picture

In this book, we have discussed the problems concerning mixing of classical and quantum mechanics, and we have given several possible solutions to the problem and a number of suggestions for the setup of working computational schemes. In the present chapter, we give some recommendations as to which methods one should use for a given type of system and problem. As can be seen from the tables and what is apparent from the discussion in the previous chapters, the quantum-classical method has been and is used for solving many different molecular dynamics problems. Recommendations, as far as molecule surface or processes in solution are concerned, have not been incorporated, the reason being that the methods here are still to some extent under development. We have seen that the quantum-classical approach can be derived in two different fashions. In one method the classical limit ħ→ 0 is taken in some degrees of freedom. In the other approach the quantum mechanical equations are parameterized in such a fashion that classical equations of motions are either pulled out of or injected into the quantum mechanical. Thus the first method involves and introduces the classical picture in certain particular degrees of freedom—in the second method the classical picture is in principle not introduced—it is just a reformulation of quantum mechanics. This reformulation has the exact dynamics as the limit. However, if exact calculations are to be performed, the reformulation may not be advantageous from a computational point of view, and, hence, standard methods are often more conveniently applied. We prefer the second approach for introducing the quantum-classical scheme because, as mentioned, it automatically has the exact formulation as the limit. The approach is most conveniently implemented through the trajectory driven DVR, or the so-called TDGH-DVR method, which gives the systematic way of approaching the quantum mechanical limit from the classical one. Thus, the method interpolates continuously between the classical and the quantum limit—a property it shares with, for instance, the FMS method and the Bohm formulation.

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