scholarly journals Quantum Propagators for Geodesic Congruences

2021 ◽  
Vol 6 (2) ◽  
Author(s):  
Miguel Socolovsky ◽  
Keyword(s):  
Quantum Probability ◽  
Probability Amplitude ◽  
Raychaudhuri Equation ◽  
Feynman Propagator

Using the Raychaudhuri equation, we show that a quantum probability amplitude (Feynman propagator) can be univocally associated to any timelike or null affinely parametrized geodesic congruence.

scholarly journals Path Integral Implementation of Relational Quantum Mechanics

2021 ◽  
Author(s):  
Jianhao M. Yang
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Path Integral ◽  
Measurement Theory ◽  
Entanglement Entropy ◽  
Quantum Probability ◽  
Probability Amplitude ◽  
Path Integral Representation ◽  
Relational Quantum Mechanics ◽  
Influence Functional

Abstract Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In the recent works (J. M. Yang, Sci. Rep. 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born's Rule, Schr\"{o}dinger Equations, and measurement theory. This paper gives a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifies the physical meaning of the relational probability amplitude, but also gives several important applications. For instance, the double slit experiment can be elegantly explained. A path integral representation of the reduced density matrix of the observed system can be derived. Such representation is shown valuable to describe the interaction history of the measured system and a series of measuring systems. More interestingly, it allows us to develop a method to calculate entanglement entropy based on path integral and influence functional. Criteria of entanglement is proposed based on the properties of influence functional, which may be used to determine entanglement due to interaction between a quantum system and a classical field.

scholarly journals Path integral implementation of relational quantum mechanics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jianhao M. Yang
Keyword(s):  
Quantum Mechanics ◽  
Reference Frame ◽  
Path Integral ◽  
Measurement Theory ◽  
Entanglement Entropy ◽  
Quantum Probability ◽  
Frame Theory ◽  
Probability Amplitude ◽  
Relational Quantum Mechanics ◽  
Measured System

AbstractRelational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In a recent paper (Yang in Sci Rep 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born’s Rule, Schrödinger Equations, and measurement theory. This paper further extends the reformulation effort in three aspects. First, it gives a clearer explanation of the key concepts behind the framework to calculate measurement probability. Second, we provide a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifies the physical meaning of the relational probability amplitude, but also allows us to elegantly explain the double slit experiment, to describe the interaction history between the measured system and a series of measuring systems, and to calculate entanglement entropy based on path integral and influence functional. In return, the implementation brings back new insight to path integral itself by completing the explanation on why measurement probability can be calculated as modulus square of probability amplitude. Lastly, we clarify the connection between our reformulation and the quantum reference frame theory. A complete relational formulation of quantum mechanics needs to combine the present works with the quantum reference frame theory.

BOUNDS ON f(G) GRAVITY FROM ENERGY CONDITIONS

2010 ◽  
Vol 25 (27) ◽  
pp. 2325-2332 ◽  
Author(s):  
PUXUN WU ◽  
HONGWEI YU
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Modified Gravity ◽  
Energy Conditions ◽  
Model Parameters ◽  
Effective Energy ◽  
Raychaudhuri Equation ◽  
Accelerating Expansion

The f(G) gravity is a theory to modify the general relativity and it can explain the present cosmic accelerating expansion without the need of dark energy. In this paper the f(G) gravity is tested with the energy conditions. Using the Raychaudhuri equation along with the requirement that the gravity is attractive in the FRW background, we obtain the bounds on f(G) from the SEC and NEC. These bounds can also be found directly from the SEC and NEC within the general relativity context by the transformations: ρ → ρm + ρE and p → pm + pE, where ρE and pE are the effective energy density and pressure in the modified gravity. With these transformations, the constraints on f(G) from the WEC and DEC are obtained. Finally, we examine two concrete examples with WEC and obtain the allowed region of model parameters.

Quantum Probability Calculus as Fuzzy-Kolmogorovian Probability Calculus

2009 ◽  
Author(s):  
Jarosław Pykacz ◽  
Luigi Accardi ◽  
Guillaume Adenier ◽  
Christopher Fuchs ◽  
Gregg Jaeger ◽  
...  
Keyword(s):  
Quantum Probability ◽  
Probability Calculus

scholarly journals Quantum gravitational optics: Effective Raychaudhuri equation

2006 ◽  
Vol 74 (4) ◽  
Author(s):  
N. Ahmadi ◽  
M. Nouri-Zonoz
Keyword(s):  
Raychaudhuri Equation

SPIN-PARITY EFFECT IN VIOLATION OF BELL'S INEQUALITIES

2013 ◽  
Vol 28 (01) ◽  
pp. 1450004 ◽  
Author(s):  
ZHIGANG SONG ◽  
J.-Q. LIANG ◽  
L.-F. WEI
Keyword(s):  
Berry Phase ◽  
Quantum Probability ◽  
Quantum Nonlocality ◽  
Entangled State ◽  
Bell’S Inequalities ◽  
Bipartite Entanglement ◽  
Spin Parity ◽  
Parity Effect ◽  
Bell's Inequalities ◽  
Spin Parity Effect

Analytic formulas of Bell correlations are derived in terms of quantum probability statistics under the assumption of measuring outcome-independence and the Bell's inequalities (BIs) are extended to general bipartite-entanglement macroscopic quantum-states (MQS) of arbitrary spins. For a spin-½ entangled state we find analytically that the violations of BIs really resulted from the quantum nonlocal correlations. However, the BIs are always satisfied for the spin-1 entangled MQS. More generally the quantum nonlocality does not lead to the violation for the integer spins since the nonlocal interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spins due to the nontrivial Berry phase, and thus the violation of BIs is understood remarkably as an effect of geometric phase. Specifically, our generic observation of the spin-parity effect can be experimentally tested with the entangled photon-pairs.

Feynman propagator in a linearly expanding universe

1983 ◽  
Vol 28 (6) ◽  
pp. 1298-1307 ◽  
Author(s):  
E. Calzetta ◽  
M. Castagnino
Keyword(s):  
Expanding Universe ◽  
Feynman Propagator

Probability amplitude structure of Fokker–Plank equation

2003 ◽  
Vol 329 (1-2) ◽  
pp. 68-80 ◽  
Author(s):  
M.S. Torres ◽  
J.M.A. Figueiredo
Keyword(s):  
Probability Amplitude ◽  
Fokker Plank Equation
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