A relativistic one-particle Time of Arrival operator for a free spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math> particle in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> dimensions

Bunao, Joseph Raphael R.; Galapon, Eric A.

doi:10.1016/j.aop.2015.03.018

Cited by 4 publications

(2 citation statements)

References 26 publications

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“…A similar process was used in [72,73] to construct Relativistic Time of Arrival Operators from their canonical commutation relations with the system Hamiltonians.…”

Section: A Quantum Spacetime Four-volume Operatormentioning

confidence: 99%

“…This does not mean however that T has no physical meaning. There are meaningful non self-adjoint quantum operators such as the momentum operator on the half-real line and the time of arrival operators for free non-relativistic and relativistic particles (see, for instance [72][73][74]). To study whether T is a legitimate Hilbert space operator, one then needs to determine if T is maximally symmetric and densely defined.…”

Section: îNmentioning

confidence: 99%

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Spacetime quanta?: the discrete spectrum of a quantum spacetime four-volume operator in unimodular loop quantum cosmology

Bunao¹

2016

Class. Quantum Grav.

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Abstract. This study considers the operatorT corresponding to the classical spacetime four-volumeT (on-shell) of a finite patch of spacetime in the context of Unimodular Loop Quantum Cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since the spacetime four-volume is canonically conjugate to the cosmological "constant", the operatorT is constructed by solving its canonical commutation relation withΛ -the operator corresponding to the classical cosmological constant on-shellΛ. This conjugacy, along with the action ofT on definite volume states reducing toT , allows us to interpret thatT is indeed a quantum spacetime four-volume operator. The discrete spectrum ofT is calculated by considering the set of all τ 's where the eigenvalue equation has a solution Φ τ in the domain ofT . It turns out that, upon assigning the maximal domain D(T ) tô T , we have Φ τ ∈ D(T ) for all τ ∈ C so that the spectrum ofT is purely discrete and is the entire complex plane. A family of operatorsT (b0,φ0) was also considered as possible self-adjoint versions ofT . They represent the restrictions ofT on their respective domains D(T (b0,φ0) ) which are just the maximal domain with additional quasi-periodic conditions. Their possible self-adjointness is motivated by their discrete spectra only containing real and discrete numbers τ m for m = 0, ±1, ±2, ....

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“…A similar process was used in [72,73] to construct Relativistic Time of Arrival Operators from their canonical commutation relations with the system Hamiltonians.…”

Section: A Quantum Spacetime Four-volume Operatormentioning

confidence: 99%

Section: îNmentioning

confidence: 99%

Spacetime quanta?: the discrete spectrum of a quantum spacetime four-volume operator in unimodular loop quantum cosmology

Bunao¹

2016

Class. Quantum Grav.

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Relativistic free-motion time-of-arrival operator for massive spin-0 particles with positive energy

Flores

Galapon

2022

Phys. Rev. A

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Synchronizing quantum and classical clocks made of quantum particles

2016

Self Cite

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We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed in Phys. Rev. A 80, 030102(R) (2009), can be eliminated up to a given order of by choosing an appropriate position-dependent phase for the object's wave-function This then implies that we can make the quantum arrival time of the object as close as possible to its corresponding classical arrival time, allowing us to synchronize a classical and quantum clock which tells time using the classical and quantum arrival time of the object, respectively . We provide an example for synchronizing such a clock by making use of a quantum object with a position-dependent phase imprinted on the object's initial wave-function with the use of an impulsive potential.

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A relativistic one-particle Time of Arrival operator for a free spin-1/2 particle in (1+1) dimensions

Cited by 4 publications

References 26 publications

Spacetime quanta?: the discrete spectrum of a quantum spacetime four-volume operator in unimodular loop quantum cosmology

Spacetime quanta?: the discrete spectrum of a quantum spacetime four-volume operator in unimodular loop quantum cosmology

Relativistic free-motion time-of-arrival operator for massive spin-0 particles with positive energy

Synchronizing quantum and classical clocks made of quantum particles

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