History state formalism for Dirac’s theory

Díaz, Nahuel Luciano; Rossignoli, R.

doi:10.1103/physrevd.99.045008

Cited by 33 publications

(38 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(i) a Dirac quantization scheme, wherein relational observables are constructed that encode correlations between evolving and clock degrees of freedom [1,2,4,, (ii) the Page-Wootters formalism, which defines a relational dynamics in terms of conditional probabilities for clock and evolving degrees of freedom [7,25,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57], and (iii) classical or quantum deparametrizations, which result in a reduced quantum theory that only treats the evolving degrees of freedom as quantum [1,2,7,10,30,31,[58][59][60][61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

“…This degeneracy is not covered by our previous construction. While quadratic clock Hamiltonians are standard in the literature on relational observables [approach (i)] and deparametrizations [approach (iii)], see e.g., [4,10,11,19,29,31], relativistic particle models have only recently been studied in the Page-Wootters formalism [approach (ii)] [45,[49][50][51]. However, Kuchař's criticism (a) that the Page-Wootters approach yields incorrect localization probabilities in relativistic settings has yet to be addressed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

2021

View full text Add to dashboard Cite

We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

2021

View full text Add to dashboard Cite

show abstract

“…Perhaps a PaW formulation of spacetime may represent a first step towards removing this asymmetry. This might help to develop relativistic generalizations of the PaW formalism, see also [31,32,33,34].…”

Section: Discussionmentioning

confidence: 99%

Time Observables in a Timeless Universe

Favalli

Smerzi

2020

Quantum

View full text Add to dashboard Cite

Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact that becomes particularly problematic in the context of quantum gravity. An unconventional solution was pioneered by Page and Wootters (PaW) in 1983. PaW showed that dynamics can be an emergent property of the entanglement between two subsystems of a static Universe. In this work we first investigate the possibility to introduce in this framework a Hermitian time operator complement of a clock Hamiltonian having an equally-spaced energy spectrum. An Hermitian operator complement of such Hamiltonian was introduced by Pegg in 1998, who named it "Age". We show here that Age, when introduced in the PaW context, can be interpreted as a proper Hermitian time operator conjugate to a "good" clock Hamiltonian. We therefore show that, still following Pegg's formalism, it is possible to introduce in the PaW framework bounded clock Hamiltonians with an unequally-spaced energy spectrum with rational energy ratios. In this case time is described by a POVM and we demonstrate that Pegg's POVM states provide a consistent dynamical evolution of the system even if they are not orthogonal, and therefore partially undistinguishables.

show abstract

“…where A, V and φ are mass independent, employing a similar strategy of Sec. III which was already employed for Dirac Hamiltonian in [12]. A minor modification follows from the mass dependent potential mφ(x): since now x|(P T + H)|Ψ m = 0 yields…”

Section: Non Relativistic Limitmentioning

confidence: 99%

“…This allows one to upgrade time from a parameter to an operator, which in turn requires to promote mass, which in both Dirac and Klein Gordon equations is assumed as a fixed parameter, to a quantum observable. This approach offers substantial conceptual advantages even if just the subspace (eigenspace) of definite mass states is considered, but in addition it opens the way to new possibilities [12], such as more general quantum states with mass fluctuations and an extended Fock space based on four dimensional entities. Moreover, the present treatment of interactions reveals that such general states are already implied when expressing the corresponding solutions in terms of the free states, in analogy with the off-shell contributions in perturbative treatments for interacting many particle systems.…”

Section: Introductionmentioning

confidence: 99%

History state formalism for scalar particles

2019

Self Cite

View full text Add to dashboard Cite

We present a covariant quantum formalism for scalar particles based on an enlarged Hilbert space. The particular physical theory can be introduced through a timeless Wheeler DeWitt-like equation, whose projection onto four-dimensional coordinates leads to the Klein Gordon equation. The standard quantum mechanical product in the enlarged space, which is invariant and positive definite, implies the usual Klein Gordon product when applied to its eigenstates. Moreover, the standard three-dimensional invariant measure emerges naturally from the flat measure in four dimensions when mass eigenstates are considered, allowing a rigorous identification between definite mass history states and the standard Wigner representation. Connections with the free propagator of scalar field theory and localized states are subsequently derived. The formalism also allows the superposition of different theories and remains valid in the presence of a fixed external field, revealing special orthogonality relations. Other details such as extended identities for the current density, the quantization of parameterized theories and the non relativistic limit, with its connection to the Page and Wooters formalism, are discussed. A related consistent second quantization formulation is also introduced.

show abstract

History state formalism for Dirac’s theory

Cited by 33 publications

References 25 publications

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

Time Observables in a Timeless Universe

History state formalism for scalar particles

Contact Info

Product

Resources

About