On relativistic entanglement and localization of particles and on their comparison with the nonrelativistic theory

Crater, Horace W.; Lusanna, Luca

doi:10.1142/s0217751x14501632

Cited by 7 publications

(14 citation statements)

References 75 publications

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“…But in quantum theory, you need to ensure that both the dynamical equations (for the operators in Heisenberg picture, say) as well as the description of quantum states in the Hilbert space are relativistically invariant. 12 The first requirement -viz. relativistic invariance of dynamical equationscan be ensured by using a relativistically invariant action or Hamiltonian; but the second requirement does not have a direct analogue in classical relativistic mechanics.…”

Section: Preview and Summarymentioning

confidence: 99%

Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts

Padmanabhan

2018

Eur. Phys. J. C

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Given the classical dynamics of a non-relativistic particle in terms of a Hamiltonian or an action, it is relatively straightforward to obtain the non-relativistic quantum mechanics (NRQM) of the system. These standard procedures, based on either the Hamiltonian or the path integral, however, do not work in the case of a relativistic particle. As a result we do not have a single-particle description of relativistic quantum mechanics (RQM). Instead, the correct approach requires a transmutation of dynamical variables from the position and momentum of a single particle to a field and its canonical momentum. Particles, along with antiparticles, reappear in a very nontrivial manner as the excitations of the field. The fact that one needs to adopt completely different languages to describe a relativistic and nonrelativistic free particle implies that obtaining the NRQM limit of QFT is conceptually nontrivial. I examine this limit in several approaches (like, for e.g., Hamiltonian dynamics, Lagrangian and Hamiltonian path integrals, field theoretic description etc.) and identify the precise issues which arise when one attempts to obtain the NRQM from QFT in each of these approaches. The dichotomy of NRQM and QFT does not originate just from the square root in the Hamiltonian or from the demand of Lorentz invariance, as is sometimes claimed. The real difficulty has its origin in the necessary existence of antiparticles to ensure a particular notion of relativistic causality. Because of these conceptual issues, it turns out that one cannot, in fact, obtain some of the popular descriptions of NRQM by any sensible limiting procedure applied to QFT. To obtain NRQM from QFT in a seamless manner, it is necessary to work with NRQM expressed in a language closer to that of QFT. This fact has several implications, especially for the operational notion of space coordinates in quantum theory. A close examination of these issues, which arise when quantum theory is combined with special a e-mail: paddy@iucaa.in relativity, could offer insights in the context of attempts to combine quantum theory with general relativity.

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Section: Preview and Summarymentioning

confidence: 99%

Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts

Padmanabhan

2018

Eur. Phys. J. C

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“…Besides this spatial non-separability there is the non-measurability of the decoupled external non-covariant canonical center of mass due to its nonlocal nature. See [55] for more details on this point and for the indications from non-relativistic quantum mechanics that also the localization of the Newton center of mass is an open problem.…”

Section: Discussionmentioning

confidence: 99%

On the relativistic micro-canonical ensemble and relativistic kinetic theory for N relativistic particles in inertial and non-inertial rest frames

Alba

Crater

Lusanna

2015

Int. J. Geom. Methods Mod. Phys.

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A new formulation of relativistic classical mechanics allows a reconsideration of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincaré generators of an interacting N -particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonical ensemble in terms of the Galilei generators.a The same happens in the parametrized Galilei theories defined in [11]. This allows us to define non-relativistic quantum mechanics in Galilean non-inertial frames. 1550049-2On the relativistic micro-canonical ensemble b With particle systems this can be done only in rotating systems till now [10]. Instead the problem is completely open for the massive Klein-Gordon field due to the no-go theorem of [12] forbidding unitary evolution in non-inertial frames. c Even if non-physical we must give the Cauchy data on a space-like 3-space, to be able to use the existence and unicity theorem for the solution of partial differential equations to predict the future. The subsequent evolution is consistent with special relativity even in the case of actionat-a-distance interactions.

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“…For a recent insight see Ref. [22,34,35]. Within the framework of the quantized scalar field in Minkowski space the center of mass operator is defined according to (60) in terms of the position operators on a given 3-surface Σ in spacetime.…”

Section: Wave Packet Statesmentioning

confidence: 99%

Manifestly covariant canonical quantization of the scalar field and particle localization

Pavšič

2018

Mod. Phys. Lett. A

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Particle localization within quantum field theory is revisited. Canonical quantization of a free scalar field theory is performed in a manifestly Lorentz covariant way with respect to an arbitrary 3-surface Σ, which is the simultaneity surface associated with the observer, whose proper time direction is orthogonal to Σ. Position on Σ is determined by a 4-vectorx µ . The corresponding quantum position operator, formed in terms of the operators a † (x), a(x), that create/annihilate particles on Σ, has thus well behaved properties under Lorentz transformations. A generic state is a superposition of the states, created with a † (x), the superposition coefficients forming multiparticle wave packet profiles-wave functions, including a single particle wave function that satisfies the covariant generalization of the Foldy equation. The covariant center of mass operator is introduced and its expectation values in a generic multiparticle state calculated.

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On relativistic entanglement and localization of particles and on their comparison with the nonrelativistic theory

Cited by 7 publications

References 75 publications

Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts

Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts

On the relativistic micro-canonical ensemble and relativistic kinetic theory for N relativistic particles in inertial and non-inertial rest frames

Manifestly covariant canonical quantization of the scalar field and particle localization

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