Spin and localization for elementary systems

Kálnay, A. J.; Torres, P. L.

doi:10.1103/physrevd.9.1670

Cited by 7 publications

(4 citation statements)

References 20 publications

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“…From the definition of |x in Eq. (21), it follows that: [4][5][6][7][8].) Furthermore, with this Lorentz invariant choice C p = 1 we also have the result…”

Section: The Problems In Defining Localized Particle Statesmentioning

confidence: 59%

“…18 The propagator K(x b , x a ) is sometimes called the Newton-Wigner propagator. (For a small sample of literature dealing with Newton-Wigner states and related topics, see [15][16][17][18][19][20][21][22][23][24][25][26][27][28].) This is the propagator you get if you forget all about Lorentz invariance and study a system with the Hamiltonian H = (p 2 + m 2 ) 1/2 as though you are doing NRQM with this Hamiltonian.…”

Section: Propagator Does Not Propagate the Wave Functionsmentioning

confidence: 99%

“…If we are assured that both these path integrals lead to the same propagator (as they do in NRQM) one would have preferred the Lagrangian path integral, at least as a formal expression. 21 Unfortunately the Hamiltonian and Lagrangian path integrals are not guaranteed to lead to the same result. In fact, we will see that the most natural definition for Lagrangian path integral does not work in the case of a relativistic particle, while the Hamiltonian path integral can be made to work with some extra tinkering of the measure.…”

Section: In Terms Of Eithermentioning

confidence: 99%

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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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“…From the definition of |x in Eq. (21), it follows that: [4][5][6][7][8].) Furthermore, with this Lorentz invariant choice C p = 1 we also have the result…”

Section: The Problems In Defining Localized Particle Statesmentioning

confidence: 59%

Section: Propagator Does Not Propagate the Wave Functionsmentioning

confidence: 99%

Section: In Terms Of Eithermentioning

confidence: 99%

See 1 more Smart Citation

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

Padmanabhan

2018

Eur. Phys. J. C

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“…Because on the one hand the talk is about wave function (or its density matrix equivalent), complex versus real-valued, and on the other hand the concept of wave function has no commonly accepted clear meaning in relativistic quantum field theory, a further clarification of this issue is necessary. Despite the vast literature on this topics [7][8][9][10][11][12][13][14][15][16][17][18], no general consensus has been established. An important insight can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

A New Perspective on Quantum Field Theory Revealing Possible Existence of Another Kind of Fermions Forming Dark Matter

Pavšič

2022

Preprint

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Quantum fields are considered as generators of infinite-dimensional Clifford algebra Cl(∞), which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a superposition of the basis elements of Cl(∞), the superposition coefficients being multiparticle complex-valued wave functions. The basis elements, that are products of the generators of Cl(∞) in the Witt basis, act as creation and annihilation operators. They create positive and negative energy states that include the bare and the Dirac vacuum as special cases. It is shown that the nonvanishing electric charge arises from an extra dimension or from doubling the number of creation and annihilation operators, which brings an extra imaginary unit ī into the description. A further extension is to consider the ī as one of the quaternionic imaginary units and consider a generic state as having values in the quaternionic algebra or, equivalently, in the complexified 2-dimensional Clifford algebra, Cl(2) ⊗ C. It contains two distinct fundamental representations of SU (2), one associated with the weak isospin doublet (ν e , e − ), and the other one with the doublet of new leptons, denoted ( + , ν ), that together with the new quarks (u , d ) can be identified with dark matter.

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On localisability and Heisenberg's fundamental field

Kálnay

1975

Int J Theor Phys

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Spin and localization for elementary systems

Cited by 7 publications

References 20 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

A New Perspective on Quantum Field Theory Revealing Possible Existence of Another Kind of Fermions Forming Dark Matter

On localisability and Heisenberg's fundamental field

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