Localization of particles in quantum field theory

1993

A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation is derived in order for the localization of a particle to represent a space-time event. It is shown that there exists a conflict between this relation and the hermiticity of a positive energy position operator.

2016

In this paper, we shall give mathematical interpretations of the particle picture by using the momentum expansion of the quantized wave function of a Schrödinger equation and the theory of special relativity. As a result, we will introduce a new notion of time. 1. Special relativity 1.1. An example. For the inertial frame of reference S on the ground, consider the inertial frame of reference S ′ moving at the constant speed V e.g. a railway bogie. Here, assume that the stand AB of this bogie is parallel to the direction of motion of S ′ and that a light equipment is put on the midpoint of AB. Let us turn on the light. Then, it is no wonder that a person on the bogie S ′ will see that the light arrives at the points A and B at the same time. On the other hand, a person on the ground S will see that, by the principle of invariant light speed, the light arrives at the point A faster than at the point B. Although turning on the light is the only one event, this example shows that the ut...

Physics of Particles and Nuclei, 2015

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to several paradoxes. The most striking of them is that coordinate wave functions of photons emitted by stars have cosmic sizes and strong arguments indicate that this contradicts observational data. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.

Communications in Mathematical Physics, 1982

Starting from the principle of locality of observables we derive localization properties of massive particle states which hold in all models of relativistic quantum theory, including gauge theories. It turns out that particles may always be regarded as well localized distributions of matter, although their mathematical description might require the introduction of non-local (unobservable) fields, which are assigned to infinite string-like regions. In spite of the non-locality of these fields one can show that such particles obey Bose-or Fermi (para) statistics, that to each particle there exists an antiparticle and that collision states of particles exist. A selfcontained exposition of the underlying physical ideas is given in the Introduction, and some perspectives for the structure of field-theoretic models arising from our analysis are discussed in the Conclusions.

arXiv (Cornell University), 2002

We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the collapse of quantum states. However, a fully consistent description in the relativistic domain requires the extension of the interpretation to quantum fields. This extension is far from straightforward. Besides the obvious difficulty of dealing with the infinite degrees of freedom of the field theory, one has to analyze and solve the objections raised by Sorkin concerning the impossibility of ideal measurements in quantum field theory. Here we show that in order to retain a causal theory it is necessary to modify the standard Wigner expression for the cases of partial causally connected local measurements. Our description could be experimentally tested. A verification of the new expression would give a stronger support to the realistic interpretations of the states in quantum mechanics.

1983

A new philosophical model makes particles and information at single points derivative. Space-time grids are not events but only ideal comparisons made by observers. Therefore the identity of space-time points and also of single particles is inherently a speculative assumption. The conservation of units can be derived and is not a foundation for events. An interaction is an actual change and can determine changed particles and a changed space-time grid from itself, both forward and backward in time. In contrast, relativity theory still retains the classical unit model in which information is localized at single points, merely positing more than one observer. One implication of the new model is that quantum mechanical solutions need not be limited by the requirements of relativity as is currently done. The model correctly predicts where difficulties should be found, and relates and explains many puzzles which are otherwise separated and inexplicable.

Quantization Relatifity and Fields, 2020

We know there is something either wrong or missing in our theoretical framework. We know this because there remain many questions unanswered, and because of some incompatibilities between quantum physics and relativity theory. We have tried many things to attempt to explain the "non-local" aspects of wavefunctions and particles, but those things are mostly ad-hoc patches and do not really explain the discrepancies between these two theoretical foundations. However uncomfortable it might be, we must evaluate carefully, and determine which portions of existing theory are proven, which portions are arbitrary or opinion, and especially, which portions are contraindicated by the evidence. Herein, we introduce a unification of Relativity and Quantum Mechanics with theoretical simplicity and economy. This requires some modification to both theories. But the modifications we recommend are supported by the evidence, and once these modifications are made, we find cause for many things which previously had no causal explanation.

2002

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest.

Fundamental Theories of Physics, 2020

Spontaneous localization theory is a quantum theory proposed by GianCarlo Ghirardi, together with Alberto Rimini and Tullio Weber in 1986. However, soon it became clear to Ghirardi that his work was more than just one theory: he actually developed a framework, a family of theories in which the wavefunction jumps, but where the ontology of the theory is underdetermined. After acknowledging that the wavefunction did not provide a satisfactory ontology, he assumed that matter was described by a continuous matter density field in three-dimensional space, whose evolution is governed by a stochastic wavefunction evolution. Alternatively, Bell assumed that the wavefunction would govern a spatiotemporal event ontology, dubbed 'flashes.' However, not much work has been done with the perhaps most obvious possibility, namely that physical objects are made of particles. This paper has two aims. First to explain the reason why people require spontaneous localization theory to be more than just a theory about the wavefunction. This is done by showing how the problem everyone in the foundation of quantum mechanics take to be the fundamental problem of quantum mechanics, namely the measurement problem, is a red herring. Then, the paper explores the possibility of spontaneous localization theories of particles. I argue that this discussion is not a mere exercise, as spontaneous localization theories of particles may be amenable to a relativistic extension which does not require a foliation, and because in general the peculiar type of indeterminism of spontaneous localization theories may help shedding new light on the nature of the tension between quantum theory and relativity.

arXiv (Cornell University), 2013

Principle of locality means that any local change (perturbation) of the stationary state wave function field propagates with finite speed, and therefore reaches distant regions of the field with time delay. If a one-particle or multi-particle non-relativistic quantum system is initially in a stationary state, and its wave function field is locally perturbed, then perturbed and non-perturbed sub-regions appear in the region. According to Schrödinger equation, borders of the perturbed sub-region propagate with infinite speed, and the perturbation instantaneously affects all infinite region. It means that Schrödinger equation predicts infinite speed of the wave function perturbations propagation. This feature of classical Schrödinger equation is traditionally interpreted as nonlocality of quantum mechanics. From physical point of view, such mathematical behavior of Schrödinger equation solutions is questionable because it is difficult to accept that in real world infinite physical objects can instantaneously appear. We introduce a hypothesis that in reality speed of propagation of the perturbed sub-region borders is equal speed of light. On this basis we develop and analyze a finite propagation speed concept for non-relativistic quantum equations. It leads to local interpretation of non-relativistic quantum mechanics consistent with principle of locality and free of local hidden variables. The theory is applied to analysis of Einstein-Podolsky-Rosen (EPR) paradox, entanglement and properties of perturbed matter waves. We proved that formulated theory agrees with results of classical experiments on electron matter waves diffraction.