Wbrew wrażeniu jakie można odnieść z większości standardowych podręczników, równania falowe Diraca, Kleina-Gordona i inne nie są podstawą kwantowej teorii pola. W niniejszym artykule staram się pokazać, jak powinna być ona poprawnie formułowana i omawiam pewne jej aspekty, które na ogół nie są przedstawiane właściwie. Celem artykułu jest spowodowanie zmiany w nauczaniu kwantowej teorii pola. Tekst został podzielony na trzy części. W niniejszej części 3 (i ostatniej) omawiam przepis LSZ pozwalający wyznaczać elementy macierzy S i inne wielkości fizyczne bez czynienia zwykłych, bardzo restrykcyjnych założeń oraz zalety i słabości formułowania kwantowej teorii pola za pomocą całek po trajektoriach.
EN
Despite the impression that can be gained from most of the standard textbooks, Dirac, Klein-Gordon and other wave equations do not constitute the basis of quantum field theory. In this article I attempt to show how it should be formulated properly and discuss some of its aspects which usually are presented unsatisfactorily. The aim of the text is to cause the change in the way quantum field theory is taught. The text is split into three parts. In this part 3 (the last one) I discuss the LSZ prescription which allows to extract S-matrix elements without making the usual, very restrictive assumptions and advantages and weak sides of formulating quantum field theory with the help of path integrals.
Wbrew wrażeniu jakie można odnieść z lektury większości standardowych podręczników, równania falowe Diraca, Kleina-Gordona i inne nie są podstawą relatywistycznej kwantowej teorii pola. W niniejszym artykule staram się pokazać, jak powinna być ona poprawnie formułowana i omawiam pewne jej aspekty, które na ogół nie są przedstawiane właściwie. Moim celem jest spowodowanie zmiany w nauczaniu kwantowej teorii pola. Tekst został podzielony na trzy części. W pierwszej przypominam krótko historyczny rozwój kwantowej teorii pola i omawiam jej sformułowanie jako kwantowej teorii oddziałujących cząstek (relatywistycznych lub nierelatywistycznych).
EN
Despite the impression that can be gained from most of the standard textbooks, Dirac, Klein-Gordon and other wave equations do not constitute the basis of relativistic quantum field theory. In this article I attempt to show how it should be formulated properly and discuss some of its aspects which usually are presented unsatisfactorily. My aim is to cause the change in the way quantum field theory is taught. The text is split into three parts. In the first one I briefly recall the quantum field theory historical development and present its formulation as a quantum theory of interacting particles (relativistic or nonrelativistic).
Wbrew wrażeniu jakie można odnieść z lektury większości standardowych podręczników, równania falowe Diraca, Kleina-Gordona i inne nie są podstawą relatywistycznej kwantowej teorii pola. W niniejszym artykule staram się pokazać, jak powinna być ona poprawnie formułowana i omawiam pewne jej aspekty, które na ogół nie są przedstawiane właściwie. Moim celem jest spowodowanie zmiany w nauczaniu kwantowej teorii pola. Tekst został podzielony na trzy części. W niniejszej drugiej części omawiam sformułowanie kwantowej teorii pola jako teorii oddziałujących pól oraz sens fizyczny procedury renormalizacji.
EN
Despite the impression that can be gained from most of the standard textbooks, Dirac, Klein-Gordon and other wave equations do not constitute the basis of relativistic quantum field theory. In this article I attempt to show how it should be formulated properly and discuss some of its aspects which usually are presented unsatisfactorily. My aim is to cause the change in the way quantum field theory is taught. The text is split into three parts. In the second part I discuss the formulation of quantum field theory as a theory of interacting fields as well as the physical sense of the renormalization procedure.
In quantum field theory it is believed that the spontaneous decay of excited atomic or molecular level is due to the interaction with continuum of field modes. Besides, the atom makes a transition from upper level to lower one so that the probability to find the atom in the excited state tends to zero. In this paper it will be shown that the mathematical model in single-photon approximation may predict another behavior of this probability generally. Namely, the probability to find the atom in the excited state may tend to a nonzero constant so that the atom is not in the pure state finally. This effect is due to that the spectrum of the complete Hamiltonian is not purely absolutely continuous and has a discrete level outside the continuous part. Namely, we state that in the corresponding invariant subspace, determining the time evolution, the spectrum of the complete Hamiltonian when the field is considered in three dimensions may be not purely absolutely continuous and may have an eigenvalue. The appearance of eigenvalue has a threshold character. If the field is considered in two dimensions the spectrum always has an eigenvalue and the decay is absent.
In previous work of the author, a convolution and multiplication product for the set of Associated Homogeneous Distributions (AHDs) with support in ℝ was defined and fully investigated. Here this definition is used to calculate the multiplication product of homogeneous distributions of the form (x±i0)z, for all z∈C. Multiplication products of AHDs generally contain an arbitrary constant if the resulting degree of homogeneity is a negative integer, i.e., if it is a critical product. However, critical products of the forms (x+i0)a.(x+i0)b and (x−i0)a.(x−i0)b, with a+b∈Z−, are exceptionally unique. This fact combined with Sokhotskii–Plemelj expressions then leads to linear dependencies of the arbitrary constants occurring in products like δ(k).δ(l), η(k).δ(l), δ(k).η(l) and η(k).η(l) for all k,l∈N (η≜1πx−1). This in turn gives a unique distribution for products like δ(k).η(l)+η(k).δ(l) and δ(k).δ(l)−η(k).η(l). The latter two products are of interest in quantum field theory and appear for instance in products of the partial derivatives of the zero-mass two-point Wightman distribution.
A black-hole is an astronomical entity which possesses infinite density at its gravitational singularity or singular point. The capacity of a black-hole to completely rip-off an entire solar system without leaving any evidence is to be noted. A debate has been going on over the past few decades regarding the information storage in black-holes. The discovery of Hawking radiation, which predicts complete evaporation of mass violates unitarity ie. Conservation of probability and energy fails. Recent discoveries suggest that regular remnant of black-hole survives evaporation , as a result information of the object devoured can be contained. These remnants are grouped into embedded sub-manifolds. These manifolds are the result of a five-dimensional constant curvature bulk in space-time. Five-dimensional gravity can be recovered from brane-world resulting from equations of bulk geometry. Gravity can be explained by space-time theory and also quantum theory in the form of Gravitons. On observing the manifold, the gravitons show deformations in dimensions, rather than being constant. The perturbations in geometry can be related to embedding functions which should remain differentiable and regular. Regularity is related to the inverse functions theorem. Manifold observations followed by a mathematical approach can possibly retain information about objects devoured by the black-hole.
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