Nevertheless, many discussions about the klein paradox are based upon singleparticle dirac equation in quantum mechanics rather than quantum field method. Pair production 270 comments on relativistic quantum field theory 272 2. Let us consider a square potential with height v 0 0 of the type showed in fig. Barrier scattering in field theory removal of klein paradox. In 1929, physicist oskar klein obtained a surprising result by applying the dirac equation to the familiar problem of electron scattering from a potential barrier. Browse other questions tagged quantumfieldtheory kleingordonequation classicalfieldtheory or ask your own question. Both the kleingordon and the dirac equation are no 1particle waveequations, but relativistic. Excellent lecture notes available online include a. Klein paradox 264 explanation 268 phonon model revisited 268 back to the step potential 270 relativistic quantum field theory.
For spinless bosons described by the klein gordon equation, this picture seems satisfactory. All three of them oftentimes take an approach di erent to the one of this course. Solution of dirac equation for a step potential and the. The guiding principle in choosing the topics presented apart to serve as introductions to later. Quantum theory for the perplexed is an exclusively rare and inspirational book on quantum mechanics that explores the neverending mysterious quantum paradoxes to bring the readers to the quantumwonderland.
The paradox presented a quantum mechanical objection to the notion of an electron confined within a nucleus. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. In many respects similar to the older, cheaper, itzykson and zuber. In physics, kaluzaklein theory kk theory is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time and considered an important precursor to string theory. The einstein unified field theory completed a direct challenge to the basic assumptions, theories and direction of modern and postmodern physics james e. The vector space sr n with the natural topol gyo given by the seminorms kk.
In quantum field theory, the paradox is resolved by the notion of pair creation by the external potential hund. A solution to the wave equation in regions i and ii is given by. However, we choose a different approach, namely the relativistic quantum hamiltonjacobi equations and the resultant quantum states. Although a cursory acquaitance with th subject of quantum field theory is helpful, the only requirement to follow the lectures it is a working knowledge of quantum mechanics and special relativity. They seem to neglect the fact that negative kinetic energy wave packets move in a. In nonrelativistic quantum mechanics, electron tunneling into a barrier is.
A complete treatment of the problem requires as far as i know a fully quantum. Inpart ii we turn to the underlying physics of the klein paradox and show that particle production. Introduction to the klein paradox es seventy years ago klein 1 published a paper where he calculated the re. The description of such a process as occurring in the course of time is just as unreal as classical paths are in nonrelativistic quantum mechanics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic selfinteractions. However, kleins result showed that if the potential is of the order of the electron mass. The topics range from the ising model, majorana fermions, the renormalization group, and the quantum hall effect. Northholland publishing company barrier scattering in field theory removal of klein paradox a. The topological dual 4 s0r n of sr n is alcled the space of temerpde distributions. Fall 2008 department of physics and astronomy, the university of tennessee at knoxville, 37996. Relativistic quantum mechanics kleingordon equation. Free quantum field theory books download ebooks online. The feynman method of the green function in quantum electrodynamics is modified to treat.
According to bohr, the klein paradox results from an unlimited mathematical application of the concept of potential or more generally of field in relativistic. The topics covered include normalmode expansions for a general elliptic operator, fock space, the casimir effect, the klein paradox, particle definition and particle creation in expanding universes, asymptotic expansion of greens functions. The golden ring to which most physicists aspire is a unified field theory. Quantum field theory lingfong li institute chapter 1 introduction 1 37. However, klein s result showed that if the potential is of the order of the electron mass. The fivedimensional 5d theory developed in three steps. Aspects of quantum field theory in curved spacetime by. Kleins paradox and quantum hamiltonian dynamics in. In this paper, along with previous investigation in payandeh et al.
Quantum simulation of the klein paradox quantum optics. The book has quantum field theory in the title, and i think the reader should ideally have taken quantum field theory before trying to tackle this book. The feynman method of the green function in quantum electrodynamics is modified to treat scattering problems with a onedimensional potential. Introduction to the klein paradoxes seventy years ago klein 1 published a paper where he calculated the re. Quantum algorithms for quantum field theories science. In the last few years the physics behind kleins paradox. He concentrated on charged scalar elds rather than spinor elds. Quantum simulation of the klein paradox quantum optics and.
Bjorken and drell treat the klein paradox in the first volume of their course on relativistic quantum field theory as a problem of the single particle equation 14. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Virtual beams and the klein paradox for the kleingordon equation. Pdf quantum simulation of the klein paradox with trapped. Paulis approach 274 using 2 x 2 matrices 275 pauli equation. A eld of a classical eld theory, such as electromagnetism. Nov 03, 2016 in quantum sans strong gravity the paradox is always physical, i. Request pdf klein paradox with spinresolved electrons and positrons using numerical solutions to relativistic quantum field theory with spacetime resolution, we. Klein paradox with spinresolved electrons and positrons. Recommended relativistic quantum mechanics and introduction to quantum field. Download book pdf relativistic quantum mechanics pp 261267 cite as.
Even when energy is inadequate for real pair creation, pair states can appear in 2nd order perturbation theory so long as e t pdf klein paradox with spinresolved electrons and positrons using numerical solutions to relativistic quantum field theory with spacetime resolution, we illustrate how an incoming. Vacuum expectation values of the current and momentum operators are calculated for both massive spin zero and massive spin onehalf fields. Kleins paradox and its resolution alex hansen and finn. Modern quantum field theory, cambridge 2008 as further reading. C 37, 1103 20, we will use the full set of free diracs solutions to remove the kleins paradox. It resulted from the analysis of dirac equation for a particle that is subject to a onedimensional impulsive repulsive force, and the epithet paradox was given because the solution was in discord with anything that the intuition would have expected. This result can only be understood in terms of particle creation at sudden potential step. System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. Although the dirac equation represents a paradigm for modern field. Mathematical aspects of quantum field theory michael keyl fu berlin 1 march 8, 2018 block course on mathematical aspects of quantum field theory held at lmu physics. The paradox was later resolved in quantum field theory by the notion of particleanti particle creation at the barrier. Schroeder, an introduction to quantum field theory this is a very clear and comprehensive book, covering everything in this course at the right level.
The meaning of this paradox was intensely debated at the time. In quantum sans strong gravity the paradox is always physical, i. This weird situation, called kleins paradox, can be understood in terms of pair creation. The topics covered include normalmode expansions for a general elliptic operator, fock space, the casimir effect, the klein paradox, particle definition and particle creation in expanding universes, asymptotic expansion of greens functions and heat kernels, and renormalisation of the stress tensor. Kleins paradox is resolved in simple diagrammatic terms arising from considerations of its analogue in classical relativistic mechanics. At both the universities the course is covered over a period of one year or two semesters at the final year m. Bjorken and drell you read that the paradox is resolved by considering the production of particleantiparticle pairs at the potential step which can be naturally incorporated in quantum field theory. Klein paradox and graphene strings and quantum gravity. I, on a course on quantum mechanics and quantum field theory that the author taught for many years, starling with 1967, at kurukshetra university and later at the university of calicut. In physics, kaluzaklein theory kk theory is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time and considered an important precursor to string theory the fivedimensional 5d theory developed in three steps. The original hypothesis came from theodor kaluza, who sent his. Introduction in the last few years the physics behind kleins paradox 1 has.
It will also cover everything in the advanced quantum field theory course, much of the standard model course, and will serve you well if you go on to do research. The same results are also obtained directly from standard operator methods of quantum field theory. Weinberg, the quantum theory of fields, vol 1 this is the rst in a three volume series by one of the masters of quantum eld theory. Relativistic quantum field theory is a mathematical scheme to describe the subatomic particles and forces. Quantum simulation of the klein paradox with trapped ions.
The basic starting point is that the axioms of special relativity on the one hand and those of quantum mechanics on the other, should be combined into one theory. Quantum field theory with local symmetry gauge principle. Relativistic quantum physics from advanced quantum. Thus the physics of the kleingordon equation, treated as a wave equation, is inconsistent. Quantum field theory sunil mukhi serc preparatory school, goa, octnov 2010 contents 1 scalar. Solution of dirac equation for a step potential and the klein. Here, a the term \ eld refers to one of the following. In this part, in the rst three chapters i write about scalar elds, elds with spin, and nonabelian elds. The effect that is known as the klein paradox 1, 2 1 is one of the cornerstones in the development of relativistic quantum mechanics. For spinless bosons described by the kleingordon equation, this picture seems satisfactory. There is a vast array of further quantum field theory texts, many of them with redeeming features.
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. It resulted from the analysis of dirac equation for a particle that is subject to a onedimensional impulsive repulsive force, and the epithet paradox was given because the solution was in discord with anything that the intuition would. Preversion done and proofread by rederikf vom ende tu munich 2 1 mail adress. Quantum field theory i chapter 0 eth zurich, hs14 prof. This clear and precise paradox suggested that an electron could not be confined within a nucleus by any potential well. The fact that we call quantum paradoxical is a testament to a its awesome predictive power and explanatory. The classic klein paradox, particle creation due to the presence of very strong electromagnetic potentials, is reconsidered. Pdf on the kleins paradox in the presence of a scalar potential. While the paradox is a much debated topic, which in part is due to its emergence in graphene 5, direct investigations of the phenomena have yet to be realised due to the immense experimental difficulties involved enormous. Kleingordon equation with electromagnetic field within a nonrelativistic theory the electromagnetic eld is described by a scalar potential x. The klein paradox is commonly solved for the case of the dirac equation within the framework of quantum field theory qft. The second part is dedicated to topological field theories.
Amazon sells an electronic version too, for about the same price. Klein paradox to illustrate this feature we will study kleins paradox in the context of the kleingordon equation given by 2 t2 r 2 m2 yx,t 0 let us consider a square potential with height v0 0 as shown in the gure, institute chapter 1 introduction 4 37. In our view, however, a successful resolution of the paradox must come about from within the framework of oneparticle relativistic quantum mechanics where the paradox was originally posed. The following chapters are dedicated to quantum electrodynamics and quantum chromodynamics, followed by the renormalization theory.
Lebedev physical institute, leninsky prospect 53, moscow, ussr received 29 december 1969 abstract. The main problem in quantum field theory is to determine the probability amplitudes be. Aug 20, 2006 the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and counterintuitive consequences of quantum. The theory will not give an observable meaning to the time dependence of interaction processes. Kleins paradox and its resolution iopscience institute of physics. Chiral tunnelling and the klein paradox in graphene nature. This book i do believe should be recommended to everyone.