Physics 198-730B: Quantum Field Theory
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Asymptotic Freedom, Quark Confinement, Proton Spin Crisis, Neutron Structure, Dark Matters, and Relative Force Strengths
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 17 February 2021 doi:10.20944/preprints202102.0395.v1 Asymptotic freedom, quark confinement, proton spin crisis, neutron structure, dark matters, and relative force strengths Jae-Kwang Hwang JJJ Physics Laboratory, Brentwood, TN 37027 USA Abstract: The relative force strengths of the Coulomb forces, gravitational forces, dark matter forces, weak forces and strong forces are compared for the dark matters, leptons, quarks, and normal matters (p and n baryons) in terms of the 3-D quantized space model. The quark confinement and asymptotic freedom are explained by the CC merging to the A(CC=-5)3 state. The proton with the (EC,LC,CC) charge configuration of p(1,0,-5) is p(1,0) + A(CC=-5)3. The A(CC=-5)3 state has the 99.6% of the proton mass. The three quarks in p(1,0,-5) are asymptotically free in the EC and LC space of p(1,0) and are strongly confined in the CC space of A(CC=-5)3. This means that the lepton beams in the deep inelastic scattering interact with three quarks in p(1,0) by the EC interaction and weak interaction. Then, the observed spin is the partial spin of p(1,0) which is 32.6 % of the total spin (1/2) of the proton. The A(CC=-5)3 state has the 67.4 % of the proton spin. This explains the proton spin crisis. The EC charge distribution of the proton is the same to the EC charge distribution of p(1,0) which indicates that three quarks in p(1,0) are mostly near the proton surface. -
An Introduction to Quantum Field Theory
AN INTRODUCTION TO QUANTUM FIELD THEORY By Dr M Dasgupta University of Manchester Lecture presented at the School for Experimental High Energy Physics Students Somerville College, Oxford, September 2009 - 1 - - 2 - Contents 0 Prologue....................................................................................................... 5 1 Introduction ................................................................................................ 6 1.1 Lagrangian formalism in classical mechanics......................................... 6 1.2 Quantum mechanics................................................................................... 8 1.3 The Schrödinger picture........................................................................... 10 1.4 The Heisenberg picture............................................................................ 11 1.5 The quantum mechanical harmonic oscillator ..................................... 12 Problems .............................................................................................................. 13 2 Classical Field Theory............................................................................. 14 2.1 From N-point mechanics to field theory ............................................... 14 2.2 Relativistic field theory ............................................................................ 15 2.3 Action for a scalar field ............................................................................ 15 2.4 Plane wave solution to the Klein-Gordon equation ........................... -
2-Loop $\Beta $ Function for Non-Hermitian PT Symmetric $\Iota
2-Loop β Function for Non-Hermitian PT Symmetric ιgφ3 Theory Aditya Dwivedi1 and Bhabani Prasad Mandal2 Department of Physics, Institute of Science, Banaras Hindu University Varanasi-221005 INDIA Abstract We investigate Non-Hermitian quantum field theoretic model with ιgφ3 interaction in 6 dimension. Such a model is PT-symmetric for the pseudo scalar field φ. We analytically calculate the 2-loop β function and analyse the system using renormalization group technique. Behavior of the system is studied near the different fixed points. Unlike gφ3 theory in 6 dimension ιgφ3 theory develops a new non trivial fixed point which is energetically stable. 1 Introduction Over the past two decades a new field with combined Parity(P)-Time rever- sal(T) symmetric non-Hermitian systems has emerged and has been one of the most exciting topics in frontier research. It has been shown that such theories can lead to the consistent quantum theories with real spectrum, unitary time evolution and probabilistic interpretation in a different Hilbert space equipped with a positive definite inner product [1]-[3]. The huge success of such non- Hermitian systems has lead to extension to many other branches of physics and interdisciplinary areas. The novel idea of such theories have been applied in arXiv:1912.07595v1 [hep-th] 14 Dec 2019 numerous systems leading huge number of application [4]-[21]. Several PT symmetric non-Hermitian models in quantum field theory have also been studied in various context [16]-[26]. Deconfinment to confinment tran- sition is realised by PT phase transition in QCD model using natural but uncon- ventional hermitian property of the ghost fields [16]. -
The Lamb Shift Experiment in Muonic Hydrogen
The Lamb Shift Experiment in Muonic Hydrogen Dissertation submitted to the Physics Faculty of the Ludwig{Maximilians{University Munich by Aldo Sady Antognini from Bellinzona, Switzerland Munich, November 2005 1st Referee : Prof. Dr. Theodor W. H¨ansch 2nd Referee : Prof. Dr. Dietrich Habs Date of the Oral Examination : December 21, 2005 Even if I don't think, I am. Itsuo Tsuda Je suis ou` je ne pense pas, je pense ou` je ne suis pas. Jacques Lacan A mia mamma e mio papa` con tanto amore Abstract The subject of this thesis is the muonic hydrogen (µ−p) Lamb shift experiment being performed at the Paul Scherrer Institute, Switzerland. Its goal is to measure the 2S 2P − energy difference in µp atoms by laser spectroscopy and to deduce the proton root{mean{ −3 square (rms) charge radius rp with 10 precision, an order of magnitude better than presently known. This would make it possible to test bound{state quantum electrody- namics (QED) in hydrogen at the relative accuracy level of 10−7, and will lead to an improvement in the determination of the Rydberg constant by more than a factor of seven. Moreover it will represent a benchmark for QCD theories. The experiment is based on the measurement of the energy difference between the F=1 F=2 2S1=2 and 2P3=2 levels in µp atoms to a precision of 30 ppm, using a pulsed laser tunable at wavelengths around 6 µm. Negative muons from a unique low{energy muon beam are −1 stopped at a rate of 70 s in 0.6 hPa of H2 gas. -
Effective Quantum Field Theories Thomas Mannel Theoretical Physics I (Particle Physics) University of Siegen, Siegen, Germany
Generating Functionals Functional Integration Renormalization Introduction to Effective Quantum Field Theories Thomas Mannel Theoretical Physics I (Particle Physics) University of Siegen, Siegen, Germany 2nd Autumn School on High Energy Physics and Quantum Field Theory Yerevan, Armenia, 6-10 October, 2014 T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Overview Lecture 1: Basics of Quantum Field Theory Generating Functionals Functional Integration Perturbation Theory Renormalization Lecture 2: Effective Field Thoeries Effective Actions Effective Lagrangians Identifying relevant degrees of freedom Renormalization and Renormalization Group T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Lecture 3: Examples @ work From Standard Model to Fermi Theory From QCD to Heavy Quark Effective Theory From QCD to Chiral Perturbation Theory From New Physics to the Standard Model Lecture 4: Limitations: When Effective Field Theories become ineffective Dispersion theory and effective field theory Bound Systems of Quarks and anomalous thresholds When quarks are needed in QCD É. T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Lecture 1: Basics of Quantum Field Theory Thomas Mannel Theoretische Physik I, Universität Siegen f q f et Yerevan, October 2014 T. Mannel, Siegen University Effective Quantum -
External Fields and Measuring Radiative Corrections
Quantum Electrodynamics (QED), Winter 2015/16 Radiative corrections External fields and measuring radiative corrections We now briefly describe how the radiative corrections Πc(k), Σc(p) and Λc(p1; p2), the finite parts of the loop diagrams which enter in renormalization, lead to observable effects. We will consider the two classic cases: the correction to the electron magnetic moment and the Lamb shift. Both are measured using a background electric or magnetic field. Calculating amplitudes in this situation requires a modified perturbative expansion of QED from the one we have considered thus far. Feynman rules with external fields An important approximation in QED is where one has a large background electromagnetic field. This external field can effectively be treated as a classical background in which we quantise the fermions (in analogy to including an electromagnetic field in the Schrodinger¨ equation). More formally we can always expand the field operators around a non-zero value (e) Aµ = aµ + Aµ (e) where Aµ is a c-number giving the external field and aµ is the field operator describing the fluctua- tions. The S-matrix is then given by R 4 ¯ (e) S = T eie d x : (a=+A= ) : For a static external field (independent of time) we have the Fourier transform representation Z (e) 3 ik·x (e) Aµ (x) = d= k e Aµ (k) We can now consider scattering processes such as an electron interacting with the background field. We find a non-zero amplitude even at first order in the perturbation expansion. (Without a background field such terms are excluded by energy-momentum conservation.) We have Z (1) 0 0 4 (e) hfj S jii = ie p ; s d x : ¯A= : jp; si Z 4 (e) 0 0 ¯− µ + = ie d x Aµ (x) p ; s (x)γ (x) jp; si Z Z 4 3 (e) 0 µ ik·x+ip0·x−ip·x = ie d x d= k Aµ (k)u ¯s0 (p )γ us(p) e ≡ 2πδ(E0 − E)M where 0 (e) 0 M = ieu¯s0 (p )A= (p − p)us(p) We see that energy is conserved in the scattering (since the external field is static) but in general the initial and final 3-momenta of the electron can be different. -
Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
Hep-Th/9609099V1 11 Sep 1996 ⋆ † Eerhspotdi Atb O Rn DE-FG02-90ER40542
IASSNS 96/95 hep-th/9609099 September 1996 ⋆ Asymptotic Freedom Frank Wilczek† School of Natural Sciences Institute for Advanced Study Olden Lane Princeton, N.J. 08540 arXiv:hep-th/9609099v1 11 Sep 1996 ⋆ Lecture on receipt of the Dirac medal for 1994, October 1994. Research supported in part by DOE grant DE-FG02-90ER40542. [email protected] † ABSTRACT I discuss how the basic phenomenon of asymptotic freedom in QCD can be un- derstood in elementary physical terms. Similarly, I discuss how the long-predicted phenomenon of “gluonization of the proton” – recently spectacularly confirmed at HERA – is a rather direct manifestation of the physics of asymptotic freedom. I review the broader significance of asymptotic freedom in QCD in fundamental physics: how on the one hand it guides the interpretation and now even the design of experiments, and how on the other it makes possible a rational, quantitative theoretical approach to problems of unification and early universe cosmology. 2 I am very pleased to accept your award today. On this occasion I think it is appropriate to discuss with you the circle of ideas around asymptotic freedom. After a few remarks about its setting in intellectual history, I will begin by ex- plaining the physical origin of asymptotic freedom in QCD; then I will show how a recent, spectacular experimental observation – the ‘gluonization’ of the proton – both confirms and illuminates its essential nature; then I will discuss some of its broader implications for fundamental physics. It may be difficult for young people who missed experiencing it, or older people with fading memories, fully to imagine the intellectual atmosphere surrounding the strong interaction in the 1960s and early 1970s. -
Lecture Notes Particle Physics II Quantum Chromo Dynamics 6
Lecture notes Particle Physics II Quantum Chromo Dynamics 6. Feynman rules and colour factors Michiel Botje Nikhef, Science Park, Amsterdam December 7, 2012 Colour space We have seen that quarks come in three colours i = (r; g; b) so • that the wave function can be written as (s) µ ci uf (p ) incoming quark 8 (s) µ ciy u¯f (p ) outgoing quark i = > > (s) µ > cy v¯ (p ) incoming antiquark <> i f c v(s)(pµ) outgoing antiquark > i f > Expressions for the> 4-component spinors u and v can be found in :> Griffiths p.233{4. We have here explicitly indicated the Lorentz index µ = (0; 1; 2; 3), the spin index s = (1; 2) = (up; down) and the flavour index f = (d; u; s; c; b; t). To not overburden the notation we will suppress these indices in the following. The colour index i is taken care of by defining the following basis • vectors in colour space 1 0 0 c r = 0 ; c g = 1 ; c b = 0 ; 0 1 0 1 0 1 0 0 1 @ A @ A @ A for red, green and blue, respectively. The Hermitian conjugates ciy are just the corresponding row vectors. A colour transition like r g can now be described as an • ! SU(3) matrix operation in colour space. Recalling the SU(3) step operators (page 1{25 and Exercise 1.8d) we may write 0 0 0 0 1 cg = (λ1 iλ2) cr or, in full, 1 = 1 0 0 0 − 0 1 0 1 0 1 0 0 0 0 0 @ A @ A @ A 6{3 From the Lagrangian to Feynman graphs Here is QCD Lagrangian with all colour indices shown.29 • µ 1 µν a a µ a QCD = (iγ @µ m) i F F gs λ j γ A L i − − 4 a µν − i ij µ µν µ ν ν µ µ ν F = @ A @ A 2gs fabcA A a a − a − b c We have introduced here a second colour index a = (1;:::; 8) to label the gluon fields and the corresponding SU(3) generators. -
Coupling Constant Unification in Extensions of Standard Model
Coupling Constant Unification in Extensions of Standard Model Ling-Fong Li, and Feng Wu Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 May 28, 2018 Abstract Unification of electromagnetic, weak, and strong coupling con- stants is studied in the extension of standard model with additional fermions and scalars. It is remarkable that this unification in the su- persymmetric extension of standard model yields a value of Weinberg angle which agrees very well with experiments. We discuss the other possibilities which can also give same result. One of the attractive features of the Grand Unified Theory is the con- arXiv:hep-ph/0304238v2 3 Jun 2003 vergence of the electromagnetic, weak and strong coupling constants at high energies and the prediction of the Weinberg angle[1],[3]. This lends a strong support to the supersymmetric extension of the Standard Model. This is because the Standard Model without the supersymmetry, the extrapolation of 3 coupling constants from the values measured at low energies to unifi- cation scale do not intercept at a single point while in the supersymmetric extension, the presence of additional particles, produces the convergence of coupling constants elegantly[4], or equivalently the prediction of the Wein- berg angle agrees with the experimental measurement very well[5]. This has become one of the cornerstone for believing the supersymmetric Standard 1 Model and the experimental search for the supersymmetry will be one of the main focus in the next round of new accelerators. In this paper we will explore the general possibilities of getting coupling constants unification by adding extra particles to the Standard Model[2] to see how unique is the Supersymmetric Standard Model in this respect[?]. -
Large-Deviation Principles, Stochastic Effective Actions, Path Entropies
Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions Eric Smith Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA (Dated: February 18, 2011) The meaning of thermodynamic descriptions is found in large-deviations scaling [1, 2] of the prob- abilities for fluctuations of averaged quantities. The central function expressing large-deviations scaling is the entropy, which is the basis for both fluctuation theorems and for characterizing the thermodynamic interactions of systems. Freidlin-Wentzell theory [3] provides a quite general for- mulation of large-deviations scaling for non-equilibrium stochastic processes, through a remarkable representation in terms of a Hamiltonian dynamical system. A number of related methods now exist to construct the Freidlin-Wentzell Hamiltonian for many kinds of stochastic processes; one method due to Doi [4, 5] and Peliti [6, 7], appropriate to integer counting statistics, is widely used in reaction-diffusion theory. Using these tools together with a path-entropy method due to Jaynes [8], this review shows how to construct entropy functions that both express large-deviations scaling of fluctuations, and describe system-environment interactions, for discrete stochastic processes either at or away from equilibrium. A collection of variational methods familiar within quantum field theory, but less commonly applied to the Doi-Peliti construction, is used to define a “stochastic effective action”, which is the large-deviations rate function for arbitrary non-equilibrium paths. We show how common principles of entropy maximization, applied to different ensembles of states or of histories, lead to different entropy functions and different sets of thermodynamic state variables. -
Casimir Effect Mechanism of Pairing Between Fermions in the Vicinity of A
Casimir effect mechanism of pairing between fermions in the vicinity of a magnetic quantum critical point Yaroslav A. Kharkov1 and Oleg P. Sushkov1 1School of Physics, University of New South Wales, Sydney 2052, Australia We consider two immobile spin 1/2 fermions in a two-dimensional magnetic system that is close to the O(3) magnetic quantum critical point (QCP) which separates magnetically ordered and disordered phases. Focusing on the disordered phase in the vicinity of the QCP, we demonstrate that the criticality results in a strong long range attraction between the fermions, with potential V (r) 1/rν , ν 0.75, where r is separation between the fermions. The mechanism of the enhanced∝ − attraction≈ is similar to Casimir effect and corresponds to multi-magnon exchange processes between the fermions. While we consider a model system, the problem is originally motivated by recent establishment of magnetic QCP in hole doped cuprates under the superconducting dome at doping of about 10%. We suggest the mechanism of magnetic critical enhancement of pairing in cuprates. PACS numbers: 74.40.Kb, 75.50.Ee, 74.20.Mn I. INTRODUCTION in the frame of normal Fermi liquid picture (large Fermi surface). Within this approach electrons interact via ex- change of an antiferromagnetic (AF) fluctuation (param- In the present paper we study interaction between 11 fermions mediated by magnetic fluctuations in a vicin- agnon). The lightly doped AF Mott insulator approach, ity of magnetic quantum critical point. To address this instead, necessarily implies small Fermi surface. In this case holes interact/pair via exchange of the Goldstone generic problem we consider a specific model of two holes 12 injected into the bilayer antiferromagnet.