# Quantum Field Theory*

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• Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay.
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• 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 ...........................
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• Fundamentals of Particle Physics
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• Introduction to Particle Physics
SFB 676 – Projekt B2 Introduction to Particle Physics Christian Sander (Universität Hamburg) DESY Summer Student Lectures – Hamburg – 20th July '11 Outline ● Introduction ● History: From Democrit to Thomson ● The Standard Model ● Gauge Invariance ● The Higgs Mechanism ● Symmetries … Break ● Shortcomings of the Standard Model ● Physics Beyond the Standard Model ● Recent Results from the LHC ● Outlook Disclaimer: Very personal selection of topics and for sure many important things are left out! 20th July '11 Introduction to Particle Physics 2 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 233 … für Chester war das nur ein Weg das Geld für das eigentlich theoretische Zeugs aufzubringen, was ihn interessierte … die Erforschung Dunkler Materie, …ähm… Quantenpartikel, Neutrinos, Gluonen, Mesonen und Quarks. Subatomare Teilchen Die Geheimnisse des Universums! Theoretisch gesehen sind sie sogar die Bausteine der Wirklichkeit ! Aber niemand weiß, ob sie wirklich existieren !? 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 234 The First Particle Physicist? By convention ['nomos'] sweet is sweet, bitter is bitter, hot is hot, cold is cold, color is color; but in truth there are only atoms and the void. Democrit, * ~460 BC, †~360 BC in Abdera Hypothesis: ● Atoms have same constituents ● Atoms different in shape (assumption: geometrical shapes) ● Iron atoms are solid and strong with hooks that lock them into a solid ● Water atoms are smooth and slippery ● Salt atoms, because of their taste, are sharp and pointed ● Air atoms are light and whirling, pervading all other materials 20th July '11 Introduction to Particle Physics 5 Corpuscular Theory of Light Light consist out of particles (Newton et al.) ↕ Light is a wave (Huygens et al.) ● Mainly because of Newtons prestige, the corpuscle theory was widely accepted (more than 100 years) Sir Isaac Newton ● Failing to describe interference, diffraction, and *1643, †1727 polarization (e.g.
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• Configuration Interaction Study of the Ground State of the Carbon Atom
Configuration Interaction Study of the Ground State of the Carbon Atom María Belén Ruiz* and Robert Tröger Department of Theoretical Chemistry Friedrich-Alexander-University Erlangen-Nürnberg Egerlandstraße 3, 91054 Erlangen, Germany In print in Advances Quantum Chemistry Vol. 76: Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems 30th July 2017 Abstract Configuration Interaction (CI) calculations on the ground state of the C atom are carried out using a small basis set of Slater orbitals [7s6p5d4f3g]. The configurations are selected according to their contribution to the total energy. One set of exponents is optimized for the whole expansion. Using some computational techniques to increase efficiency, our computer program is able to perform partially-parallelized runs of 1000 configuration term functions within a few minutes. With the optimized computer programme we were able to test a large number of configuration types and chose the most important ones. The energy of the 3P ground state of carbon atom with a wave function of angular momentum L=1 and ML=0 and spin eigenfunction with S=1 and MS=0 leads to -37.83526523 h, which is millihartree accurate. We discuss the state of the art in the determination of the ground state of the carbon atom and give an outlook about the complex spectra of this atom and its low-lying states. Keywords: Carbon atom; Configuration Interaction; Slater orbitals; Ground state *Corresponding author: e-mail address: [email protected] 1 1. Introduction The spectrum of the isolated carbon atom is the most complex one among the light atoms. The ground state of carbon atom is a triplet 3P state and its low-lying excited states are singlet 1D, 1S and 1P states, more stable than the corresponding triplet excited ones 3D and 3S, against the Hund’s rule of maximal multiplicity.
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• Feynman Diagrams, Momentum Space Feynman Rules, Disconnected Diagrams, Higher Correlation Functions
PHY646 - Quantum Field Theory and the Standard Model Even Term 2020 Dr. Anosh Joseph, IISER Mohali LECTURE 05 Tuesday, January 14, 2020 Topics: Feynman Diagrams, Momentum Space Feynman Rules, Disconnected Diagrams, Higher Correlation Functions. Feynman Diagrams We can use the Wick’s theorem to express the n-point function h0jT fφ(x1)φ(x2) ··· φ(xn)gj0i as a sum of products of Feynman propagators. We will be interested in developing a diagrammatic interpretation of such expressions. Let us look at the expression containing four ﬁelds. We have h0jT fφ1φ2φ3φ4g j0i = DF (x1 − x2)DF (x3 − x4) +DF (x1 − x3)DF (x2 − x4) +DF (x1 − x4)DF (x2 − x3): (1) We can interpret Eq. (1) as the sum of three diagrams, if we represent each of the points, x1 through x4 by a dot, and each factor DF (x − y) by a line joining x to y. These diagrams are called Feynman diagrams. In Fig. 1 we provide the diagrammatic interpretation of Eq. (1). The interpretation of the diagrams is the following: particles are created at two spacetime points, each propagates to one of the other points, and then they are annihilated. This process can happen in three diﬀerent ways, and they correspond to the three ways to connect the points in pairs, as shown in the three diagrams in Fig. 1. Thus the total amplitude for the process is the sum of these three diagrams. PHY646 - Quantum Field Theory and the Standard Model Even Term 2020 ⟨0|T {ϕ1ϕ2ϕ3ϕ4}|0⟩ = DF(x1 − x2)DF(x3 − x4) + DF(x1 − x3)DF(x2 − x4) +DF(x1 − x4)DF(x2 − x3) 1 2 1 2 1 2 + + 3 4 3 4 3 4 Figure 1: Diagrammatic interpretation of Eq.
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• Effective Field Theories, Reductionism and Scientific Explanation Stephan
To appear in: Studies in History and Philosophy of Modern Physics Eﬀective Field Theories, Reductionism and Scientiﬁc Explanation Stephan Hartmann∗ Abstract Eﬀective ﬁeld theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that eﬀec- tive ﬁeld theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, ﬂexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the speciﬁc mechanisms at work at a given energy scale. So will all of physics eventually converge on eﬀective ﬁeld theories? This paper argues that good scientiﬁc research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and eﬀective ﬁeld theories. All of them have their appropriate functions in the research process, and all of them are indispens- able. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientiﬁc theorising is inherently pluralistic, and has implications for the debates about reductionism and scientiﬁc explanation. Keywords: Eﬀective Field Theory; Quantum Field Theory; Renormalisation; Reductionism; Explanation; Pluralism. ∗Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pitts- burgh, PA 15260, USA (e-mail: [email protected]) (correspondence address); and Sektion Physik, Universit¨at M¨unchen, Theresienstr. 37, 80333 M¨unchen, Germany. 1 1 Introduction There is little doubt that eﬀective ﬁeld theories are nowadays a very popular tool in quantum physics.
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• Electromagnetic Field Theory