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Salam-The Physicist Salam-the physicist November 21, 2012 Salam-the physicist Modern Physics: 1900-1940s Black body radiation: 2 dρ ≈ ν dν (Classically) 3 ν dν 0 dρ ≈ (Planck s result) eβν − 1 Energy is quantized! ⇒ Quantum theory Salam-the physicist Michelson-Morley experiment ⇓ Einsten’s special theory of relativity (1905) Time dilation, length contraction Salam-the physicist 2 E = m c Salam-the physicist Einstein’s general theory of relativity (1915) Gravity is the curvature of spacetime! Salam-the physicist Electron, Proton, Neutron, Muon, Photon Electromagnetic force (mediated by photon) Strong Nuclear force (keeps the protons in the nucleus, thought to be mediated by mesons) Salam-the physicist Schr¨odinger’s non-relativistic equation to Dirac Equation 2 ∂ψ ~ 2 i~ = − ∇ + V ψ ∂t 2m ↓ ∂ψ i~ = i~ ~α · ∇~ + V ψ ∂t Dirac equation predicted the existence of the antiparticle of electron Positron was found in 1932 Beginning of Quantum Field Theory (which can deal with arbitrary number of particles and antiparticles at the same time) Salam-the physicist The theory of light and matter (Photons and electrons/positrons): Quantum Electrodynamics 1 2 L = ψ¯ i6∂ − m ψ − F − eψ¯6A ψ 4 interaction electrons/positrons photons | {z } |{z} | {z } Salam-the physicist Probability of such processes ∼ ∞ Salam-the physicist p − k pk p 4 m Σ(p) d k Z k2(k − p)2 Correction to the mass of the electron: m 7→ m + δm Λ2 δm ∼ log 2 m Mass renormalization mphy = m + δm Breakdown of the theory? Salam-the physicist Renormalization of QED Freeman Dyson Salam-the physicist Overlapping divergences Salam-the physicist PHYSICAL REVIEW VOLUM E 82, NUM B ER 2 APRIL 15. i9$1 Overlapping Divergences anti the S-Matrix AaDUs SCRAM SI. Jobe's College, Cambridge, England {Received September 29, 1950) By extending considerations given by Dyson, general rules are obtained for isolating divergent parts from integrals corresponding to overlapping graphs, and a proof is obtained for the appearance of an extra factor ZI I from "b divergences. " In the last section the possibility of renormalization for scalar meson- nucleon interactions is demonstrated. L INTRODUCTION vertex u or b of Fig. 1. Here N his treatment of spinor electrodynamics Dyson' - ~ has de6ned operators A„, Z*, and II* corresponding Z (W2q p) o dtldtoFo(pi ti)Geo(pq tl) to)Hv(p) to)) (1) to the three types of primitive divergent graphs in the theory. In the calculation of the contribution to F„ where 1 — —o. arising from a reducible vertex part Vg it is possible to iy(p ti) F ti)= —V. break down unambiguously into an irreducible (p Vg tio (p —t,)'+ ~o vertex part plus various inserted self-energy (5) and vertex (V) parts. The divergences introduced by the zy(p ti to)— — latter can be removed in a well-dehned manner because G„„(p,ti, to) = 7„7„,—ti —to)'+ 2 any two of the insertions made in Vz are either com- (p pletely non-overlapping or else are so arranged that one iy(p t ) «—1— is completely contained in the other. This procedure H.(p, to) = fails, however, in the calculation of the contributions (p —to)'+ o' to' to Z* or II* from reducible self-energy graphs. Con- Not only is the double integral over t&t2 linearly diver- sidering, for example, the electron self-energy, there is gent, but it also diverges logarithmically if the integra- just one irreducible graph W, (Fig. 1). V parts inserted tion is performed over either tj or t2, while the other at one of the two end vertices u or b appear simultane- variable is held fixed. In order to isolate these diver- ously as vertex insertions at the other vertex. Corre- gences, we use (here and in the subsequent work) the spondingly, the contribution to Z* arising from a invariant separation procedure outlined in Sec. VI of reducible part 8'g is, in general, an integral which D involves divergences corresponding to each of the ways II. Rewrite as follows: in which 8'z might have been built up by insertion of Eq. (1) V parts at either or both vertices of lV~. Dyson has =o called these "b-divergences" and their expected effect z(Wog p) J J dtldtzLFo(p) tl)Gyo(p) tiq tz)Hy(pq tz) is appearance of an extra factor Zi ' in his Eqs. (88) and (89). In order to demonstrate the possibility of Fo(po ti)Go(p—o ti 0)& (P t) renormalization, it is vital that this factor should appear; and it is the purpose of this paper to attempt a F„(P,ti)G„„(po—, 0, to)P„(po, tz) 7 formal proof. The considerations presented here throw some on the of renormalization for ~' light prospects +e'~ dtiF„(po) ti)G.o(po, ti, 0) I scalar electrodynamics. EJ ) II. SEPARATION OF OVERLAPPING DIVERGENCES ~dt, X( tdta„(p, t,) (+. ( F„(p, t,) ) Dyson' (unpublished) has defined a formal mathe- ) E~ ) matical procedure for the isolation of the divergent t' part from an integral representing overlapping diver- I X dtZG. o(PO& 01& tz)&~(PO& tz) ~& (2) gent graphs. This procedure is illustrated most readily ~ by an example. Figure 2 represents an electron self-energy graph could be obtained the insertion of a V at / which by part / / / / I ' F. Dyson, Phys. Rev. 75, 1736 {1949},referred to as D II, I J. I \ in this paper. o ' The only published calculation for an integral corresponding to an overlapping {fourth order} graph is that of R. Jost and J. M. Luttinger, Helv. Phys. Acta 23, 201 {1949), who have followed Dyson's procedure. FIG. 1. Salam received Cambridge university’s Smith prize Salam-the physicist Neutrinos and parity violation 1 Neutrinos are spin 2 particles which interact very weakly with other particles They carry no charge and therefore do not feel the electromagnetic force Neutron 7→ Proton + Electron + Neutrino Postulated by Wolfgang Pauli in 1930 Salam-the physicist Neutrinos were detected in 1956 (Reined and Cowan at Hanford, WA) Salam-the physicist Parity : (x, y, z) 7→ (−x, −y, −z) It was believed that fundamental laws are invariant under parity transformation. Salam-the physicist In 1956 T. D. Lee and C. N. Yang postulated that parity is violated weak interactions (kind of interactions neutrinos were involved in) Salam-the physicist Around the same time (1956) Salam was also thinking about parity and its possible relation to the masslessness of the neutrino (there was no good reason for the neutrinos to me massless) In late 1956 he related the masslessness of the neutrino with the parity violation and wrote a preprint on it Discouraged by Pauli Salam did not publish the result until late 1957. Salam-the physicist Parity violation was found in beta decay experiments in January 1957. Salam-the physicist Salam-the physicist Supersymmetry and superspace The four fundamental forces: Electromagnetism, Weakforce, Electroweak force Strong force, Gravity | {z } The theory (theories) that combines Electroweak and the Strong force is called Grand Unified Theory The theory that combines all four forces is called Theory of Everything Salam-the physicist We live in a space whihc has three space dimensions and one time dimension. The space dimensions can be rotated into each other x cosθ sinθ x 7→ y −sinθ cosθ y Salam-the physicist Even time and spacce can be rotated into each other (special relativity) ct coshθ sinhθ ct 7→ x sinhθ coshθ x Time dilation, length contraction and other phenomena which occur at high speed are consequence of such a ”rotation” Salam-the physicist Supersymmetry suggest that there are other fermionic ”dimensions” which are measured by quantities η1, η2 These mysterious numbers which are coordinates in the fermionic directions have the property: 2 2 η1 = 0 , η2 == 0 η1η2 = −η2η1 Salam-the physicist Supersymmetry is a symmetry which rotates x, y, z, t, η1, η2 into each other As a consequence of this symmetry particles come in pairs (A, B) 1 such that the spin of the two particle A and B differs by 2 . Photon has a superpartner photino quarks have squarks electron has selectron Salam-the physicist With John Strathdee as a collaborator Salam wrote many papers on supersymmetry. A specially influential paper was ”Supersymmetry and Superfields” Fortsch. Phys. 26, 57-142 (1978) Salam-the physicist In this paper they developed the idea of a superfield: f (x, y, z, t) 7→ Φ(x, y, z, t, η)= φ0(x, y, z, t)+ η φ1(x, y, z, t) Salam-the physicist Scientific Writings — Abdus Salam home → abdus salam → bibliography → papers Timeline Bibliography Scientific Writings Books Biographies Papers Speeches Clippings Awards Recollections 1943 A Problem of Ramanujam. Links (Fourth Year Student, Government College, Lahore) . Marie Curie Library Math. Student XI, nos.1-2, 50-51 (1943). ICTP Home ICTP Portal 1950 Differential Identities in Three-Field Renormalization Problem. Phys. Rev. 79, 910-911 (1950). 1951 Release date: Divergent Integrals in Renormalizable Field Theories. 19 September 2011 Phys. Rev. 84, 426-431 (1951). - Download the promo (mp4) - Overlapping Divergences and the S-matrix. Phys. Rev. 82, 217-227 (1951). The Renormalization of Meson Theories. (with P.T. Matthews). Rev. Mod. Phys. 23, 311-314 (1951). 1952 The Intermediate Coupling Theory of the Pseudoscalar Meson-Nucleon Interaction. (with P.T. Matthews). Phys. Rev. 86, 715-726 (1952). Recent Advances in Nuclear Theory and Experiment. Pak. J. Sci. 4, no.1, 4-10 (1952). Renormalization of Scalar Electrodynamics Using β-Formalism. Proc. Roy. Soc. (London) A211, 276-284 (1952). Renormalized S-Matrix for Scalar Electrodynamics. Phys. Rev. 86, 731-744 (1952). 1953 Cosmological Theory.
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