Advanced Topics in Quantum Field Theory. A Lecture Course by M. Shifman PDF

By M. Shifman

ISBN-10: 0521190843

ISBN-13: 9780521190848

"Since the appearance of Yang-Mills theories and supersymmetry within the Seventies, quantum box idea - the root of the trendy description of actual phenomena on the primary point - has passed through innovative advancements. this can be the 1st systematic and entire textual content dedicated in particular to fashionable box concept, bringing readers to the innovative of present examine. The e-book emphasizes nonperturbative phenomena and supersymmetry. It features a thorough dialogue of assorted stages of gauge theories, prolonged gadgets and their quantization, and international supersymmetry from a contemporary viewpoint. that includes broad cross-referencing from conventional subject matters to contemporary breakthroughs within the box, it prepares scholars for self sufficient learn. The aspect packing containers summarizing the most effects and over 70 routines make this an imperative booklet for graduate scholars and researchers in theoretical physics"

Part I. ahead of Supersymmetry: 1. levels of gauge theories; 2. Kinks and area partitions; three. Vortices and flux tubes (strings); four. Monopoles and skyrmions; five. Instantons; 6. Isotropic (anti)ferromagnet: O(3) sigma version and extensions, together with CP(N--1); 7. False-vacuum decay and comparable issues; eight. Chiral anomaly; nine. Confinement in 4D gauge theories and versions in decrease dimensions --
Part II. creation to Supersymmetry: 10. fundamentals of supersymmetry with emphasis on gauge theories; eleven. Supersymmetric solitons.

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Example text

1 Abelian theories The simplest example of the spontaneous breaking of gauge symmetries is provided by the quantum electrodynamics (QED)3 of a charged scalar field whose self-interaction is described by the potential depicted in Fig. 5. This theory is obtained by gauging the 3 Strictly speaking, QED per se is under-defined at short distances, where the effective coupling grows and hits the Landau pole. Thus to make it consistent an ultraviolet completion is needed at short distances. For instance, one can embed QED into an asymptotically free theory.

13) where the potential energy U (φ) in fact depends only on |φ|, for instance, U (φ) = m2 |φ|2 + 12 g 2 |φ|4 . 14) In this case the Lagrangian is invariant under a (global) phase rotation of the field φ: φ ∗ → e−iα φ ∗ . 15) If the mass parameter m2 is positive, the minimum of the potential energy is achieved at φ = 0. This is the unbroken phase. The vacuum is unique. There are two particles, that is, two elementary excitations, corresponding to Re φ and Im φ. The mass of both these elementary excitations is m.

2) where m2 and g 2 are constants. We will assume that g 2 is small, so that a quasiclassical treatment applies. It is obvious that the system described by Eqs. 2) possesses a discrete Z2 symmetry: The symmetry Z2 as an example of the discrete global symmetry φ(x) −→ −φ(x) . 3) Indeed, only even powers of φ enter the action. 3) must be performed for all x simultaneously. For the time being we will treat our theory purely classically but will use quantummechanical language. We will refer to the lowest energy state (the ground state) as the vacuum.

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Advanced Topics in Quantum Field Theory. A Lecture Course by M. Shifman


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