There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

The Pythia program can be used to generate high-energy-physics ''events'', i.e. sets of outgoing particles produced in the interactions between two incoming particles. The objective is to provide as accurate as possible a representation of event properties in a wide range of reactions, within and beyond the Standard Model, with emphasis on those where strong interactions play a role, directly or indirectly, and therefore multihadronic final states are produced. The physics is then not understood well enough to give an exact description; instead the program has to be based on a combination of analytical results and various QCD-based models. This physics input is summarized here, for areas such as hard subprocesses, initial- and final-state parton showers, underlying events and beam remnants, fragmentation and decays, and much more. Furthermore, extensive information is provided on all program elements: subroutines and functions, switches and parameters, and particle and process data. This should allow the user to tailor the generation task to the topics of interest.

/pdf/pythia-6-4-physics-and-manual-3dvwmijpnq.pdf

PYTHIA 6.4 Physics and Manual

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Table Of Integrals Series And Products

The PYTHIA program can be used to generate high-energy-physics `events', i.e. sets of outgoing particles produced in the interactions between two incoming particles. The objective is to provide as accurate as possible a representation of event properties in a wide range of reactions, with emphasis on those where strong interactions play a role, directly or indirectly, and therefore multihadronic final states are produced. The physics is then not understood well enough to give an exact description; instead the program has to be based on a combination of analytical results and various QCD-based models. This physics input is summarized here, for areas such as hard subprocesses, initial- and final-state parton showers, beam remnants and underlying events, fragmentation and decays, and much more. Furthermore, extensive information is provided on all program elements: subroutines and functions, switches and parameters, and particle and process data. This should allow the user to tailor the generation task to the topics of interest. The information in this edition of the manual refers to PYTHIA version 6.200, of 31 August 2001. The official reference to the latest published version is T. Sj\"ostrand, P. Ed\'en, C. Friberg, L. L\"onnblad, G. Miu, S. Mrenna and E. Norrbin, Computer Physics Commun. 135 (2001) 238.

PYTHIA 6.2: Physics and manual

A gauge theory involves two kinds of particles, those which carry ‘charge’ and those which ‘mediate’ interactions between currents by coupling directly to charge. In the former class are the fundamental fermions and nonabelian gauge bosons, whereas the latter consists solely of gauge bosons, both abelian and nonabelian. The physical nature of charge depends on the specific theory. Three such kinds of charge, called color, weak isospin, and weak hypercharge, appear in the Standard Model. The values of these charges are not predicted from the gauge symmetry, but must rather be determined experimentally for each particle. The strength of coupling between a gauge boson and a particle is determined by the particle's charge, e.g. the electron-photon coupling constant is –e, whereas the u -quark and photon couple with strength 2e/3. Because nonabelian gauge bosons are both charge carriers and mediators, they undergo self-interactions. These produce substantial nonlinearities and make the solution of nonabelian gauge theories a formidable mathematical problem. Gauge symmetry does not generally determine particle masses. A fermion mass term, although violating chiral symmetry, is consistent with gauge invariance. Although gauge-boson mass would seem to be at odds with the principle of gauge symmetry, the Weinberg-Salam model contains a dynamical procedure, the Higgs mechanism, for generating mass for both gauge bosons and fermions alike. Quantum Electrodynamics Historically, the first of the gauge field theories was electrodynamics. Its modern version, Quantum Electrodynamics (QED) , is the most thoroughly verified physical theory yet constructed.

Interactions of the Standard Model

In the philosophy of science, the origin of an arrow of time is viewed as problematic. We describe here how this arrow really follows from the causal structure of quantum physics. This connection is not really new -- it is just overlooked in most discussions of the arrow of time.

Quantum causality determines the arrow of time

In the fall of 1649 on the docks of a large slave trading port, sailors strained, sweated, and swore through their work, hauling cargo, hoisting sails, and mending rigging, making ready for a voyage to the colonies. As the sailors prepared to weigh anchor, a crowd of parents gathered along the shoreline, grieving for their children who had been kidnapped and brought aboard the ship. As their children struggled for breath in the suffocating stench and stifling heat of the ship’s hold, the parents grew despondent, desperate to redeem their children from a future of death-dealing labor in the scorching fields of the English Chesapeake or Caribbean. A sympathetic witness noted that when the slave ship began to sail into the distance, the parents followed along the water’s edge, “crying and mourning for their children’s redemption from slavery” (Bullock, 1649 , pp. 13–14; Harlow, 1923 , p. 300; Linebaugh & Rediker, 2000 , p. 110).

Child Slavery and the Global Economy: Historical Perspectives on a Contemporary Problem

We motivate and explore the possibility that extra SU(N) gauge groups may exist independently of the standard model groups, yet not be subgroups of some grand unified group. We study the running of the coupling constants as potential evidence for a common origin of all the gauge theories. Several different examples are displayed. Some of the multiple options involve physics at the TeV scale.

Gauge federation as an alternative to unification

I briefly summarized some recent work which uses the techniques of effective field theory to make quantum predictions in general relativity. In contrast to conventional expectations, these are in fact well behaved. The leading quantum correction to the interaction of two heavy masses is used as a specific example.

Gravity and effective field theory: A talk for phenomenologists

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