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

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature$\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K$ where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

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Particle Creation by Black Holes

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.

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PYTHIA 6.4 Physics and Manual

According to ’t Hooft the combination of quantum mechanics and gravity requires the three‐dimensional world to be an image of data that can be stored on a two‐dimensional projection much like a holographic image. The two‐dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three‐dimensional phenomena. After outlining ’t Hooft’s proposal we give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high‐energy particle collisions are described. The phenomenon of particle growth with momentum was previously discussed in the context of string theory and was related to information spreading near black hole horizons. The considerations of this paper indicate that the effect is much more rapid at all but the earliest times. In fact the rate of spreading is found to saturate the bound fro...

/pdf/the-world-as-a-hologram-3uruhmlw61.pdf

The world as a hologram

The Renormalization group and the epsilon expansion

In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per- form a series of calculations designed to illustrate various useful techniques and concepts in electromagnetic, weak, and strong interactions. these include defining and implementing the renormalization program and evaluating effects of radia- tive corrections, such as the Lamb shift, in low-order calculations. The necessary background for the book is pro- vided by a course in nonrelativistic quantum mechanics at the general level of Schiff's text, QUANTUM MECHANICS.

Relativistic Quantum Mechanics

The space-time evolution of the hadronic matter produced in the central rapidity region in extreme relativistic nucleus-nucleus collisions is described. We find, in agreement with previous studies, that quark-gluon plasma is produced at a temperature &200— 300 MeV, and that it should survive over a time scale & 5 fm/c. Our description relies on the existence of a flat central plateau and on the applicability of hydrodynamics.

/pdf/highly-relativistic-nucleus-nucleus-collisions-the-central-11u4k6l7j1.pdf

Highly relativistic nucleus-nucleus collisions: The central rapidity region

Relativistic Quantum Fields

Consequences of the local commutation relations of vector and axial currents proposed by Gell-Mann are explored: (1) A recipe for detecting and isolating Schwinger terms in the commutators, proportional to derivatives of the δ function, is discussed. (2) Under assumptions of smooth asymptotic behavior of form factors for forward scattering of the isovector current from a proton, we show that the U(3)⊗U(3) algebra for the time components of the currents implies the U(6)⊗U(6) algebra for space components, at least for spin-averaged diagonal single-particle states. (3) The derivation of the Adler-Weisberger formula for GAGV is sharpened by giving arguments that, at fixed energy, the forward π−p Green's function satisfies an unsubtracted dispersion relation in the pion mass. (4) A lower bound for inelastic electron-nucleon scattering at high momentum transfer is derived on the basis of U(6)⊗U(6). (5) The contribution of very virtual photons to the hyperfine anomaly in hydrogen is shown to be related to an equal-time commutator of currents; this contribution is crudely estimated to be <4 parts per million (ppm). (6) The logarithmically divergent part of electromagnetic mass differences of hadrons is shown to be proportional to matrix elements of the equal-time commutator of the electromagnetic current with its time derivative. It is suggested that this "divergent" part be identified with the Coleman-Glashow "tadpoles"; this suggestion is discussed in the framework of a simple quark model. (7) The logarithmically divergent part of the electromagnetic correction to the process π−→π0+e−+ν¯ is, on the basis of the U(6)⊗U(6) current algebra, shown to be nonvanishing, and is computed. (8) A speculative argument is presented that the rate e++e−→hadrons is comparable to the rate e++e−→μ++μ− in the limit of large energies.

http://inspirehep.net/record/49843/files/slac-pub-0165.pdf

Applications of the Chiral U ( 6 ) ⊗ U ( 6 ) Algebra of Current Densities

By combining the ${q}_{0}\ensuremath{\rightarrow}i\ensuremath{\infty}$ method for asymptotic sum rules with the $P\ensuremath{\rightarrow}\ensuremath{\infty}$ method of Fubini and Furlan, we relate the structure functions ${W}_{2}$ and ${W}_{1}$ in inelastic lepton-nucleon scattering to matrix elements of commutators of currents at almost equal times at infinite momentum. We argue that the infinite-momentum limit for these commutators does not diverge, but may vanish. If the limit is nonvanishing, we predict $\ensuremath{\nu}{W}_{2}(\ensuremath{\nu}, {q}^{2})\ensuremath{\rightarrow}{f}_{2}(\frac{\ensuremath{\nu}}{{q}^{2}})$ and ${W}_{1}(\ensuremath{\nu}, {q}^{2})\ensuremath{\rightarrow}{f}_{1}(\frac{\ensuremath{\nu}}{{q}^{2}})$ as $\ensuremath{\nu}$ and ${q}^{2}$ tend to $\ensuremath{\infty}$. From a similar analysis for neutrino processes, we conclude that at high energies the total neutrino-nucleon cross sections rise linearly with neutrino laboratory energy until nonlocality of the weak current-current coupling sets in. The sum of $\ensuremath{\nu}p$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}p$ cross sections is determined by the equal-time commutator of the Cabibbo current with its time derivative, taken between proton states at infinite momentum.

/pdf/asymptotic-sum-rules-at-infinite-momentum-2m6lgob3k7.pdf

James D. Bjorken

Papers

Relativistic Quantum Mechanics

Highly relativistic nucleus-nucleus collisions: The central rapidity region

Relativistic Quantum Fields

Applications of the Chiral U ( 6 ) ⊗ U ( 6 ) Algebra of Current Densities

Asymptotic Sum Rules at Infinite Momentum